# Non-TOC Topics

*Part of the IBM SPSS Amos online Help, rendered for AI use. See `llms.txt` for the index.*

<a id="t_non-toc_topics"></a>
# Non-TOC Topics

Enter topic text here.

<a id="t_chooseagroupingvariabledialog"></a>
## Choose a Grouping Variable dialog

*Help context ID: 3130*

Use this dialog to analyse only cases for which a particular variable takes on a particular value.

[DbVariableForm]

<a id="t_variables1"></a>
### Variables

*Help context ID: 3132*

Lists the variables in the data file.

To select cases based on the value of a variable:

1. Select the variable
2. Press **OK**

See also:

[To analyse a subset of cases.](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyseasubsetofcases)

[ListView1]

<a id="t_novariable1"></a>
### No Variable

*Help context ID: 3131*

Uses all cases in the data file. (Does not use a grouping variable.)

See also:

[To analyse a subset of cases.](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyseasubsetofcases)

<a id="t_choosevalueforgroupdialog"></a>
## Choose Value for Group dialog

*Help context ID: 3120*

Use this dialog to analyse only cases for which a particular variable takes on a particular value.

See also:

[To analyse a subset of cases.](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyseasubsetofcases)

[DbValueForm]

<a id="t_distributionofgroupingvariable1"></a>
### Distribution of grouping variable

*Help context ID: 3122*

Displays a frequency distribution of the grouping variable.

[ListView1]

<a id="t_novalue1"></a>
### No Value

*Help context ID: 3121*

Uses all cases in the data set. (Ignores the grouping variable.)

<a id="t_selectadatatabledialog"></a>
## Select a Data Table dialog

*Help context ID: 3350*

When a data file (such as an Excel file or an Access file) contains multiple data sets (also called data tables), this dialog lists the data tables so that you can pick one.

[DataTableForm]

<a id="t_listofdatatablesamosgraphics"></a>
### List of data tables (Amos Graphics)

*Help context ID: 3351*

A list of the data sets (also called data tables) in a data file (such as an Excel file or an Access file) that contains multiple data sets.

[List1]

<a id="t_viewdataselectadatatabledialog"></a>
### View Data (Select a Data Table Dialog)

*Help context ID: 3352*

Displays the selected data set.

<a id="t_setdefaultobjectpropertiesdialog"></a>
## Set Default Object Properties dialog

*Help context ID: 3500*

Use the **Set Default Object Properties** dialog to use the currently selected object as a pattern for creating new objects.

[frmObjectDefaults]

<a id="t_setdefaultsfortheseproperties1"></a>
### Set defaults for these properties

*Help context ID: 3511*

Specifies which properties of the currently selected object are to be used for newly created objects.

<a id="t_colorsdefaultobjectproperties"></a>
### Colors (Default Object Properties)

*Help context ID: 3501*

Put a check mark next to **Colors **to draw future objects with the same colors as the currently selected object. (If you do not put a check mark next to **Colors**, then the default colors for newly created objects will remain unchanged.)

[chkColors]

<a id="t_penwidthdefaultobjectproperties"></a>
### Pen width (Default Object Properties)

*Help context ID: 3502*

Put a check mark next to **Pen width **to draw future objects with the same pen width as the currently selected object. (If you do not put a check mark next to **Pen width **, then the default pen width for newly created objects will remain unchanged.)

[chkPenWidth]

<a id="t_variablenamefont1"></a>
### Variable name font

*Help context ID: 3504*

Put a check mark next to **Variable name font **to use the font of the currently selected variable's name for variables drawn in the future. (If you do not put a check mark next to **Variable name font**, then the default font for the names of new variables will remain unchanged.)

[chkNameFont]

<a id="t_titlefont1"></a>
### Title font

*Help context ID: 3505*

Put a check mark next to **Title font **to use the font of the currently selected figure caption for future figure captions. (If you do not put a check mark next to **Title font**, then the default font for figure captions will remain unchanged.)

[chkTitleFont]

<a id="t_parameterfontdefaultobjectproperties"></a>
### Parameter font (Default Object Properties)

*Help context ID: 3506*

Put a check mark next to **Parameter font **to use the parameter font of the currently selected object for objects drawn in the future. (If you do not put a check mark next to **Parameter font**, then the default font for parameters will remain unchanged.)

[chkParameterFont]

<a id="t_parameterorientation1"></a>
### Parameter orientation

*Help context ID: 3507*

Put a check mark next to **Parameter orientation **to use the parameter orientation (**horizontal**, **oblique**, or "**oblique, inverted**") of the currently selected object for objects drawn in the future. (If you do not put a check mark next to **Parameter orientation **, then the default orientation for parameters will remain unchanged.)

[chkParameterOrientation]

<a id="t_visibilitydefaultobjectproperties"></a>
### Visibility (Default Object Properties)

*Help context ID: 3508*

Put a check mark next to **Visibility **to hide those portions of objects drawn in the future that are hidden in the currently selected object. (For example, if the current object's parameters are hidden, then the parameters associated with newly drawn objects will be hidden.)

[chkVisibility]

<a id="t_defaultobjectpropertiesallgroups"></a>
### All groups (Default Object Properties)

*Help context ID: 3512*

Put a check mark next to **All groups **to use the **All groups** setting of the currently selected object for all objects that you draw in the future.

- If the current object has a check mark next to **All groups** then objects that you draw in the future will automatically have a check mark next to **All groups**.
- If the current object doesn't have a check mark next to **All groups** then objects that you draw in the future will not have a check mark next to **All groups**.

[chkAllGroups]

<a id="t_setdefaultpropertiesin"></a>
### Set default properties in...

*Help context ID: 3509*

Put a check mark next to **This path diagram** to change the default properties of newly created objects in the current path diagram.

Put a check mark next to **Normal template** to change the default properties of objects drawn in new path diagrams that are initially created with** File**®**New.**

There may be additional check boxes.. If so, put a check mark next to "xxxx template" in order to change the default properties of objects in new path diagrams that are initially created with the template "xxxx", using **File**®**New with Template**.

[List1]

<a id="t_browsedefaultobjectproperties"></a>
### Browse (Default Object Properties)

*Help context ID: 3510*

Display templates in a directory other than the default template directory (the Templates subdirectory of the Amos program directory.)

<a id="t_showoptionsdialog"></a>
## Show Options dialog

*Help context ID: 3310*

Use this dialog to show or hide grid lines, row and column headings, and other spreadsheet features.

[ShowOptions]

<a id="t_showgridlines1"></a>
### Show grid lines

*Help context ID: 3311*

Shows grid lines on the spreadsheet.

[Gridlines]

<a id="t_showeditbar1"></a>
### Show edit bar

*Help context ID: 3312*

Displays an edit bar above the spreadsheet, where you can edit the contents of the selected cell.

[EditBar]

<a id="t_showcolumnheadings1"></a>
### Show column headings

*Help context ID: 3313*

Shows column headings at the top of the spreadsheet.

[ColHeadings]

<a id="t_showformulas1"></a>
### Show formulas

*Help context ID: 3314*

When this box is checked, formulas that you enter in the spreadsheet are displayed (rather than the numeric result of applying the formula).

[Formulas]

<a id="t_showrowheadings1"></a>
### Show row headings

*Help context ID: 3315*

Shows row headings at the right of the spreadsheet.

[RowHeadings]

<a id="t_outputannotation"></a>
## Output Annotation

<a id="t_title1"></a>
### Title

*Help context ID: 348*

###### A title and description for the entire analysis, comprising all groups and all models. See [To specify a title and description](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tospecifyatitleanddescriptionfortheanalysis1).

<a id="t_notesthatrefertotheentireanalysis1"></a>
### Notes that refer to the entire analysis

Various messages that relate to the entire analysis, and that do not pertain to any particular model or group appear here.

<a id="t_bootstrapconfidenceintervalsarenotavailablewhenthebollenstinebootstrapisperformed"></a>
### Bootstrap confidence intervals are not available when the Bollen-Stine bootstrap is performed.

*Help context ID: 751*

You can't perform a Bollen-Stine bootstrap and at the same time obtain bootstrap confidence intervals. Only the Bollen-Stine bootstrap is performed. It will be necessary to repeat the analysis to obtain bootstrap confidence intervals.

[To perform a Bollen-Stine bootstrap test of model fit](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformabollenstinebootstraptestofmodelfit).

[To obtain bootstrap confidence intervals by the percentile method](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

[To obtain bias-corrected confidence intervals](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests)

<a id="t_warningparameterconstraintsareimplausible"></a>
### Warning: Parameter constraints are implausible

*Help context ID: 769*

###### This message appears when you require two or more parameters to be equal where it wouldn't usually make sense to do so. For example, this message will appear if you require the variance of some variable to be equal to a regression weight that occurs elsewhere in the model. Usually, it only makes sense to require a variance to be equal to another variance, a covariance to be equal to another covariance, and so on.

<a id="t_notesthatrefertoasinglegroup1"></a>
### Notes that refer to a single group

*Help context ID: 860, 7030*

###### Messages that relate to a single group appear here. For example, a group's sample size is reported here.

<a id="t_themodelisnonrecursive1"></a>
### The model is nonrecursive

*Help context ID: 609*

###### In everyday usage, a nonrecursive model is one in which some variable has an (indirect) effect on itself. That is, in the path diagram of the model, it is possible to start at some variable and, by following a path of single-headed arrows, return to the original variable.

<a id="t_themodelisrecursive1"></a>
### The model is recursive

*Help context ID: 610*

###### In everyday usage, a recursive model is one in which no variable in the model has an effect on itself. That is, in the path diagram of the model, it is *not* possible to start at any variable and, by following a path of single-headed arrows, return to the same variable.

<a id="t_notesthatrefertoasinglemodel1"></a>
### Notes that refer to a single model

*Help context ID: 879, 7040*

###### Messages that relate to a single model appear here. For example, the message "Minimum was achieved" is displayed here when a model was fitted successfully.

<a id="t_computationofdegreesoffreedom1"></a>
### Computation of degrees of freedom

*Help context ID: 690*

###### This portion of the output shows how Amos arrives at degrees of freedom as the difference between the number of distinct sample moments and the number of distinct parameters that have to be estimated.

The number of distinct sample moments always includes variances and covariances. It also includes sample means when you [estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).

In counting up the number of distinct parameters to be estimated, several parameters that are constrained to be equal to each other count as a single parameter. Parameters that are fixed at a constant value do not count at all. This is why the 'number of distinct parameters to be estimated' can be less than the total number of regression weights, variances, covariances, means and intercepts in the model.

In the analysis of data from several groups, the number of distinct sample moments and the number of distinct parameters to be estimated are grand totals over all groups.

<a id="t_degreesoffreedomcorrectedfornonidentifiability"></a>
### Degrees of freedom (corrected for nonidentifiability)

*Help context ID: 795*

###### Amos guesses at the correct degrees of freedom by subtracting the number of constraints that (probably) need to be imposed in order to achieve identifiability from the degrees of freedom shown elsewhere under the heading [Computation of degrees of freedom](#t_computationofdegreesoffreedom1). The correctness of the resulting figure depends upon Amos's ability to diagnose nonidentifiability, which is discussed in [Appendix D](https://ai-docs.amosdevelopment.com/07-appendices.md#t_appendixdnumericaldiagnosisofnonidentifiability1).

This message appears when

- you have [elected to fit unidentified models](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tofitunidentifiedmodels1), and
- the specified model is actually unidentified.

<a id="t_discrepancyfunctionxxxxx"></a>
### Discrepancy function = xxxxx

###### This message appears when you do either of the following:

- [Perform scale-free least squares (SLS) estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformscalefreeleastsquaresslsestimation).
- [Perform unweighted least squares (ULS) estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformunweightedleastsquaresulsestimation).

**xxxxx** is the minimum value of the discrepancy function, *C*, in [Appendix B](https://ai-docs.amosdevelopment.com/07-appendices.md#t_appendixbdiscrepancyfunctions1).

<a id="t_functionofloglikelihoodxxxxx"></a>
### Function of log likelihood = xxxxx

*Help context ID: 790*

###### **xxxxx** is $-2 \log L+K$, where *L* is the likelihood function and *K* is a constant that depends only on the sample size of each group and the number of observed variables in each group. This statistic can be used for model comparisons when some data values are missing. (See Example 17.)

The "Function of log likelihood" statistic is not normally reported by Amos Graphics. Instead, Amos Graphics automatically fits the saturated model (a step that is required for calculating the likelihood ratio chi square statistic), and then reports the chi square statistic. You get the "function of log likelihood" statistic, and not the chi square statistic, under either of the following conditions.

- **Fit neither model** is selected on the **Estimation** tab of the [Analysis Properties](https://ai-docs.amosdevelopment.com/02-amos-graphics-reference-guide-part-1.md#t_viewanalysisproperties) window.
- Amos Graphics tried and failed to fit the saturated model.

In an Amos program, you must provide the code necessary to fit the saturated model in order to calculate the likelihood ratio chi square statistic.

<a id="t_iterationlimitreached1"></a>
### Iteration limit reached

*Help context ID: 647*

###### The iteration limit was reached before a local minimum was found.

See [To specify an iteration limit](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tospecifyaniterationlimit1).

<a id="t_minimizationwasunsuccessful1"></a>
### Minimization was unsuccessful

*Help context ID: 646*

###### Amos was unable to estimate the parameters of your model. When this message occurs it is usually a sign that the specified model fits the data very poorly, either because the model is wrong or because the sample size is too small. On the other hand, there is no guarantee that Amos will succeed with a well-fitting model.

<a id="t_minimumwasachieved1"></a>
### Minimum was achieved

*Help context ID: 818*

###### Amos reached a local minimum.

<a id="t_probabilitylevelxxxxx"></a>
### Probability level = xxxxx

*Help context ID: 798*

###### If the appropriate distributional assumptions are met and if the specified model is correct, then the value** xxxxx** is the approximate probability of getting a chi-square statistic as large as the chi-square statistic obtained from the current set of data. For example, if **xxxxx** is .05 or less, the departure of the data from the model is significant at the .05 level.

The appropriateness of hypothesis testing in model fitting, even when the necessary distributional assumptions are met, is routinely questioned (*e.g.*, [Bollen & Long, 1993](https://ai-docs.amosdevelopment.com/08-references.md#t_bollen__long_1993)).

<a id="t_probabilitylevelcannotbecomputed1"></a>
### Probability level cannot be computed

*Help context ID: 797*

###### The model has zero degrees of freedom. The model should fit the data perfectly, and the chi-square statistic should be zero. Consequently, no probability level can be assigned to the chi-square statistic. The model is untestable.

<a id="t_thespecifiedmodelisprobablyunidentified1"></a>
### The specified model is probably unidentified

*Help context ID: 888, 889*

The following message indicates that a model appears to be unidentified.

The specified model is probably unidentified. In order to achieve identifiability, it will probably be necessary to impose xxxxx additional constraint(s).

The (probably) unidentified parameters are marked.

The method that Amos uses for determining that a model is unidentified, and for determining how many additional constraints are required to make the model identified, is fallible. However, it is usually right. See [Appendix D](https://ai-docs.amosdevelopment.com/07-appendices.md#t_appendixdnumericaldiagnosisofnonidentifiability1).

<a id="t_theprobablyunidentifiedparametersaremarked"></a>
### The (probably) unidentified parameters are marked

*Help context ID: 810*

This message is followed by a list of the parameters of the model. Those that appear to be unidentified are marked with the word **unidentified**. Parameters that are not marked as unidentified are probably identified. Although this classification of parameters as identified and unidentified is usually right, it is fallible (see Appendix D). This portion of the output may be useful in deciding how to impose additional parameter constraints in order to achieve identifiability.

<a id="t_thissolutionisnotadmissible1"></a>
### This solution is not admissible

*Help context ID: 772*

This message indicates that some variance estimates are negative, or that some exogenous variables have an estimated covariance matrix that is not positive definite. It suggests either that your model is wrong or that the sample is too small ([Jöreskog & Sörbom, 1984](https://ai-docs.amosdevelopment.com/08-references.md#t_joereskog__soerbom_1984)).

It is possible to prevent the occurrence of negative variance estimates, and it may even be possible to prevent the occurrence of inadmissible solutions in general, by restricting the search for a solution to admissible parameter values. However, Amos does not do this.

<a id="t_timelimitreached1"></a>
### Time limit reached

*Help context ID: 648*

###### The time limit was reached before a local minimum was found.

To specify a time limit, use the [Time](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_timemethod) method of the **AmosEngine** class. (In Amos Graphics, there is no time limit.)

<a id="t_notesthatrefertoasinglemodelinasinglegroup1"></a>
### Notes that refer to a single model in a single group

*Help context ID: 915, 7050*

###### Messages that relate to the fitting of an individual model to an individual group appear here. For example, in the case of nonrecursive models, a stability index is displayed here for each model-group combination.

<a id="t_stabilityindexforthefollowingvariablesisxxxxx1"></a>
### Stability index for the following variables is xxxxx

*Help context ID: 773*

###### The following list of variables constitutes a 'nonrecursive subset' of the variables in the model. That is, in the path diagram of the model, it is possible to start at any one of the variables in the subset, and, by following a path of single-headed arrows, return to the original variable while never leaving the subset. Suppose there are *k* variables in the nonrecursive subset and consider the *k* by *k* matrix that gives the direct effects of these *k* variables on each other. Then **xxxxx** is the modulus of the largest eigenvalue of that matrix.

If there is only one nonrecursive subset in the model, the stability index displayed here is identical to the stability index described by [Fox (1980)](https://ai-docs.amosdevelopment.com/08-references.md#t_fox_1980) and [Bentler and Freeman (1983)](https://ai-docs.amosdevelopment.com/08-references.md#t_bentler__freeman_1983). If there are several nonrecursive subsets in the model, a stability index is displayed for each one. If there are multiple stability indices, the largest one is equal to Fox's stability index. If all stability indices are less than one, the system of linear equations associated with the model is called 'stable'. If any stability index is one or greater, the system is called 'unstable'. A recursive model contains no nonrecursive subsets, and the associated linear system is stable. (Fox's stability index is zero for recursive models.)

Unstable systems present problems of interpretation. Parameter estimates that yield unstable systems are 'impossible' in the same way that [inadmissible](#t_thissolutionisnotadmissible1) solutions are impossible. An unstable system of linear equations suggests that your model is wrong or that the sample size is too small.

<a id="t_thefollowingvariancesarenegative"></a>
### The following variances are negative

*Help context ID: 770*

###### Although variances cannot be negative, Amos can produce variance *estimates* that are negative. The solution is then called inadmissible.

For more, see the discussion of the message: "This solution is not admissible".

<a id="t_thefollowingcovariancematrixisnotpositivedefinite"></a>
### The following covariance matrix is not positive definite

*Help context ID: 771*

###### Amos can produce estimates of variances and covariances that yield covariance matrices that are not positive definite ([Wothke, 1993](https://ai-docs.amosdevelopment.com/08-references.md#t_wothke_1993)). Such a solution is said to be inadmissible. Amos does not attempt to distinguish between a solution that is outside the admissible region and one that is on or near its boundary.

For more, see the discussion of the message: "This solution is not admissible".

<a id="t_yourmodelcontainsthefollowingvariables1"></a>
### Your model contains the following variables

*Help context ID: 763, 7060*

###### All variables in the model are listed here, classified as either observed or unobserved, and as either endogenous or exogenous. A summary table shows the number of variables in each category, as well as the total number of variables in the model.

Spelling or typing errors in the input file can usually be detected by inspecting this display, since variant spellings of a variable name are interpreted as names for distinct variables.

<a id="t_summaryofparameters1"></a>
### Summary of Parameters

*Help context ID: 753, 7070*

###### This table shows the numbers of model parameters that fall into various categories. The columns of the table are:

- **Weights**: regression weights
- **Covariances**: self explanatory
- **Variances**: self explanatory
- **Means**: self explanatory
- **Intercepts**: self explanatory

The rows of the table are:

- **Fixed**: parameters whose values are fixed at a constant value
- **Labeled**: parameters that are labeled
- **Unlabeled**: parameters that are neither fixed nor labeled. Such parameters are free to take on any value. (Labeled parameters can also be free -- a parameter that has been associated with a unique label is free to take on any value.)
- **Total**: self explanatory

For models in which means and intercepts are explicit model parameters, the Summary of Parameters table includes means and intercepts that are fixed at zero. Prior to Amos 24, means and intercepts that were fixed at zero were not included in the Summary of Parameters table.

<a id="t_assessmentofnormality1"></a>
### Assessment of Normality

*Help context ID: 675, 7080*

###### Statistics for assessing the normality of the observed variables in the model. See [To obtain tests for normality and outliers](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtaintestsfornormalityandoutliers1).

For more information, see the [NormalityCheck](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_normalitycheckmethod) method of the **AmosEngine** class.

<a id="t_observationsfarthestfromthecentroidmahalanobisdistance"></a>
### Observations farthest from the centroid (Mahalanobis distance)

*Help context ID: 682, 7090*

###### A listing of cases farthest away from the centroid (Mahalanobis distance). See [To obtain tests for normality and outliers](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtaintestsfornormalityandoutliers1).

For more information, see the [NormalityCheck](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_normalitycheckmethod) method of the **AmosEngine** class.

<a id="t_minimizationhistory"></a>
### Minimization History

*Help context ID: 501, 7100*

###### The value of the discrepancy function at the end of each iteration. The discrepancy function value for iteration 0 is its value when minimization starts.

[To obtain a minimization history](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainaminimizationhistory1)

<a id="t_nestedmodelcomparisons1"></a>
### Nested Model Comparisons

*Help context ID: 960, 7140*

###### Amos examines every pair of models in which one model of the pair can be obtained by constraining the parameters of the other. For every such pair of "nested" models, several statistics for comparing the two models are displayed here.

Let the more constrained of the two models have a discrepancy of $\hat{C}_{r}$ with degrees of freedom $d_{r}$, and let the less constrained model have a discrepancy of $\hat{C}_{m}$ with degrees of freedom $d_{m}$. Then Amos computes the statistic $\hat{C}_{r}-\hat{C}_{m}$, which, if the more constrained model is correct, has a chi-square distribution with degrees of freedom equal to $d_{r}-d_{m}$. It can be used to test the null hypothesis that the more constrained model is correct under the assumption that the less constrained model is correct. Amos also reports the changes in the fit measures, [NFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_nfi2), [TLI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_tli2), [RFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rfi2) and [IFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ifi2), described in Appendix C.

Here is an example of a model comparison, where Model B is the less constrained model and Model A is the more constrained model:


| Assuming model Model B to be correct: ModelDFCMINPNFIDelta-1IFIDelta-2RFIrho-1TLIrho2 Model A165.160.000.031.031.075.075 |
| --- |

The output shows that Model A can be obtained by constraining Model B. Under the hypothesis that Model B is correct, a test of the additional constraints of Model A can be based on the chi-square statistic 65.160, which has 1 degree of freedom. The probability of a chi-square statistic with 1 degree of freedom exceeding 65.160 is indistinguishable from zero to three decimal places. Therefore Model A would be rejected at any conventional significance level. In adding one constraint to Model B to obtain Model A, [NFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_nfi2) and [IFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ifi2)** both increase by .031 while **[RFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rfi2) and [TLI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_tli2) both increase by .075.

<a id="t_estimates1"></a>
### Estimates

*Help context ID: 803, 804, 805, 806, 807, 808, 809, 7150*

###### Estimates of the following model parameters:

- Regression weights
- Variances of exogenous variables
- Covariances among exogenous variables
- Means of exogenous variables
- Intercepts for predicting endogenous variables

Estimates of the following quantities also appear here when requested.

- Squared multiple correlations (See [To estimate squared multiple correlations](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatesquaredmultiplecorrelations1).)
- Correlations among the exogenous variables (See [To estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).)
- Standardized regression weights (See [To estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).)

See also:

[Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_columnsofthetableofestimates1"></a>
### Columns of the table of estimates

*Help context ID: 351, 393, 394, 593, 924*

###### For each estimate, one or more of the following items are displayed

- **Estimate**: The estimate.
- **S.E.**: Approximate standard error. (Not available for correlations and standardized regression weights. Also not available for ULS or SLS estimation.)
- **C.R.**: *Critical ratio*. The critical ratio is the parameter estimate divided by an estimate of its standard error. If the appropriate distributional assumptions are met, this statistic has a standard normal distribution under the null hypothesis that the parameter has a population value of zero. For example, if an estimate has a critical ratio greater than two (in absolute value), the estimate is significantly different from zero at the .05 level. Even without distributional assumptions, the critical ratios have the following interpretation: For any unconstrained parameter, the *square* of its critical ratio is, approximately, the amount by which the chi- square statistic would *increase* if the analysis were repeated with that parameter fixed at zero. (Not available for correlations and standardized regression weights. Also not available for ULS or SLS estimation.)
- **Label**: If you have named a parameter (see [To name a parameter](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tonameaparameter1)), the name appears in this column. You need to know the names of parameters in order to read the display of [covariances among parameters](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecovariancesamongparameterestimates1), [correlations among parameters](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsamongparameterestimates1) and [critical ratios for differences between parameters](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtaincriticalratiosfordifferencesbetweenparameters1). If necessary, Amos makes up names for any parameters that you have not named. Amos's made-up names appear in the **Label** column along with the ones you supply.

When you [request bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1), additional columns appear under the subheading **Bootstrap**. As an example, the following output shows Bootstrap output for the squared multiple correlations in Model 2R of Example 20 . There were *B*=1000 bootstrap samples.


|   | SE | SE- SE | Mean | Bias | SE- Bias |
| --- | --- | --- | --- | --- | --- |
| paragrap | 0.061 | 0.001 | 0.753 | 0.000 | 0.002 |
| wordmean | 0.064 | 0.001 | 0.685 | -0.001 | 0.002 |
| sentence | 0.057 | 0.001 | 0.680 | 0.000 | 0.002 |
| lozenges | 0.131 | 0.003 | 0.528 | -0.008 | 0.004 |
| cubes | 0.077 | 0.002 | 0.289 | 0.005 | 0.002 |
| visperc | 0.133 | 0.003 | 0.416 | 0.017 | 0.004 |

The columns of the table are labeled:

- **SE**: Bootstrap estimates of standard error. In the example above, the squared multiple correlation for **WORDMEAN** has a standard deviation of .064 across 1000 bootstrap samples.
- **SE-SE**: An approximate standard error for the standard error in the preceding column, given by $s / \sqrt{2 B}$ where *s* is the standard error from the preceding column and *B* is the number of bootstrap samples. In the example above, the squared multiple correlation for WORDMEAN has a standard error that is estimated to be .064 with a standard error of approximately $.064 / \sqrt{2000}=.001$.
- **Mean**: The mean across bootstrap samples of the quantity being estimated. In the example the squared multiple correlation for **WORDMEAN** has a mean of .685 across bootstrap samples.
- **Bias**: The difference between the average of *B* estimates obtained from *B* bootstrap samples, and the single estimate obtained from the original sample. In the example above, the squared multiple correlation for **WORDMEAN** has a mean of .685 across bootstrap samples, while the estimate (not shown above) obtained from the original sample is .686. The difference, .685 – .686 = –.001, is an estimate of the bias in estimating the squared multiple correlation.
- **SE-Bias**: An approximate standard error for the bias estimate in the preceding column. The formula used is $s / \sqrt{B}$, where *s* is the approximate standard error in the S.E. column and *B* is the number of bootstrap samples. In the example above, the squared multiple correlation for WORDMEAN has an estimated bias of –.001 with a standard error of approximately $.064 / \sqrt{1000}=.002$. Since the estimated bias is smaller in magnitude than its standard error, there is little evidence that the squared multiple correlation is biased.

When you [request bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests), the following columns appear under the subheading **BC Confidence**.

- **Lower**: Lower bound on the bias-corrected confidence interval.
- **Upper**: Upper bound on the bias-corrected confidence interval.
- **P**: Estimated probability of getting a sample value this far from zero if the population value is zero ([Efron & Tibshirani, 1993](https://ai-docs.amosdevelopment.com/08-references.md#t_efron__tibshirani_1993)).

When you [request percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests), the same columns appear under the subheading **PC Confidence**.

For an example of **BC Confidence** output, see the [ConfidenceBC](https://ai-docs.amosdevelopment.com/04-programming-with-amos-part-1.md#t_confidencebcmethod) method of the **AmosEngine** class.

For an example of **PC Confidence** output, see the [ConfidencePC](https://ai-docs.amosdevelopment.com/04-programming-with-amos-part-1.md#t_confidencepcmethod) method of the **AmosEngine** class.

<a id="t_regressionweights1"></a>
### Regression Weights

*Help context ID: 569, 7160*

###### Estimates of regression weights. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_standardizedregressionweights1"></a>
### Standardized Regression Weights

*Help context ID: 813, 7170*

###### Estimates of standardized regression weights. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

See also [To estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_means1"></a>
### Means

*Help context ID: 571, 7180*

###### Estimates of means of exogenous variables. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_intercepts1"></a>
### Intercepts

*Help context ID: 572, 7190*

###### Estimates of intercepts for predicting endogenous variables. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_covariances1"></a>
### Covariances

*Help context ID: 573, 7200*

###### Estimates of covariances among exogenous variables. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_correlations1"></a>
### Correlations

*Help context ID: 574, 7210*

###### Estimates of correlations among exogenous variables. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

See also:

[To estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_variances1"></a>
### Variances

*Help context ID: 575, 7220*

###### Estimates of variances of exogenous variables. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

<a id="t_squaredmultiplecorrelationsoutput"></a>
### Squared Multiple Correlations (output)

*Help context ID: 576, 7230*

###### Estimates of squared multiple correlations. See [Columns of the table of estimates](#t_columnsofthetableofestimates1).

See also:

[To estimate squared multiple correlations](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatesquaredmultiplecorrelations1)

<a id="t_modificationindices"></a>
### Modification Indices

*Help context ID: 815, 7240*

###### Each parameter that has a modification index greater than a specified threshold (see [To obtain modification indices](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainmodificationindices1) to find out how to specify the threshold.) appears here, together with two numbers in columns labeled:

**M.I.**: modification index

**Par Change**: estimated parameter change

If no modification indices are displayed, this means that none exceed the specified threshold.

For more information about modification indices, and an example, see the [Mods](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_modsmethod) method of the **AmosEngine** class.

<a id="t_bootstrapdetails"></a>
### Bootstrap Details

*Help context ID: 911*

###### For each bootstrap sample, a list of integers is displayed. The list should be read from left to right, beginning with the first row if there is more than one row. The first integer tells how often the first observation in the original sample appeared in the bootstrap sample. The second integer tells how often the second observation appeared, and so on.

See [To report detailed information about each bootstrap sample](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toreportdetailedinformationabouteachbootstrapsample1).

<a id="t_summaryofbootstrapiterations1"></a>
### Summary of Bootstrap Iterations

*Help context ID: 538, 7260*

###### This table appears when you [perform a bootstrap](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) and [request a minimization history](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainaminimizationhistory1). The table gives information about how many iterations were required to fit the model to the bootstrap samples. Here is an example of output based on a total of 1000 bootstrap samples.


| Summary of Bootstrap Iterations IterationsMethod 0Method 1Method 21000200030004000500060007080803109085010014111101440120118013010301408801505501603101703701803201901215Total09946 0 bootstrap samples were unused because of a singular covariance matrix. 19 bootstrap samples were unused because a solution was not found. 1000 usable bootstrap samples were obtained. |
| --- |

The columns of the table are labeled:

- **Iterations**: Number of iterations
- **Method 0**: Minimization method 0 -- a minimization algorithm that is slow and unreliable for difficult minimization problems, but fast for easy ones. This method is not used in the current release of Amos, and the **Method 0** column always contains zeros.
- **Method 1**: Minimization method 1 -- a pretty fast and reliable minimization algorithm. This is the first minimization method that Amos tries on each bootstrap sample.
- **Method 2**: Minimization method 2 -- Amos's most reliable minimization algorithm. If method 1 fails during bootstrapping, method 2 is tried.

In the example above, the "8" in the seventh row of the **Method 1** column indicates that, for eight bootstrap samples, method 1 reached a minimum in seven iterations. The "121" in the 19-th row of the **Method 1** column indicates that, for 121 bootstrap samples, method 1 reached a minimum in 19 *or more* iterations. The "5" in the 19-th row of the **Method 2** column indicates that, for five bootstrap samples, method 2 reached a minimum in 19 or more iterations. The **Total** row shows that method 1 succeeded 994 times and method 2 succeeded 6 times.

The final three lines in the example above show that, in addition to the 1000 bootstrap samples for which a local minimum was reached, there were 19 bootstrap samples for which no local minimum was found.

<a id="t_thetimelimitwasreachedduringbootstrapping1"></a>
### The time limit was reached during bootstrapping

*Help context ID: 549*

###### The time limit specified with the [Time](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_timemethod) method of the **AmosEngine** class was reached during bootstrapping. (In Amos Graphics, there is no time limit.)

<a id="t_bootstrapdistributions1"></a>
### Bootstrap Distributions

*Help context ID: 597, 7270*

###### Each histogram, along with its associated mean and standard deviation, describes the distribution of some quantity across *B* bootstrap samples. Let $\mathbf{a}_{b}$ contain the sample moments from the *b*-th bootstrap sample, let $\hat{\gamma}_{b}$ be the value of $\gamma$ that minimizes $C\left(\boldsymbol{\alpha}(\gamma), \mathbf{a}_{b}\right)$, and let $\hat{\boldsymbol{\alpha}}_{b}=\boldsymbol{\alpha}\left(\hat{\gamma}_{b}\right)$. Most of the histograms show the distribution (across bootstrap samples) of some discrepancy function — either $C\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right)$ or $C\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right)$.

<a id="t_adfdiscrepancyimpliedvspop"></a>
### ADF discrepancy (implied vs pop)

*Help context ID: 7619*

###### The histogram shows the distribution of the *B* quantities,

$C_{A D F}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right), \quad b=1, \ldots, B$.

This distribution is automatically displayed whenever you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ADF estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformasymptoticallydistributionfreeadfestimation). When you do not use ADF estimation, you can specifically [request the distribution of the ADF discrepancy](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainthedistributionoftheadfdiscrepancyacrossbootstrapsamples1).

<a id="t_adfdiscrepancyimpliedvssample"></a>
### ADF discrepancy (implied vs sample)

*Help context ID: 7621*

###### The histogram shows the distribution of the *B* quantities,

$C_{A D F}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

This distribution is displayed when you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ADF estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformasymptoticallydistributionfreeadfestimation).

<a id="t_glsdiscrepancyimpliedvspop"></a>
### GLS discrepancy (implied vs pop)

*Help context ID: 7623*

###### The histogram shows the distribution of the *B* quantities,

$C_{G L S}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}\right), \quad b=1, \ldots, B$.

This distribution is automatically displayed whenever you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using GLS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformgeneralizedleastsquaresglsestimation). When you do not use GLS estimation, you can specifically [request the distribution of the GLS discrepancy](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainthedistributionoftheglsdiscrepancyacrossbootstrapsamples1).

<a id="t_glsdiscrepancyimpliedvssample"></a>
### GLS discrepancy (implied vs sample)

*Help context ID: 7625*

###### The histogram shows the distribution of the *B* quantities,

$C_{G L S}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

This distribution is displayed when you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using GLS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformgeneralizedleastsquaresglsestimation).

<a id="t_mldiscrepancyimpliedvspop"></a>
### ML discrepancy (implied vs pop)

*Help context ID: 7613*

###### The histogram shows the distribution of the *B* quantities,

$C_{M L}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right)=C_{K L}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right)-C_{K L}(\mathbf{a}, \mathbf{a}), \quad b=1, \ldots, B$.

This distribution is automatically displayed whenever you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ML estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformmaximumlikelihoodmlestimation). When you do not use ML estimation, you can specifically [request the distribution of the ML discrepancy](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainthedistributionofthemldiscrepancyacrossbootstrapsamples1).

<a id="t_mldiscrepancyimpliedvssample"></a>
### ML discrepancy (implied vs sample)

*Help context ID: 7611*

###### The histogram shows the distribution of the *B* quantities,

$C_{M L}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

This distribution is displayed when you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ML estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformmaximumlikelihoodmlestimation).

By way of illustration, here is the distribution of $C_{M L}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right)$ for Model 2R of Example 20, where the minimum of the discrepancy function in fitting the model to the original sample was $C_{M L}(\hat{\boldsymbol{\alpha}}, \mathbf{a})=3.638$.


| ML discrepancy (implied vs sample) (Default model) \|--------------------------------- 1.566\|\* 3.935\|\*\*\*\*\*\*\*\* 6.305\|\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 8.674\|\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 11.044\|\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 13.413\|\*\*\*\*\*\*\*\*\*\*\*\*\* 15.783\|\*\*\*\*\*\*\*\*\* N = 100018.152\|\*\*\*\*\*\*\* Mean = 11.48520.522\|\*\*\*\*\* S. e. = .17722.891\|\*\*\* 25.261\|\*\* 27.630\|\* 30.000\|\* 32.369\|\* 34.739\|\* \|--------------------------------- |
| --- |

The difference between $C_{M L}(\hat{\boldsymbol{\alpha}}, \mathbf{a})=3.638$ and $\overline{C_{M L}\left(\hat{\boldsymbol{\alpha}}, \mathbf{a}_{b}\right)}=(1 / B) \sum_{b=1}^{B} C_{M L}\left(\hat{\boldsymbol{\alpha}}, \mathbf{a}_{b}\right)=11.485$ is 7.847, which is in close agreement with a result of [Steiger, Shapiro and Browne (1985)](https://ai-docs.amosdevelopment.com/08-references.md#t_steiger__shapiro__browne_1985) and [McDonald (1989)](https://ai-docs.amosdevelopment.com/08-references.md#t_mcdonald_1989), according to which the difference should be *d* = 8.

<a id="t_slsdiscrepancyimpliedvspop"></a>
### SLS discrepancy (implied vs pop)

*Help context ID: 7627*

###### The histogram shows the distribution of the *B* quantities,

$C_{S L S}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right), \quad b=1, \ldots, B$.

This distribution is automatically displayed whenever you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using SLS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformscalefreeleastsquaresslsestimation). When you do not use SLS estimation, you can specifically [request the distribution of the SLS discrepancy](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainthedistributionoftheslsdiscrepancyacrossbootstrapsamples1).

<a id="t_slsdiscrepancyimpliedvssample"></a>
### SLS discrepancy (implied vs sample)

*Help context ID: 7629*

###### The histogram shows the distribution of the *B* quantities,

$C_{S L S}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

This distribution is displayed when you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using SLS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformscalefreeleastsquaresslsestimation).

<a id="t_ulsdiscrepancyimpliedvspop"></a>
### ULS discrepancy (implied vs pop)

*Help context ID: 7631*

###### The histogram shows the distribution of the *B* quantities,

$C_{U L S}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right), \quad b=1, \ldots, B$.

This distribution is automatically displayed whenever you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ULS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformunweightedleastsquaresulsestimation). When you do not use ULS estimation, you can specifically [request the distribution of the ULS discrepancy](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainthedistributionoftheulsdiscrepancyacrossbootstrapsamples1).

<a id="t_ulsdiscrepancyimpliedvssample"></a>
### ULS discrepancy (implied vs sample)

*Help context ID: 7633*

###### The histogram shows the distribution of the *B* quantities,

$C_{U L S}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

This distribution is displayed when you [obtain bootstrap standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1) while [using ULS estimation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformunweightedleastsquaresulsestimation).

<a id="t_kloveroptimismunstabilized"></a>
### K-L overoptimism (unstabilized)

*Help context ID: 7615*

###### The histogram shows the distribution of the *B* quantities,

$R_{b}=C_{K I}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}\right)-C_{K I}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}_{b}\right), \quad b=1, \ldots, B$.

<a id="t_kloveroptimismstabilized"></a>
### K-L overoptimism (stabilized)

*Help context ID: 7617*

###### The histogram shows the distribution of the *B* quantities,

$$
\begin{array}{l}
R_{b}{ }^{*}=R_{b}+\sum_{\xi=1}^{G} k^{(\xi)}\left[\operatorname{tr}\left(\mathbf{S}_{b}^{(\xi)} \mathbf{S}^{(\xi)^{-1}}\right)-p^{(\xi)}\left(\frac{N^{(\xi)}-1}{N^{(\xi)}}\right)\right] \\
+\sum_{\xi=1}^{G} k^{(\xi)}\left[\left(\overline{\mathbf{x}}_{b}^{(\xi)}-\overline{\mathbf{x}}^{(\xi)}\right)^{\prime} \mathbf{S}^{(\xi)^{-1}}\left(\overline{\mathbf{x}}_{b}^{(\xi)}-\overline{\mathbf{x}}^{(\xi)}\right)-\frac{p^{(\xi)}}{N^{(\xi)}}\right], \\
b=1, \ldots, B,
\end{array}
$$

where $k^{(g)}=N^{(g)}-1$ when the [emulisrel6](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tousetheemulisrel6option1) option is used, and ![7402](https://ai-docs.amosdevelopment.com/Images/7402.png) otherwise.

Each bracketed term has zero expectation, so that $R_{b}{ }^{*}$ and $R_{b}$ have the same expectation. Experience has shown that $R_{b}{ }^{*}$ is substantially less variable across bootstrap samples than is $R_{b}$.

<a id="t_matrixpermutationstest1"></a>
### Matrix Permutations Test

*Help context ID: 741, 7280*

###### These results appear when you [perform a permutations test](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toperformapermutationstest1).

For more information, see the [Permute](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_permutemethod) method of the **AmosEngine** class.

<a id="t_permutationstestdetails"></a>
### Permutations Test Details

*Help context ID: 729*

###### These results appear when you [obtain permutations test details](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpermutationstestdetails1).

For more information, see the [PermuteDetail](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_permutedetailmethod) method of the **AmosEngine** class.

<a id="t_matrices1"></a>
### Matrices

*Help context ID: 7300*

###### Select the output that you want to view from the listboxes at the left of the **Table Viewer** window.

<a id="t_allimpliedcovariancesestimates"></a>
### All Implied Covariances - Estimates

*Help context ID: 522, 7310*

###### The covariance matrix displayed here is an estimate of the population covariance matrix of all the variables in the model (observed and unobserved) under the hypothesis that the model is correct.

This matrix is displayed when you [obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).

<a id="t_allimpliedcovariancesbootstrapstandarderrors"></a>
### All Implied Covariances - Bootstrap Standard Errors

*Help context ID: 7311*

###### This table contains bootstrap standard errors for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_allimpliedcovariancesconfidenceintervalsbc"></a>
### All Implied Covariances - Confidence Intervals (BC)

*Help context ID: 7312*

###### This table contains bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovarianceslowerboundsbc"></a>
### All Implied Covariances - Lower Bounds (BC)

*Help context ID: 7313*

###### This table contains the lower boundaries of bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovariancesupperboundsbc"></a>
### All Implied Covariances - Upper Bounds (BC)

*Help context ID: 7314*

###### This table contains the upper boundaries of bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovariancestwotailedsignificancebc"></a>
### All Implied Covariances - Two Tailed Significance (BC)

*Help context ID: 7315*

###### This table contains two-tailed significance levels for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovariancesconfidenceintervalspc"></a>
### All Implied Covariances - Confidence Intervals (PC)

*Help context ID: 7316*

###### This table contains bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovarianceslowerboundspc"></a>
### All Implied Covariances - Lower Bounds (PC)

*Help context ID: 7317*

###### This table contains the lower boundaries of bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovariancesupperboundspc"></a>
### All Implied Covariances - Upper Bounds (PC)

*Help context ID: 7318*

###### This table contains the upper boundaries of bootstrap confidence intervals for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcovariancestwotailedsignificancepc"></a>
### All Implied Covariances - Two Tailed Significance (PC)

*Help context ID: 7319*

###### This table contains two-tailed significance levels for the [implied covariance matrix of all variables](#t_allimpliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationsestimates"></a>
### All Implied Correlations - Estimates

*Help context ID: 523, 7320*

###### The correlation matrix displayed here is an estimate of the population correlation matrix of all the variables in the model (observed and unobserved) under the hypothesis that the model is correct.

This matrix is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_allimpliedcorrelationsbootstrapstandarderrors"></a>
### All Implied Correlations - Bootstrap Standard Errors

*Help context ID: 7321*

###### This table contains bootstrap standard errors for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_allimpliedcorrelationsconfidenceintervalsbc"></a>
### All Implied Correlations - Confidence Intervals (BC)

*Help context ID: 7322*

This table contains bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationslowerboundsbc"></a>
### All Implied Correlations - Lower Bounds (BC)

*Help context ID: 7323*

This table contains the lower boundaries of bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationsupperboundsbc"></a>
### All Implied Correlations - Upper Bounds (BC)

*Help context ID: 7324*

This table contains the upper boundaries of bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationstwotailedsignificancebc"></a>
### All Implied Correlations - Two Tailed Significance (BC)

*Help context ID: 7325*

This table contains two-tailed significance levels for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationsconfidenceintervalspc"></a>
### All Implied Correlations - Confidence Intervals (PC)

*Help context ID: 7326*

This table contains bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationslowerboundspc"></a>
### All Implied Correlations - Lower Bounds (PC)

*Help context ID: 7327*

This table contains the lower boundaries of bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationsupperboundspc"></a>
### All Implied Correlations - Upper Bounds (PC)

*Help context ID: 7328*

This table contains the upper boundaries of bootstrap confidence intervals for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedcorrelationstwotailedsignificancepc"></a>
### All Implied Correlations - Two Tailed Significance (PC)

*Help context ID: 7329*

This table contains two-tailed significance levels for the [implied correlations among all variables](#t_allimpliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeansestimates"></a>
### All Implied Means - Estimates

*Help context ID: 524, 7330*

The means displayed here are estimates of the population means of all the variables in the model (observed and unobserved) under the hypothesis that the model is correct.

These results are displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)

<a id="t_allimpliedmeansbootstrapstandarderrors"></a>
### All Implied Means - Bootstrap Standard Errors

*Help context ID: 7331*

This table contains bootstrap standard errors for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_allimpliedmeansconfidenceintervalsbc"></a>
### All Implied Means - Confidence Intervals (BC)

*Help context ID: 7332*

This table contains bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeanslowerboundsbc"></a>
### All Implied Means - Lower Bounds (BC)

*Help context ID: 7333*

This table contains the lower boundaries of bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeansupperboundsbc"></a>
### All Implied Means - Upper Bounds (BC)

*Help context ID: 7334*

This table contains the upper boundaries of bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeanstwotailedsignificancebc"></a>
### All Implied Means - Two Tailed Significance (BC)

*Help context ID: 7335*

This table contains two-tailed significance levels for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1)
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeansconfidenceintervalspc"></a>
### All Implied Means - Confidence Intervals (PC)

*Help context ID: 7336*

This table contains bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeanslowerboundspc"></a>
### All Implied Means - Lower Bounds (PC)

*Help context ID: 7337*

This table contains the lower boundaries of bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeansupperboundspc"></a>
### All Implied Means - Upper Bounds (PC)

*Help context ID: 7338*

This table contains the upper boundaries of bootstrap confidence intervals for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_allimpliedmeanstwotailedsignificancepc"></a>
### All Implied Means - Two Tailed Significance (PC)

*Help context ID: 7339*

This table contains two-tailed significance levels for the [implied means of all variables](#t_allimpliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for all variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforallvariables1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectsestimates"></a>
### Direct Effects - Estimates

*Help context ID: 531, 7340*

The direct effect of each column variable on each row variable.

This table is displayed when you [estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects).

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_directeffectestimate"></a>
### Direct Effect - Estimate

*Help context ID: 8340*

The direct (unmediated) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to the direct (unmediated) effect of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1, %RowLabel() %xcreases(m()) by %absm(). This is in addition to any indirect (mediated) effect that %ColumnLabel() may have on %RowLabel().

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_directeffectsbootstrapstandarderrors"></a>
### Direct Effects - Bootstrap Standard Errors

*Help context ID: 7341*

This table contains bootstrap standard errors for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_directeffectbootstrapstandarderror"></a>
### Direct Effect - Bootstrap Standard Error

*Help context ID: 8341*

%m() is a bootstrap estimate of the standard error of the direct (unmediated) effect of %ColumnLabel() on %RowLabel() .

<a id="t_directeffectsconfidenceintervalsbc"></a>
### Direct Effects - Confidence Intervals (BC)

*Help context ID: 7342*

This table contains bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectslowerboundsbc"></a>
### Direct Effects - Lower Bounds (BC)

*Help context ID: 7343*

This table contains the lower boundaries of bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectlowerboundbc"></a>
### Direct Effect - Lower Bound (BC)

*Help context ID: 8343*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You [can specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectsupperboundsbc"></a>
### Direct Effects - Upper Bounds (BC)

*Help context ID: 7344*

This table contains the upper boundaries of bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectupperboundbc"></a>
### Direct Effect - Upper Bound (BC)

*Help context ID: 8344*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You [can specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectstwotailedsignificancebc"></a>
### Direct Effects - Two Tailed Significance (BC)

*Help context ID: 7345*

This table contains two-tailed significance levels for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffecttwotailedsignificancebc"></a>
### Direct Effect - Two Tailed Significance (BC)

*Help context ID: 8345*

The direct (unmediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_directeffectsconfidenceintervalspc"></a>
### Direct Effects - Confidence Intervals (PC)

*Help context ID: 7346*

This table contains bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectslowerboundspc"></a>
### Direct Effects - Lower Bounds (PC)

*Help context ID: 7347*

This table contains the lower boundaries of bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectlowerboundpc"></a>
### Direct Effect - Lower Bound (PC)

*Help context ID: 8347*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectsupperboundspc"></a>
### Direct Effects - Upper Bounds (PC)

*Help context ID: 7348*

This table contains the upper boundaries of bootstrap confidence intervals for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectupperboundpc"></a>
### Direct Effect - Upper Bound (PC)

*Help context ID: 8348*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffectstwotailedsignificancepc"></a>
### Direct Effects - Two Tailed Significance (PC)

*Help context ID: 7349*

This table contains two-tailed significance levels for [direct effects](#t_directeffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_directeffecttwotailedsignificancepc"></a>
### Direct Effect - Two Tailed Significance (PC)

*Help context ID: 8349*

The direct (unmediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_standardizeddirecteffectsestimates"></a>
### Standardized Direct Effects - Estimates

*Help context ID: 534, 7350*

The direct effect of each column variable on each row variable after standardizing all variables.

This table is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_standardizeddirecteffectestimate"></a>
### Standardized Direct Effect - Estimate

*Help context ID: 8350*

The standardized direct (unmediated) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to the direct (unmediated) effect of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1 standard deviation, %RowLabel() %xcreases(m()) by %absm() standard deviations. This is in addition to any indirect (mediated) effect that %ColumnLabel() may have on %RowLabel().

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_standardizeddirecteffectsbootstrapstandarderrors"></a>
### Standardized Direct Effects - Bootstrap Standard Errors

*Help context ID: 7351*

This table contains bootstrap standard errors for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_standardizeddirecteffectbootstrapstandarderror"></a>
### Standardized Direct Effect - Bootstrap Standard Error

*Help context ID: 8351*

%m() is a bootstrap estimate of the standard error of the standardized direct (unmediated) effect of %ColumnLabel() on %RowLabel().

<a id="t_standardizeddirecteffectsconfidenceintervalsbc"></a>
### Standardized Direct Effects - Confidence Intervals (BC)

*Help context ID: 7352*

This table contains bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectslowerboundsbc"></a>
### Standardized Direct Effects - Lower Bounds (BC)

*Help context ID: 7353*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests)

<a id="t_standardizeddirecteffectlowerboundbc"></a>
### Standardized Direct Effect - Lower Bound (BC)

*Help context ID: 8353*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectsupperboundsbc"></a>
### Standardized Direct Effects - Upper Bounds (BC)

*Help context ID: 7354*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests)

<a id="t_standardizeddirecteffectupperboundbc"></a>
### Standardized Direct Effect - Upper Bound (BC)

*Help context ID: 8354*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectstwotailedsignificancebc"></a>
### Standardized Direct Effects - Two Tailed Significance (BC)

*Help context ID: 7355*

This table contains two-tailed significance levels for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffecttwotailedsignificancebc"></a>
### Standardized Direct Effect - Two Tailed Significance (BC)

*Help context ID: 8355*

The standardized direct (unmediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_standardizeddirecteffectsconfidenceintervalspc"></a>
### Standardized Direct Effects - Confidence Intervals (PC)

*Help context ID: 7356*

This table contains bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectslowerboundspc"></a>
### Standardized Direct Effects - Lower Bounds (PC)

*Help context ID: 7357*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectlowerboundpc"></a>
### Standardized Direct Effect - Lower Bound (PC)

*Help context ID: 8357*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectsupperboundspc"></a>
### Standardized Direct Effects - Upper Bounds (PC)

*Help context ID: 7358*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectupperboundpc"></a>
### Standardized Direct Effect - Upper Bound (PC)

*Help context ID: 8358*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized direct (unmediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffectstwotailedsignificancepc"></a>
### Standardized Direct Effects - Two Tailed Significance (PC)

*Help context ID: 7359*

This table contains two-tailed significance levels for [standardized direct effects](#t_standardizeddirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizeddirecteffecttwotailedsignificancepc"></a>
### Standardized Direct Effect - Two Tailed Significance (PC)

*Help context ID: 8359*

The standardized direct (unmediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_factorscoreweightsestimates"></a>
### Factor Score Weights - Estimates

*Help context ID: 521, 7360*

The table displayed here gives regression weights for predicting the unobserved variables from the observed variables. The table is organized with a row for each unobserved variable and a column for each observed variable.

This matrix is displayed when you [estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).

<a id="t_factorscoreweightestimate"></a>
### Factor Score Weight - Estimate

*Help context ID: 8360*

When the measured variable %ColumnLabel() goes up by 1 unit, the predicted value for the latent variable %RowLabel() %xcreases(m()) by %absm() units.

<a id="t_factorscoreweightsbootstrapstandarderrors"></a>
### Factor Score Weights - Bootstrap Standard Errors

*Help context ID: 7361*

This table contains bootstrap standard errors for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_factorscoreweightbootstrapstandarderror"></a>
### Factor Score Weight - Bootstrap Standard Error

*Help context ID: 8361*

%m() is a bootstrap estimate of the standard error of the regression weight applied to %ColumnLabel() when using all of the measured variables to predict the latent variable %RowLabel().

<a id="t_factorscoreweightsconfidenceintervalsbc"></a>
### Factor Score Weights - Confidence Intervals (BC)

*Help context ID: 7362*

This table contains bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightslowerboundsbc"></a>
### Factor Score Weights - Lower Bounds (BC)

*Help context ID: 7363*

This table contains the lower boundaries of bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightlowerboundbc"></a>
### Factor Score Weight - Lower Bound (BC)

*Help context ID: 8363*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the regression weight applied to $$ColumnLabel()$$ when using all of the measured variables to predict the latent variable $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightsupperboundsbc"></a>
### Factor Score Weights - Upper Bounds (BC)

*Help context ID: 7364*

This table contains the upper boundaries of bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightupperboundbc"></a>
### Factor Score Weight - Upper Bound (BC)

*Help context ID: 8364*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the regression weight applied to $$ColumnLabel()$$ when using all of the measured variables to predict the latent variable $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightstwotailedsignificancebc"></a>
### Factor Score Weights - Two Tailed Significance (BC)

*Help context ID: 7365*

This table contains two-tailed significance levels for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweighttwotailedsignificancebc"></a>
### Factor Score Weight - Two Tailed Significance (BC)

*Help context ID: 8365*

The 'factor score weight' for using %ColumnLabel() to predict %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_factorscoreweightsconfidenceintervalspc"></a>
### Factor Score Weights - Confidence Intervals (PC)

*Help context ID: 7366*

This table contains bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightslowerboundspc"></a>
### Factor Score Weights - Lower Bounds (PC)

*Help context ID: 7367*

This table contains the lower boundaries of bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightlowerboundpc"></a>
### Factor Score Weight - Lower Bound (PC)

*Help context ID: 8367*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the regression weight applied to $$ColumnLabel()$$ when using all of the measured variables to predict the latent variable $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightsupperboundspc"></a>
### Factor Score Weights - Upper Bounds (PC)

*Help context ID: 7368*

This table contains the upper boundaries of bootstrap confidence intervals for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightupperboundpc"></a>
### Factor Score Weight - Upper Bound (PC)

*Help context ID: 8368*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the regression weight applied to $$ColumnLabel()$$ when using all of the measured variables to predict the latent variable $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweightstwotailedsignificancepc"></a>
### Factor Score Weights - Two Tailed Significance (PC)

*Help context ID: 7369*

This table contains two-tailed significance levels for [factor score weights](#t_factorscoreweightsestimates). It is displayed when you simultaneously:

- [Estimate factor score weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatefactorscoreweights1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_factorscoreweighttwotailedsignificancepc"></a>
### Factor Score Weight - Two Tailed Significance (PC)

*Help context ID: 8369*

The 'factor score weight' for using %ColumnLabel() to predict %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_impliedcovariancesestimates"></a>
### Implied Covariances - Estimates

*Help context ID: 7370*

The covariance matrix displayed here is an estimate of the population covariance matrix of the observed variables under the hypothesis that the model is correct.

This matrix is displayed when you [obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).

<a id="t_impliedcovarianceestimate1"></a>
### Implied Covariance - Estimate

*Help context ID: 8310, 8370*

%m() is an estimate of the %CovDesc(RowLabel(), ColumnLabel()). For a saturated model, the implied %CovOrVar(RowLabel(), ColumnLabel()) is the same as the sample %CovOrVar(RowLabel(), ColumnLabel()). For an overidentified model (one with positive degrees of freedom), the implied %CovOrVar(RowLabel(), ColumnLabel()) between two measured variables can be different from the sample %CovOrVar(RowLabel(), ColumnLabel()). In that case, if the model is correct the implied %CovOrVar(RowLabel(), ColumnLabel()) is a better estimate of the population %CovOrVar(RowLabel(), ColumnLabel()) than the sample %CovOrVar(RowLabel(), ColumnLabel()) is.

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_impliedcovariancesbootstrapstandarderrors"></a>
### Implied Covariances - Bootstrap Standard Errors

*Help context ID: 7371*

This table contains bootstrap standard errors for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_impliedcovariancebootstrapstandarderror"></a>
### Implied Covariance - Bootstrap Standard Error

*Help context ID: 8311, 8371*

%m() is a bootstrap estimate of the standard error of the implied %CovDesc(RowLabel(), ColumnLabel()).

<a id="t_impliedcovariancesconfidenceintervalsbc"></a>
### Implied Covariances - Confidence Intervals (BC)

*Help context ID: 7372*

This table contains bias-corrected bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovarianceslowerboundsbc"></a>
### Implied Covariances - Lower Bounds (BC)

*Help context ID: 7373*

This table contains the lower boundaries of bias-corrected bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancelowerboundbc"></a>
### Implied Covariance - Lower Bound (BC)

*Help context ID: 8313, 8373*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancesupperboundsbc"></a>
### Implied Covariances - Upper Bounds (BC)

*Help context ID: 7374*

This table contains the upper boundaries of bias-corrected bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovarianceupperboundbc"></a>
### Implied Covariance - Upper Bound (BC)

*Help context ID: 8314, 8374*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancestwotailedsignificancebc"></a>
### Implied Covariances - Two Tailed Significance (BC)

*Help context ID: 7375*

This table contains two-tailed significance levels for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancetwotailedsignificancebc"></a>
### Implied Covariance - Two Tailed Significance (BC)

*Help context ID: 8315, 8375*

The implied %CovDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "bc").

<a id="t_impliedcovariancesconfidenceintervalspc"></a>
### Implied Covariances - Confidence Intervals (PC)

*Help context ID: 7376*

This table contains percentile-based bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovarianceslowerboundspc"></a>
### Implied Covariances - Lower Bounds (PC)

*Help context ID: 7377*

This table contains the lower boundaries of percentile-based bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancelowerboundpc"></a>
### Implied Covariance - Lower Bound (PC)

*Help context ID: 8317, 8377*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the implied $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancesupperboundspc"></a>
### Implied Covariances - Upper Bounds (PC)

*Help context ID: 7378*

This table contains the upper boundaries of percentile-based bootstrap confidence intervals for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovarianceupperboundpc"></a>
### Implied Covariance - Upper Bound (PC)

*Help context ID: 8318, 8378*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the implied $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancestwotailedsignificancepc"></a>
### Implied Covariances - Two Tailed Significance (PC)

*Help context ID: 7379*

This table contains two-tailed significance levels for [implied covariances among observed variables](#t_impliedcovariancesestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcovariancetwotailedsignificancepc"></a>
### Implied Covariance - Two Tailed Significance (PC)

*Help context ID: 8319, 8379*

The implied %CovDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "pc").

<a id="t_impliedcorrelationsestimates"></a>
### Implied Correlations - Estimates

*Help context ID: 7380*

The correlation matrix displayed here is an estimate of the population correlation matrix of the observed variables under the hypothesis that the model is correct.

This matrix is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_impliedcorrelationestimate"></a>
### Implied Correlation - Estimate

*Help context ID: 8320, 8380*

%choose("The model-implied correlation between %RowLabel() and itself is %m().", "%m() is an estimate of the correlation between %RowLabel() and %ColumnLabel(). For a saturated model, the implied correlation is the same as the sample correlation. For an overidentified model (one with positive degrees of freedom), the implied correlation between two measured variables can be different from the sample correlation. In that case, if the model is correct the implied correlation is a better estimate of the population correlation than the sample correlation is.")

<a id="t_impliedcorrelationsbootstrapstandarderrors"></a>
### Implied Correlations - Bootstrap Standard Errors

*Help context ID: 7381*

This table contains bootstrap standard errors for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_impliedcorrelationbootstrapstandarderror"></a>
### Implied Correlation - Bootstrap Standard Error

*Help context ID: 8321, 8381*

%m() is a bootstrap estimate of the standard error of the implied correlation between %choose("%RowLabel() and itself", "%RowLabel() and %ColumnLabel()").

<a id="t_impliedcorrelationsconfidenceintervalsbc"></a>
### Implied Correlations - Confidence Intervals (BC)

*Help context ID: 7382*

This table contains bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationslowerboundsbc"></a>
### Implied Correlations - Lower Bounds (BC)

*Help context ID: 7383*

This table contains the lower boundaries of bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationlowerboundbc"></a>
### Implied Correlation - Lower Bound (BC)

*Help context ID: 8323, 8383*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied correlation between $$RowLabel()$$ and $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationsupperboundsbc"></a>
### Implied Correlations - Upper Bounds (BC)

*Help context ID: 7384*

This table contains the upper boundaries of bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationupperboundbc"></a>
### Implied Correlation - Upper Bound (BC)

*Help context ID: 8324, 8384*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied correlation between $$RowLabel()$$ and $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationstwotailedsignificancebc"></a>
### Implied Correlations - Two Tailed Significance (BC)

*Help context ID: 7385*

This table contains two-tailed significance levels for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationtwotailedsignificancebc"></a>
### Implied Correlation - Two Tailed Significance (BC)

*Help context ID: 8325, 8385*

The implied %CorrDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "bc").

<a id="t_impliedcorrelationsconfidenceintervalspc"></a>
### Implied Correlations - Confidence Intervals (PC)

*Help context ID: 7386*

This table contains bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationslowerboundspc"></a>
### Implied Correlations - Lower Bounds (PC)

*Help context ID: 7387*

This table contains the lower boundaries of bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationlowerboundpc"></a>
### Implied Correlation - Lower Bound (PC)

*Help context ID: 8327, 8387*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the implied correlation between $$RowLabel()$$ and $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationsupperboundspc"></a>
### Implied Correlations - Upper Bounds (PC)

*Help context ID: 7388*

This table contains the upper boundaries of bootstrap confidence intervals for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationupperboundpc"></a>
### Implied Correlation - Upper Bound (PC)

*Help context ID: 8328, 8388*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the implied correlation between $$RowLabel()$$ and $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationstwotailedsignificancepc"></a>
### Implied Correlations - Two Tailed Significance (PC)

*Help context ID: 7389*

This table contains two-tailed significance levels for [implied correlations among observed variables](#t_impliedcorrelationsestimates). It is displayed when you simultaneously:

- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedcorrelationtwotailedsignificancepc"></a>
### Implied Correlation - Two Tailed Significance (PC)

*Help context ID: 8329, 8389*

The implied %CorrDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "pc").

<a id="t_impliedmeansestimates"></a>
### Implied Means - Estimates

*Help context ID: 527, 7390*

The means displayed here are estimates of the population means of the observed variables under the hypothesis that the model is correct.

These results are displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).

<a id="t_impliedmeanestimate"></a>
### Implied Mean - Estimate

*Help context ID: 8330, 8390*

%m() is an estimate of the mean of %ColumnLabel(). For a saturated model, this model-implied mean is the same as the sample mean. For an overidentified model (one with positive degrees of freedom), the implied mean of a measured variable can be different from the sample mean. In that case, if the model is correct the implied mean is a better estimate of the population mean than the sample mean is.

<a id="t_impliedmeansbootstrapstandarderrors"></a>
### Implied Means - Bootstrap Standard Errors

*Help context ID: 7391*

This table contains bootstrap standard errors for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_impliedmeanbootstrapstandarderror"></a>
### Implied Mean - Bootstrap Standard Error

*Help context ID: 8331, 8391*

%m() is a bootstrap estimate of the standard error of the implied mean of %ColumnLabel().

<a id="t_impliedmeansconfidenceintervalsbc"></a>
### Implied Means - Confidence Intervals (BC)

*Help context ID: 7392*

This table contains bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanslowerboundsbc"></a>
### Implied Means - Lower Bounds (BC)

*Help context ID: 7393*

This table contains the lower boundaries of bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanlowerboundbc"></a>
### Implied Mean - Lower Bound (BC)

*Help context ID: 8333, 8393*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeansupperboundsbc"></a>
### Implied Means - Upper Bounds (BC)

*Help context ID: 7394*

This table contains the upper boundaries of bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanupperboundbc"></a>
### Implied Mean - Upper Bound (BC)

*Help context ID: 8334, 8394*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the implied mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanstwotailedsignificancebc"></a>
### Implied Means - Two Tailed Significance (BC)

*Help context ID: 7395*

This table contains two-tailed significance levels for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeantwotailedsignificancebc"></a>
### Implied Mean - Two Tailed Significance (BC)

*Help context ID: 8335, 8395*

The model-implied mean of %ColumnLabel() %isbootsignificant("%m()", "bc").

<a id="t_impliedmeansconfidenceintervalspc"></a>
### Implied Means - Confidence Intervals (PC)

*Help context ID: 7396*

This table contains bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanslowerboundspc"></a>
### Implied Means - Lower Bounds (PC)

*Help context ID: 7397*

This table contains the lower boundaries of bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanlowerboundpc"></a>
### Implied Mean - Lower Bound (PC)

*Help context ID: 8337, 8397*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the implied mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeansupperboundspc"></a>
### Implied Means - Upper Bounds (PC)

*Help context ID: 7398*

This table contains the upper boundaries of bootstrap confidence intervals for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanupperboundpc"></a>
### Implied Mean - Upper Bound (PC)

*Help context ID: 8338, 8398*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the implied mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeanstwotailedsignificancepc"></a>
### Implied Means - Two Tailed Significance (PC)

*Help context ID: 7399*

This table contains two-tailed significance levels for [implied means of observed variables](#t_impliedmeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Obtain implied moments for observed variables](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainimpliedmomentsforobservedvariables1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_impliedmeantwotailedsignificancepc"></a>
### Implied Mean - Two Tailed Significance (PC)

*Help context ID: 8339, 8399*

The model-implied mean of %ColumnLabel() %isbootsignificant("%m()", "pc").

<a id="t_indirecteffectsestimates"></a>
### Indirect Effects - Estimates

*Help context ID: 532, 7400*

The indirect effect of each column variable on each row variable.

This table is displayed when you [estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects).

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_indirecteffectestimate"></a>
### Indirect Effect - Estimate

*Help context ID: 8400*

The indirect (mediated) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to the indirect (mediated) effect of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1, %RowLabel() %xcreases(m()) by %absm(). This is in addition to any direct (unmediated) effect that %ColumnLabel() may have on %RowLabel().

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_indirecteffectsbootstrapstandarderrors"></a>
### Indirect Effects - Bootstrap Standard Errors

*Help context ID: 7401*

This table contains bootstrap standard errors for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_indirecteffectbootstrapstandarderror"></a>
### Indirect Effect - Bootstrap Standard Error

*Help context ID: 8401*

%m() is a bootstrap estimate of the standard error of the indirect (mediated) effect of %ColumnLabel() on %RowLabel().

<a id="t_indirecteffectsconfidenceintervalsbc"></a>
### Indirect Effects - Confidence Intervals (BC)

*Help context ID: 7402*

This table contains bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectslowerboundsbc"></a>
### Indirect Effects - Lower Bounds (BC)

*Help context ID: 7403*

This table contains the lower boundaries of bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectlowerboundbc"></a>
### Indirect Effect - Lower Bound (BC)

*Help context ID: 8403*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectsupperboundsbc"></a>
### Indirect Effects - Upper Bounds (BC)

*Help context ID: 7404*

This table contains the upper boundaries of bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectupperboundbc"></a>
### Indirect Effect - Upper Bound (BC)

*Help context ID: 8404*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectstwotailedsignificancebc"></a>
### Indirect Effects - Two Tailed Significance (BC)

*Help context ID: 7405*

This table contains two-tailed significance levels for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffecttwotailedsignificancebc"></a>
### Indirect Effect - Two Tailed Significance (BC)

*Help context ID: 8405*

The indirect (mediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_indirecteffectsconfidenceintervalspc"></a>
### Indirect Effects - Confidence Intervals (PC)

*Help context ID: 7406*

This table contains bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectslowerboundspc"></a>
### Indirect Effects - Lower Bounds (PC)

*Help context ID: 7407*

This table contains the lower boundaries of bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectlowerboundpc"></a>
### Indirect Effect - Lower Bound (PC)

*Help context ID: 8407*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectsupperboundspc"></a>
### Indirect Effects - Upper Bounds (PC)

*Help context ID: 7408*

This table contains the upper boundaries of bootstrap confidence intervals for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectupperboundpc"></a>
### Indirect Effect - Upper Bound (PC)

*Help context ID: 8408*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffectstwotailedsignificancepc"></a>
### Indirect Effects - Two Tailed Significance (PC)

*Help context ID: 7409*

This table contains two-tailed significance levels for [indirect effects](#t_indirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_indirecteffecttwotailedsignificancepc"></a>
### Indirect Effect - Two Tailed Significance (PC)

*Help context ID: 8409*

The indirect (mediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_standardizedindirecteffectsestimates"></a>
### Standardized Indirect Effects - Estimates

*Help context ID: 535, 7410*

The indirect effect of each column variable on each row variable after standardizing all variables.

This table is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_standardizedindirecteffectestimate"></a>
### Standardized Indirect Effect - Estimate

*Help context ID: 8410*

The standardized indirect (mediated) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to the indirect (mediated) effect of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1 standard deviation, %RowLabel() %xcreases(m()) by %absm() standard deviations. This is in addition to any direct (unmediated) effect that %ColumnLabel() may have on %RowLabel().

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_standardizedindirecteffectsbootstrapstandarderrors"></a>
### Standardized Indirect Effects - Bootstrap Standard Errors

*Help context ID: 7411*

This table contains bootstrap standard errors for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_standardizedindirecteffectbootstrapstandarderror"></a>
### Standardized Indirect Effect - Bootstrap Standard Error

*Help context ID: 8411*

%m() is a bootstrap estimate of the standard error of the standardized indirect (mediated) effect of %ColumnLabel() on %RowLabel().

<a id="t_standardizedindirecteffectsconfidenceintervalsbc"></a>
### Standardized Indirect Effects - Confidence Intervals (BC)

*Help context ID: 7412*

This table contains bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectslowerboundsbc"></a>
### Standardized Indirect Effects - Lower Bounds (BC)

*Help context ID: 7413*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectlowerboundbc"></a>
### Standardized Indirect Effect - Lower Bound (BC)

*Help context ID: 8413*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectsupperboundsbc"></a>
### Standardized Indirect Effects - Upper Bounds (BC)

*Help context ID: 7414*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectupperboundbc"></a>
### Standardized Indirect Effect - Upper Bound (BC)

*Help context ID: 8414*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectstwotailedsignificancebc"></a>
### Standardized Indirect Effects - Two Tailed Significance (BC)

*Help context ID: 7415*

This table contains two-tailed significance levels for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffecttwotailedsignificancebc"></a>
### Standardized Indirect Effect - Two Tailed Significance (BC)

*Help context ID: 8415*

The standardized indirect (mediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_standardizedindirecteffectsconfidenceintervalspc"></a>
### Standardized Indirect Effects - Confidence Intervals (PC)

*Help context ID: 7416*

This table contains bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectslowerboundspc"></a>
### Standardized Indirect Effects - Lower Bounds (PC)

*Help context ID: 7417*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectlowerboundpc"></a>
### Standardized Indirect Effect - Lower Bound (PC)

*Help context ID: 8417*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectsupperboundspc"></a>
### Standardized Indirect Effects - Upper Bounds (PC)

*Help context ID: 7418*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectupperboundpc"></a>
### Standardized Indirect Effect - Upper Bound (PC)

*Help context ID: 8418*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized indirect (mediated) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffectstwotailedsignificancepc"></a>
### Standardized Indirect Effects - Two Tailed Significance (PC)

*Help context ID: 7419*

This table contains two-tailed significance levels for [standardized indirect effects](#t_standardizedindirecteffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedindirecteffecttwotailedsignificancepc"></a>
### Standardized Indirect Effect - Two Tailed Significance (PC)

*Help context ID: 8419*

The standardized indirect (mediated) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_residualcovariances1"></a>
### Residual Covariances

*Help context ID: 614, 7420*

The symmetric matrix displayed here contains the differences between [sample covariances](#t_samplecovariancesestimates) and [implied covariances](#t_impliedcovariancesestimates). If the model is correct, these differences should be small.

Residual covariances are displayed when you [obtain residual moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainresidualmoments1)

<a id="t_residualcovariance"></a>
### Residual Covariance

*Help context ID: 1614, 8420*

The sample %CovDesc(RowLabel(), ColumnLabel()) is %absm() %larger_smaller(m()) than the model-implied %CovOrVar(RowLabel(), ColumnLabel()).

<a id="t_standardizedresidualcovariances1"></a>
### Standardized Residual Covariances

*Help context ID: 661, 7430*

In the symmetric matrix displayed here, each residual covariance (see [Residual Covariances](#t_residualcovariances1)), has been divided by an estimate of its standard error ([Jöreskog & Sörbom, 1984](https://ai-docs.amosdevelopment.com/08-references.md#t_joereskog__soerbom_1984)). In sufficiently large samples, these *standardized residual covariances* have a standard normal distribution if the model is correct. So, if the model is correct, most of them should be less than two in absolute value.

This table appears when you [request residual moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainresidualmoments1).

<a id="t_standardizedresidualcovariance"></a>
### Standardized Residual Covariance

*Help context ID: 1661, 8430*

$$m()$$ is the residual $$CovDesc(RowLabel(), ColumnLabel())$$ divided by an estimate of its standard error ([Jöreskog & Sörbom, 1984](https://ai-docs.amosdevelopment.com/08-references.md#t_joereskog__soerbom_1984)). The residual $$CovDesc(RowLabel(), ColumnLabel())$$ is the difference between the sample $$CovOrVar(RowLabel(), ColumnLabel())$$ and the model-implied $$CovOrVar(RowLabel(), ColumnLabel())$$. With a correct model, most standardized residuals should be less than two in absolute value.

<a id="t_residualmeans1"></a>
### Residual Means

*Help context ID: 616, 7440*

The values displayed are differences between [sample means](#t_samplemeansestimates) and [implied means](#t_impliedmeansestimates). If the model is correct, these differences should be small.

Residual means are displayed when you simultaneously:

- [Obtain residual moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainresidualmoments1).
- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).

<a id="t_residualmean"></a>
### Residual Mean

*Help context ID: 1616, 8440*

The sample mean of %ColumnLabel() is %absm() %larger_smaller(m()) than the model-implied mean.

<a id="t_standardizedresidualmeans1"></a>
### Standardized Residual Means

*Help context ID: 662, 7450*

Each figure displayed here is a residual mean (see [Residual Means](#t_residualmeans1)), divided by an estimate of its standard deviation. In sufficiently large samples, these *standardized residual means* have a standard normal distribution if the model is correct. So, if the model is correct, most of them should be less than two (in absolute value).

This table appears when you [request residual moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainresidualmoments1).

<a id="t_standardizedresidualmean"></a>
### Standardized Residual Mean

*Help context ID: 1662, 8450*

%m() is the residual mean of %ColumnLabel() divided by an estimate of its standard error. (The residual mean is the difference between the sample mean and the model-implied mean.) With a correct model, most standardized residual means should be less than two (in absolute value).

<a id="t_samplecovariancesestimates"></a>
### Sample Covariances - Estimates

*Help context ID: 528, 7460*

Sample covariances are reported when you [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).

When you [analyze unbiased sample covariances](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyzeunbiasedsamplecovariances1),

$\left.\mathbf{S}^{(g)}=\frac{1}{N_{g}-1} \sum_{i=1}^{N^{(g)}}\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right) \mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)^{\prime}$,

is displayed.

When you [analyze biased (maximum likelihood) sample covariances](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyzebiasedmaximumlikelihoodsamplecovariances),

$\mathbf{S}^{(g)}=\frac{1}{N_{g}} \sum_{i=1}^{N^{(g)}}\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)^{\prime}$,

is displayed.

<a id="t_samplecovarianceestimate"></a>
### Sample Covariance - Estimate

*Help context ID: 8460*

The sample $$CovDesc(RowLabel(), ColumnLabel())$$ is $$m()$$. When you [analyze unbiased sample covariances](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyzeunbiasedsamplecovariances1), the formula

$\left.\mathbf{S}^{(g)}=\frac{1}{N_{g}-1} \sum_{i=1}^{N^{(g)}}\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right) \mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)^{\prime}$,

is used.

When you [analyze biased (maximum likelihood) sample covariances](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toanalyzebiasedmaximumlikelihoodsamplecovariances), the formula

$\mathbf{S}^{(g)}=\frac{1}{N_{g}} \sum_{i=1}^{N^{(g)}}\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)\left(\mathbf{x}_{i}^{(g)}-\overline{\mathbf{x}}^{(g)}\right)^{\prime}$,

is used.

<a id="t_samplecovariancesbootstrapstandarderrors"></a>
### Sample Covariances - Bootstrap Standard Errors

*Help context ID: 7461*

This table contains bootstrap standard errors for [sample covariances](#t_samplecovariancesestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_samplecovariancebootstrapstandarderror"></a>
### Sample Covariance - Bootstrap Standard Error

*Help context ID: 8461*

%m() is a bootstrap estimate of the standard error of the sample %CovDesc(RowLabel(), ColumnLabel()).

<a id="t_samplecovariancesconfidenceintervalsbc"></a>
### Sample Covariances - Confidence Intervals (BC)

*Help context ID: 7462*

This table contains bootstrap confidence intervals for [sample covariances](#t_samplecovariancesestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovarianceslowerboundsbc"></a>
### Sample Covariances - Lower Bounds (BC)

*Help context ID: 7463*

This table contains the lower boundaries of bootstrap confidence intervals for population variances and covariances. It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancelowerboundbc"></a>
### Sample Covariance - Lower Bound (BC)

*Help context ID: 8463*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the population $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancesupperboundsbc"></a>
### Sample Covariances - Upper Bounds (BC)

*Help context ID: 7464*

This table contains the upper boundaries of bootstrap confidence intervals for population variances and covariances. It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovarianceupperboundbc"></a>
### Sample Covariance - Upper Bound (BC)

*Help context ID: 8464*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the population $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancestwotailedsignificancebc"></a>
### Sample Covariances - Two Tailed Significance (BC)

*Help context ID: 7465*

This table contains two-tailed significance levels for [sample covariances](#t_samplecovariancesestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancetwotailedsignificancebc"></a>
### Sample Covariance - Two Tailed Significance (BC)

*Help context ID: 8465*

The sample %CovDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "bc").

<a id="t_samplecovariancesconfidenceintervalspc"></a>
### Sample Covariances - Confidence Intervals (PC)

*Help context ID: 7466*

This table contains bootstrap confidence intervals for population variances and covariances. It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovarianceslowerboundspc"></a>
### Sample Covariances - Lower Bounds (PC)

*Help context ID: 7467*

This table contains the lower boundaries of bootstrap confidence intervals for population variances and covariances. It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancelowerboundpc"></a>
### Sample Covariance - Lower Bound (PC)

*Help context ID: 8467*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the population $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancesupperboundspc"></a>
### Sample Covariances - Upper Bounds (PC)

*Help context ID: 7468*

This table contains the upper boundaries of bootstrap confidence intervals for population variances and covariances. It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovarianceupperboundpc"></a>
### Sample Covariance - Upper Bound (PC)

*Help context ID: 8468*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the population $$CovDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancestwotailedsignificancepc"></a>
### Sample Covariances - Two Tailed Significance (PC)

*Help context ID: 7469*

This table contains two-tailed significance levels for [sample covariances](#t_samplecovariancesestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecovariancetwotailedsignificancepc"></a>
### Sample Covariance - Two Tailed Significance (PC)

*Help context ID: 8469*

The sample %CovDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "pc").

<a id="t_samplecorrelationsestimates"></a>
### Sample Correlations - Estimates

*Help context ID: 529, 7470*

Sample correlations are displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_samplecorrelationestimate"></a>
### Sample Correlation - Estimate

*Help context ID: 8470*

%choose("The sample correlation between %RowLabel() and itself is %m().", "The sample correlation between %RowLabel() and %ColumnLabel() is %m().")

<a id="t_samplecorrelationsbootstrapstandarderrors"></a>
### Sample Correlations - Bootstrap Standard Errors

*Help context ID: 7471*

This table contains bootstrap standard errors for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_samplecorrelationbootstrapstandarderror"></a>
### Sample Correlation - Bootstrap Standard Error

*Help context ID: 8471*

%m() is a bootstrap estimate of the standard error of %choose("the sample correlation between %RowLabel() and itself.", "the sample correlation between %RowLabel() and %ColumnLabel().")

<a id="t_samplecorrelationsconfidenceintervalsbc"></a>
### Sample Correlations - Confidence Intervals (BC)

*Help context ID: 7472*

This table contains bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationslowerboundsbc"></a>
### Sample Correlations - Lower Bounds (BC)

*Help context ID: 7473*

This table contains the lower boundaries of bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationlowerboundbc"></a>
### Sample Correlation - Lower Bound (BC)

*Help context ID: 8473*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the $$CorrDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationsupperboundsbc"></a>
### Sample Correlations - Upper Bounds (BC)

*Help context ID: 7474*

This table contains the upper boundaries of bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationupperboundbc"></a>
### Sample Correlation - Upper Bound (BC)

*Help context ID: 8474*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the $$CorrDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationstwotailedsignificancebc"></a>
### Sample Correlations - Two Tailed Significance (BC)

*Help context ID: 7475*

This table contains two-tailed significance levels for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationtwotailedsignificancebc"></a>
### Sample Correlation - Two Tailed Significance (BC)

*Help context ID: 8475*

The sample %CorrDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "bc").

<a id="t_samplecorrelationsconfidenceintervalspc"></a>
### Sample Correlations - Confidence Intervals (PC)

*Help context ID: 7476*

This table contains bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationslowerboundspc"></a>
### Sample Correlations - Lower Bounds (PC)

*Help context ID: 7477*

This table contains the lower boundaries of bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationlowerboundpc"></a>
### Sample Correlation - Lower Bound (PC)

*Help context ID: 8477*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the $$CorrDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationsupperboundspc"></a>
### Sample Correlations - Upper Bounds (PC)

*Help context ID: 7478*

This table contains the upper boundaries of bootstrap confidence intervals for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationupperboundpc"></a>
### Sample Correlation - Upper Bound (PC)

*Help context ID: 8478*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the $$CorrDesc(RowLabel(), ColumnLabel())$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationstwotailedsignificancepc"></a>
### Sample Correlations - Two Tailed Significance (PC)

*Help context ID: 7479*

This table contains two-tailed significance levels for [sample correlations](#t_samplecorrelationsestimates). It is displayed when you simultaneously:

- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplecorrelationtwotailedsignificancepc"></a>
### Sample Correlation - Two Tailed Significance (PC)

*Help context ID: 8479*

The sample %CorrDesc(RowLabel(), ColumnLabel()) %isbootsignificant("%m()", "pc").

<a id="t_samplemeansestimates"></a>
### Sample Means - Estimates

*Help context ID: 530, 7480*

Sample means are reported when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).

<a id="t_samplemeanestimate"></a>
### Sample Mean - Estimate

*Help context ID: 8480*

The sample mean of %ColumnLabel() is %m().

<a id="t_samplemeansbootstrapstandarderrors"></a>
### Sample Means - Bootstrap Standard Errors

*Help context ID: 7481*

This table contains bootstrap standard errors for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_samplemeanbootstrapstandarderror"></a>
### Sample Mean - Bootstrap Standard Error

*Help context ID: 8481*

%m() is a bootstrap estimate of the standard error of the sample mean of %ColumnLabel().

<a id="t_samplemeansconfidenceintervalsbc"></a>
### Sample Means - Confidence Intervals (BC)

*Help context ID: 7482*

This table contains bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanslowerboundsbc"></a>
### Sample Means - Lower Bounds (BC)

*Help context ID: 7483*

This table contains the lower boundaries of bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanlowerboundbc"></a>
### Sample Mean - Lower Bound (BC)

*Help context ID: 8483*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the population mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeansupperboundsbc"></a>
### Sample Means - Upper Bounds (BC)

*Help context ID: 7484*

This table contains the upper boundaries of bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanupperboundbc"></a>
### Sample Mean - Upper Bound (BC)

*Help context ID: 8484*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the population mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanstwotailedsignificancebc"></a>
### Sample Means - Two Tailed Significance (BC)

*Help context ID: 7485*

This table contains two-tailed significance levels for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeantwotailedsignificancebc"></a>
### Sample Mean - Two Tailed Significance (BC)

*Help context ID: 8485*

The sample mean of %ColumnLabel() %isbootsignificant("%m()", "bc").

<a id="t_samplemeansconfidenceintervalspc"></a>
### Sample Means - Confidence Intervals (PC)

*Help context ID: 7486*

This table contains bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanslowerboundspc"></a>
### Sample Means - Lower Bounds (PC)

*Help context ID: 7487*

This table contains the lower boundaries of bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanlowerboundpc"></a>
### Sample Mean - Lower Bound (PC)

*Help context ID: 8487*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the population mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeansupperboundspc"></a>
### Sample Means - Upper Bounds (PC)

*Help context ID: 7488*

This table contains the upper boundaries of bootstrap confidence intervals for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanupperboundpc"></a>
### Sample Mean - Upper Bound (PC)

*Help context ID: 8488*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the population mean of $$ColumnLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeanstwotailedsignificancepc"></a>
### Sample Means - Two Tailed Significance (PC)

*Help context ID: 7489*

This table contains two-tailed significance levels for [sample means](#t_samplemeansestimates). It is displayed when you simultaneously:

- [Estimate means and intercepts](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatemeansandintercepts1).
- [Display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_samplemeantwotailedsignificancepc"></a>
### Sample Mean - Two Tailed Significance (PC)

*Help context ID: 8489*

The sample mean of %ColumnLabel() %isbootsignificant("%m()", "pc").

<a id="t_sampleeigenvalues1"></a>
### Sample Eigenvalues

*Help context ID: 7490*

The determinant, eigenvalues and condition number of the sample covariance matrix are displayed here, as well as the eigenvalues and condition number of the sample correlation matrix.

<a id="t_conditionnumberofthesamplecorrelationmatrix"></a>
### Condition number (of the sample correlation matrix)

*Help context ID: 7603*

The condition number of the sample correlation matrix is its largest eigenvalue divided by its smallest eigenvalue. Some programs report the condition number of a data matrix, ![7407](https://ai-docs.amosdevelopment.com/Images/7407.png), whose columns are scaled so that $\mathbf{X}^{\prime} \mathbf{X}$ is the sample correlation matrix. That condition number is the square root of the condition number reported by Amos.

The condition number of the sample correlation matrix is reported when all the following conditions are met.

- You [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- You [estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- The sample correlation matrix is positive definite

<a id="t_conditionnumberofthesamplecovariancematrix"></a>
### Condition number (of the sample covariance matrix)

*Help context ID: 7604*

The condition number of the sample covariance matrix, $S^{(g)}$, is its largest eigenvalue divided by its smallest eigenvalue. Some programs report the condition number of a data matrix, ![7410](https://ai-docs.amosdevelopment.com/Images/7410.png), whose columns are scaled so that $\mathbf{S}^{(g)}=\mathbf{X}^{\prime} \mathbf{X}$. That condition number is the square root of the condition number reported by Amos.

The condition number of the sample covariance matrix is reported when both of the following conditions are met.

- You [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- The sample covariance matrix is positive definite

<a id="t_determinantofthesamplecovariancematrix"></a>
### Determinant (of the sample covariance matrix)

*Help context ID: 629*

In the case of positive definite covariance matrices, a determinant near zero indicates that at least one observed variable is nearly linearly dependent on the others. The consequences of this depend on the specified model and on the discrepancy function. From a numerical point of view, a determinant near zero may make it difficult to estimate the parameters of the model. From a statistical point of view, a determinant near zero may imply poor estimates of some parameters (which will show up as large estimated standard errors).

The determinant of the sample covariance matrix is displayed when

- you [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1),

and

- the sample sample covariance matrix is positive definite.

<a id="t_eigenvaluesofthesamplecorrelationmatrix"></a>
### Eigenvalues (of the sample correlation matrix)

*Help context ID: 7601*

The eigenvalues of the sample correlation matrix are displayed when both of the following conditions are met.

- You [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).
- You [estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

<a id="t_eigenvaluesofthesamplecovariancematrix"></a>
### Eigenvalues (of the sample covariance matrix)

*Help context ID: 7602*

The eigenvalues of the sample covariance matrix are displayed when you [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1).

<a id="t_thesamplecovariancematrixisnotpositivedefinite1"></a>
### The sample covariance matrix is not positive definite

*Help context ID: 630*

This message appears in place of the determinant of the sample covariance matrix when the sample covariance matrix is not positive definite. (The determinant is calculated only for positive definite matrices.) [Wothke (1993)](https://ai-docs.amosdevelopment.com/08-references.md#t_wothke_1993) discusses the issue of covariance matrices that fail to be positive definite.

This message is displayed when

- you [display sample moments](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_todisplaysamplemoments1)

and

- the sample covariance matrix is not positive definite.

<a id="t_totaleffectsestimates"></a>
### Total Effects - Estimates

*Help context ID: 520, 7500*

The total effect (combined direct and indirect effect) of each column variable on each row variable.

This table is displayed when you [estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects).

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_totaleffectestimate"></a>
### Total Effect - Estimate

*Help context ID: 8500*

The total (direct and indirect) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to both direct (unmediated) and indirect (mediated) effects of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1, %RowLabel() %xcreases(m()) by %absm().

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_totaleffectsbootstrapstandarderrors"></a>
### Total Effects - Bootstrap Standard Errors

*Help context ID: 7501*

This table contains bootstrap standard errors for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_totaleffectbootstrapstandarderror"></a>
### Total Effect - Bootstrap Standard Error

*Help context ID: 8501*

%m() is a bootstrap estimate of the standard error of the total (direct and indirect) effect of %ColumnLabel() on %RowLabel().

<a id="t_totaleffectsconfidenceintervalsbc"></a>
### Total Effects - Confidence Intervals (BC)

*Help context ID: 7502*

This table contains bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectslowerboundsbc"></a>
### Total Effects - Lower Bounds (BC)

*Help context ID: 7503*

This table contains the lower boundaries of bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectlowerboundbc"></a>
### Total Effect - Lower Bound (BC)

*Help context ID: 8503*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectsupperboundsbc"></a>
### Total Effects - Upper Bounds (BC)

*Help context ID: 7504*

This table contains the upper boundaries of bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectupperboundbc"></a>
### Total Effect - Upper Bound (BC)

*Help context ID: 8504*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectstwotailedsignificancebc"></a>
### Total Effects - Two Tailed Significance (BC)

*Help context ID: 7505*

This table contains two-tailed significance levels for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffecttwotailedsignificancebc"></a>
### Total Effect - Two Tailed Significance (BC)

*Help context ID: 8505*

The total (direct and indirect) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_totaleffectsconfidenceintervalspc"></a>
### Total Effects - Confidence Intervals (PC)

*Help context ID: 7506*

This table contains bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectslowerboundspc"></a>
### Total Effects - Lower Bounds (PC)

*Help context ID: 7507*

This table contains the lower boundaries of bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectlowerboundpc"></a>
### Total Effect - Lower Bound (PC)

*Help context ID: 8507*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectsupperboundspc"></a>
### Total Effects - Upper Bounds (PC)

*Help context ID: 7508*

This table contains the upper boundaries of bootstrap confidence intervals for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectupperboundpc"></a>
### Total Effect - Upper Bound (PC)

*Help context ID: 8508*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffectstwotailedsignificancepc"></a>
### Total Effects - Two Tailed Significance (PC)

*Help context ID: 7509*

This table contains two-tailed significance levels for [total effects](#t_totaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_totaleffecttwotailedsignificancepc"></a>
### Total Effect - Two Tailed Significance (PC)

*Help context ID: 8509*

The total (direct and indirect) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_standardizedtotaleffectsestimates"></a>
### Standardized Total Effects - Estimates

*Help context ID: 533, 7510*

The total effect of each column variable on each row variable after standardizing all variables.

This table is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)

See [Definition of direct, indirect and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_definitionofdirectindirectandtotaleffects1).

<a id="t_standardizedtotaleffectestimate"></a>
### Standardized Total Effect - Estimate

*Help context ID: 8510*

The standardized total (direct and indirect) effect of %ColumnLabel() on %RowLabel() is %m(). That is, due to both direct (unmediated) and indirect (mediated) effects of %ColumnLabel() on %RowLabel(), when %ColumnLabel() goes up by 1 standard deviation, %RowLabel() %xcreases(m()) by %absm() standard deviations.

For further discussion of direct, indirect and total effects, see Kline ([2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), p. 134).

<a id="t_standardizedtotaleffectsbootstrapstandarderrors"></a>
### Standardized Total Effects - Bootstrap Standard Errors

*Help context ID: 7511*

This table contains bootstrap standard errors for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bootstrap estimates of standard errors](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbootstrapestimatesofstandarderrors1).

<a id="t_standardizedtotaleffectbootstrapstandarderror"></a>
### Standardized Total Effect - Bootstrap Standard Error

*Help context ID: 8511*

%m() is a bootstrap estimate of the standard error of the standardized total (direct and indirect) effect of %ColumnLabel() on %RowLabel().

<a id="t_standardizedtotaleffectsconfidenceintervalsbc"></a>
### Standardized Total Effects - Confidence Intervals (BC)

*Help context ID: 7512*

This table contains bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectslowerboundsbc"></a>
### Standardized Total Effects - Lower Bounds (BC)

*Help context ID: 7513*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectlowerboundbc"></a>
### Standardized Total Effect - Lower Bound (BC)

*Help context ID: 8513*

$$m()$$ is the lower endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectsupperboundsbc"></a>
### Standardized Total Effects - Upper Bounds (BC)

*Help context ID: 7514*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectupperboundbc"></a>
### Standardized Total Effect - Upper Bound (BC)

*Help context ID: 8514*

$$m()$$ is the upper endpoint of a two-sided bias-corrected bootstrap confidence interval for the standardized total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectstwotailedsignificancebc"></a>
### Standardized Total Effects - Two Tailed Significance (BC)

*Help context ID: 7515*

This table contains two-tailed significance levels for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain bias-corrected confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainbiascorrectedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffecttwotailedsignificancebc"></a>
### Standardized Total Effect - Two Tailed Significance (BC)

*Help context ID: 8515*

The standardized total (direct and indirect) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "bc").

<a id="t_standardizedtotaleffectsconfidenceintervalspc"></a>
### Standardized Total Effects - Confidence Intervals (PC)

*Help context ID: 7516*

This table contains bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectslowerboundspc"></a>
### Standardized Total Effects - Lower Bounds (PC)

*Help context ID: 7517*

This table contains the lower boundaries of bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectlowerboundpc"></a>
### Standardized Total Effect - Lower Bound (PC)

*Help context ID: 8517*

$$m()$$ is the lower endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectsupperboundspc"></a>
### Standardized Total Effects - Upper Bounds (PC)

*Help context ID: 7518*

This table contains the upper boundaries of bootstrap confidence intervals for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectupperboundpc"></a>
### Standardized Total Effect - Upper Bound (PC)

*Help context ID: 8518*

$$m()$$ is the upper endpoint of a two-sided percentile-based bootstrap confidence interval for the standardized total (direct and indirect) effect of $$ColumnLabel()$$ on $$RowLabel()$$. The confidence level is 90 percent by default. You can [specify a different confidence level](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffectstwotailedsignificancepc"></a>
### Standardized Total Effects - Two Tailed Significance (PC)

*Help context ID: 7519*

This table contains two-tailed significance levels for [standardized total effects](#t_standardizedtotaleffectsestimates). It is displayed when you simultaneously:

- [Estimate indirect, direct and total effects](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimateindirectdirectandtotaleffects)
- [Estimate correlations and standardized regression weights](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsandstandardizedregressionweights1)
- [Obtain percentile-based confidence intervals and significance tests](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtainpercentilebasedbootstrapconfidenceintervalsandsignificancetests).

<a id="t_standardizedtotaleffecttwotailedsignificancepc"></a>
### Standardized Total Effect - Two Tailed Significance (PC)

*Help context ID: 8519*

The standardized total (direct and indirect) effect of %ColumnLabel() on %RowLabel() %isbootsignificant("%m()", "pc").

<a id="t_correlationsofestimatesoutput"></a>
### Correlations of Estimates (output)

*Help context ID: 777, 7520*

This matrix has a row and column for each parameter of the model. Each off-diagonal entry in the matrix gives an estimate of the correlation between two parameter estimates. If you have assigned names to the parameters, those names are used to label the rows and columns of this matrix. If not, Amos makes up its own names.

You can find the parameter names next to the parameter estimates, in the **Label** column. (Click **Estimates** in the listbox at the left edge of the **Table Viewer** window.)

This matrix is displayed when you [estimate correlations among parameter estimates](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecorrelationsamongparameterestimates1).

<a id="t_correlationbetweentwoestimates"></a>
### Correlation between Two Estimates

*Help context ID: 780*

%choose("The correlation between the estimate of %RowLabel() and itself is %m().", "%m() is an estimate of the correlation between the estimate of %RowLabel() and the estimate of %ColumnLabel().")

<a id="t_variancecovariancematrixofestimates"></a>
### Variance-covariance Matrix of Estimates

*Help context ID: 776*

This matrix has a row and a column for each parameter of the model. Each off-diagonal entry in the matrix gives an estimate of the covariance between two parameter estimates. Each diagonal entry gives the variance of a single parameter estimate. If you have assigned names to the parameters, those names are used to label the rows and columns. If not, Amos makes up its own names.

You can find the parameter names next to the parameter estimates, in the **Label** column. (Click **Estimates** in the listbox at the left edge of the **Table Viewer** window.)

This matrix is displayed when you [estimate covariances among parameter estimates](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toestimatecovariancesamongparameterestimates1).

<a id="t_variancecovarianceforestimates"></a>
### Variance/Covariance for Estimates

*Help context ID: 779*

%m() is the estimated %CovDesc("the estimate of " + RowLabel(), "the estimate of " + ColumnLabel()).

<a id="t_criticalratiosfordifferencesbetweenparameters1"></a>
### Critical Ratios for Differences between Parameters

*Help context ID: 778*

This matrix has a row and column for each parameter of the model. Each off-diagonal entry in the matrix gives a statistic for testing the hypothesis that some two model parameters are equal in the population. If you have assigned names to the parameters, those names are used to label the rows and columns of this matrix. If not, Amos makes up its own names.

You can find the parameter names next to the parameter estimates, in the **Label** column. (Click **Estimates** in the listbox at the left edge of the **Table Viewer** window.)

This matrix is displayed when you [obtain critical ratios for differences between parameters](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_toobtaincriticalratiosfordifferencesbetweenparameters1).

<a id="t_criticalratiofordifferencebetweentwoparameters"></a>
### Critical Ratio for Difference between Two Parameters

*Help context ID: 781*

%m() is the difference between the estimate of %RowLabel() and the estimate of %ColumnLabel(), divided by an estimate of the standard error of the difference. With a correct model, under suitable [assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions), if %RowLabel() and %ColumnLabel() are equal in the population, this critical ratio or z statistic has a standard normal distribution.

<a id="t_numberofbootstrapsamples2"></a>
### Number of Bootstrap Samples

*Help context ID: 7609*

There were %m() bootstrap samples.

<a id="t_standarderrorofmean1"></a>
### Standard Error of Mean

*Help context ID: 7610*

The mean across bootstrap samples has a standard error of %m().

<a id="t_meanofmaximumlikelihooddiscrepanciesimpliedvssample"></a>
### Mean of Maximum Likelihood Discrepancies (implied vs sample)

*Help context ID: 7612*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{M L}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}_{b}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofmaximumlikelihooddiscrepanciesimpliedvspopulation"></a>
### Mean of Maximum Likelihood Discrepancies (implied vs population)

*Help context ID: 7614*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{M I}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}\right)=\frac{1}{B} \sum_{b=1}^{B}\left[C_{K I}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}\right)-C_{K I}(\mathbf{a}, \mathbf{a})\right]
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofkullbackliebleroveroptimismunstabilized"></a>
### Mean of Kullback-Leibler Overoptimism (unstabilized)

*Help context ID: 7616*

%m() is the mean

![7414](https://ai-docs.amosdevelopment.com/Images/7414.gif)

where *B* is the number of bootstrap samples.

<a id="t_meanofkullbackliebleroveroptimismstabilized"></a>
### Mean of Kullback-Leibler Overoptimism (stabilized)

*Help context ID: 7618*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} R_{b}^{*}
$$

where *B* is the number of bootstrap samples and

$$
\begin{aligned}
R_{b} * & =\left[C_{K I}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}\right)-C_{K I}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}_{b}\right)\right]+\sum_{g-1}^{G} k^{(g)}\left[\operatorname{tr}\left(\mathbf{S}_{b}^{(g)} \mathbf{S}^{(g)^{-1}}\right)-p^{(g)}\left(\frac{N^{(g)}-1}{N^{(g)}}\right)\right] \\
+ & \sum_{g-1}^{G} k^{(g)}\left[\left(\mathbf{x}_{b}^{(g)}-\mathbf{x}^{(g)}\right)^{\prime} \mathbf{S}^{(g)^{-1}}\left(\mathbf{x}_{b}^{(g)}-\mathbf{x}^{(g)}\right)-\frac{p^{(g)}}{N^{(g)}}\right], \\
b & =1, \ldots, B,
\end{aligned}
$$

where $k^{(g)}=N^{(g)}-1$ when the [emulisrel6](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_tousetheemulisrel6option1) option is used, and ![7418](https://ai-docs.amosdevelopment.com/Images/7418.png) otherwise.

<a id="t_meanofadfdiscrepanciesimpliedvssample"></a>
### Mean of ADF Discrepancies (implied vs sample)

*Help context ID: 7622*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{A D F}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}_{b}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofadfdiscrepanciesimpliedvspopulation"></a>
### Mean of ADF Discrepancies (implied vs population)

*Help context ID: 7620*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{A D F}\left(\hat{\boldsymbol{\alpha}}_{b}, \mathbf{a}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofglsdiscrepanciesimpliedvssample"></a>
### Mean of GLS Discrepancies (implied vs sample)

*Help context ID: 7626*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{G L S}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}_{b}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofglsdiscrepanciesimpliedvspopulation"></a>
### Mean of GLS Discrepancies (implied vs population)

*Help context ID: 7624*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{G L S}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofslsdiscrepanciesimpliedvssample"></a>
### Mean of SLS Discrepancies (implied vs sample)

*Help context ID: 7630*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{S L S}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}_{b}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofslsdiscrepanciesimpliedvspopulation"></a>
### Mean of SLS Discrepancies (implied vs population)

*Help context ID: 7628*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{S L S}\left(\hat{\boldsymbol{a}}_{b}, \mathbf{a}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofulsdiscrepanciesimpliedvssample"></a>
### Mean of ULS Discrepancies (implied vs sample)

*Help context ID: 7634*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{U L S}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}_{b}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_meanofulsdiscrepanciesimpliedvspopulation"></a>
### Mean of ULS Discrepancies (implied vs population)

*Help context ID: 7632*

%m() is the mean

$$
\frac{1}{B} \sum_{b=1}^{B} C_{U L S}\left(\hat{\mathbf{a}}_{b}, \mathbf{a}\right)
$$

where *B* is the number of bootstrap samples.

<a id="t_executiontimesummary1"></a>
### Execution time summary

*Help context ID: 884*

Execution time (in seconds) broken down into the following categories:

**Minimization**: Minimization of the discrepancy function

**Miscellaneous**: Anything not falling into another category, but consisting mostly of input parsing, output formatting and the computation of modification indices.

**Bootstrap**: self explanatory

**Total**: self explanatory

<a id="t_annotationofvalues"></a>
### Annotation of values

<a id="t_annotationofscalarvalues"></a>
#### Annotation of scalar values

<a id="t_estimateofregressionweight1"></a>
##### Estimate of regression weight

*Help context ID: 9000*

When %col(3) goes up by 1, %col(1) %xcreases(m()) by %absm().

%WasFixedNotEstimated("regression weight")

<a id="t_standarderrorofregressionweight"></a>
##### Standard error of regression weight

*Help context ID: 9001*

The regression weight estimate, %col(4), has a standard error of about %m().

<a id="t_criticalratioforregressionweight"></a>
##### Critical ratio for regression weight

*Help context ID: 9002*

Dividing the regression weight estimate by the estimate of its standard error gives

z = %col(4)/%col(5) = %m().

In other words, the regression weight estimate is %absm() standard errors %abovebelow(m()) zero.

<a id="t_levelofsignificanceforregressionweight"></a>
##### Level of significance for regression weight

*Help context ID: 9003*

The probability of getting a critical ratio as large as %mathabs(col(6)) in absolute value is %pvalue(m()). In other words, the regression weight for %col(3) in the prediction of %col(1) is %howsignificant(m()).

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_estimateofcovariance"></a>
##### Estimate of covariance

*Help context ID: 9040*

The covariance between %col(1) and %col(3) %is_fixed_estimated().

<a id="t_standarderrorofcovariance"></a>
##### Standard error of covariance

*Help context ID: 9041*

The covariance estimate, %col(4), has a standard error of about %m().

<a id="t_criticalratioforcovariance"></a>
##### Critical ratio for covariance

*Help context ID: 9042*

Dividing the covariance estimate by the estimate of its standard error gives

z = %col(4)/%col(5) = %m().

In other words, the covariance estimate is %absm() standard errors %abovebelow(m()) zero.

<a id="t_levelofsignificanceforcovariance"></a>
##### Level of significance for covariance

*Help context ID: 9043*

The probability of getting a critical ratio as large as %mathabs(col(6)) in absolute value is %pvalue(m()). In other words, the covariance between %col(1) and %col(3) is %howsignificant(m()).

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_estimateofvariance"></a>
##### Estimate of variance

*Help context ID: 9060*

The variance of %col(1) %is_fixed_estimated().

<a id="t_standarderrorofvariance"></a>
##### Standard error of variance

*Help context ID: 9061*

The variance estimate, %col(4), has a standard error of about %m().

<a id="t_criticalratioforvariance"></a>
##### Critical ratio for variance

*Help context ID: 9062*

Dividing the variance estimate by the estimate of its standard error gives

z = %col(4)/%col(5) = %m().

In other words, the variance estimate is %absm() standard errors %abovebelow(m()) zero.

<a id="t_levelofsignificanceforvariance"></a>
##### Level of significance for variance

*Help context ID: 9063*

The probability of getting a critical ratio as large as %mathabs(col(6)) in absolute value is %pvalue(m()). In other words, the variance estimate for %col(1) is %howsignificant(m()).

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_estimateofmean"></a>
##### Estimate of mean

*Help context ID: 9020*

The mean of %col(1) %is_fixed_estimated().

<a id="t_standarderrorofmean"></a>
##### Standard error of mean

*Help context ID: 9021*

The estimate of the mean, %col(4), has a standard error of about %m().

<a id="t_criticalratioformean"></a>
##### Critical ratio for mean

*Help context ID: 9022*

Dividing the estimate of the mean by the estimate of its standard error gives

z = %col(4)/%col(5) = %m().

In other words, the estimate of the mean is %absm() standard errors %abovebelow(m()) zero.

<a id="t_levelofsignificanceformean"></a>
##### Level of significance for mean

*Help context ID: 9023*

The probability of getting a critical ratio as large as %mathabs(col(6)) in absolute value is %pvalue(m()). In other words, the mean of %col(1) is %howsignificant(m()).

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_estimateofintercept"></a>
##### Estimate of intercept

*Help context ID: 9030*

The intercept in the equation for predicting %col(1) %is_fixed_estimated().

<a id="t_standarderrorofintercept"></a>
##### Standard error of intercept

*Help context ID: 9031*

The estimate of the intercept, %col(4), has a standard error of about %m().

<a id="t_criticalratioforintercept"></a>
##### Critical ratio for intercept

*Help context ID: 9032*

Dividing the estimate of the intercept by the estimate of its standard error gives

z = %col(4)/%col(5) = %m().

In other words, the estimate of the intercept is %absm() standard errors %abovebelow(m()) zero.

<a id="t_levelofsignificanceforintercept"></a>
##### Level of significance for intercept

*Help context ID: 9033*

The probability of getting a critical ratio as large as %mathabs(col(6)) in absolute value is %pvalue(m()). In other words, the intercept in the equation for predicting %col(1) is %howsignificant(m()).

These statements are approximately correct for large samples under suitable assumptions. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_estimateofstandardizedregressionweight"></a>
##### Estimate of standardized regression weight

*Help context ID: 9010*

When %col(3) goes up by 1 standard deviation, %col(1) %xcreases(m()) by %absm() standard deviations.

<a id="t_estimateofcorrelation"></a>
##### Estimate of correlation

*Help context ID: 9050*

%m() is the estimated correlation between %col(1) and %col(3).

<a id="t_estimateofsquaredmultiplecorrelation"></a>
##### Estimate of squared multiple correlation

*Help context ID: 9070*

It is estimated that the predictors of %col(1) explain %percent(m()) percent of its variance. In other words, the error variance of %col(1) is approximately %otherpercent(m()) percent of the variance of %col(1) itself.

<a id="t_modificationindexforregressionweight"></a>
##### Modification index for regression weight

*Help context ID: 9080*

%modi(RegDesc(col(1),col(3)))

<a id="t_estimatedparameterchangeforregressionweight"></a>
##### Estimated parameter change for regression weight

*Help context ID: 9081*

%parchange(RegDesc(col(1),col(3)))

<a id="t_modificationindexformean"></a>
##### Modification index for mean

*Help context ID: 9082*

%modi(MeanDesc(col(1)))

<a id="t_estimatedparameterchangeformean"></a>
##### Estimated parameter change for mean

*Help context ID: 9083*

%parchange(MeanDesc(col(1)))

<a id="t_modificationindexforintercept"></a>
##### Modification index for intercept

*Help context ID: 9084*

%modi(InterceptDesc(col(1)))

<a id="t_estimatedparameterchangeforintercept"></a>
##### Estimated parameter change for intercept

*Help context ID: 9085*

%parchange(InterceptDesc(col(1)))

<a id="t_modificationindexforcovariance"></a>
##### Modification index for covariance

*Help context ID: 9086*

%modi(CovDesc(col(1),col(3)))

<a id="t_estimatedparameterchangeforcovariance"></a>
##### Estimated parameter change for covariance

*Help context ID: 9087*

%parchange(CovDesc(col(1),col(3)))

<a id="t_modificationindexforvariance"></a>
##### Modification index for variance

*Help context ID: 9088*

%modi(VarianceDesc(col(1)))

<a id="t_estimatedparameterchangeforvariance"></a>
##### Estimated parameter change for variance

*Help context ID: 9089*

%parchange(VarianceDesc(col(1)))

<a id="t_cminvalue"></a>
##### CMIN value

*Help context ID: 7801*

The %col(1) model has a discrepancy of %m().

<a id="t_dfvalue"></a>
##### DF value

*Help context ID: 7802*

The %col(1) model has %m() degrees of freedom.

<a id="t_pvalue"></a>
##### P value

*Help context ID: 7803*

Assuming that the %col(1) model is correct, the probability of getting a discrepancy as large as %col(3) is %m().

<a id="t_nparvalue"></a>
##### NPAR value

*Help context ID: 7804*

The %col(1) model has %m() parameters.

<a id="t_cmindfvalue"></a>
##### CMIN/DF value

*Help context ID: 7805*

For the %col(1) model, the discrepancy divided by degrees of freedom is %col(3) / %col(4) = %m().

<a id="t_rmrvalue"></a>
##### RMR value

*Help context ID: 7807*

[RMR](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rmr2) = %m() for the %col(1) model.

<a id="t_gfivalue"></a>
##### GFI value

*Help context ID: 7808*

[GFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_gfi2) = %m() for the %col(1) model.

<a id="t_agfivalue"></a>
##### AGFI value

*Help context ID: 7809*

[AGFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_agfi2) = %m() for the %col(1) model.

<a id="t_pgfivalue"></a>
##### PGFI value

*Help context ID: 7810*

[PGFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_pgfi2) = %m() for the %col(1) model.

<a id="t_nfivalue"></a>
##### NFI value

*Help context ID: 7812*

[NFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_nfi2) = %m() for the %col(1) model.

<a id="t_rfivalue"></a>
##### RFI value

*Help context ID: 7813*

[RFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rfi2) = $$m()$$ for the $$col(1)$$ model.

<a id="t_ifivalue"></a>
##### IFI value

*Help context ID: 7814*

[IFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ifi2) = %m() for the %col(1) model.

<a id="t_tlivalue"></a>
##### TLI value

*Help context ID: 7815*

[TLI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_tli2) = %m() for the %col(1) model.

<a id="t_cfivalue"></a>
##### CFI value

*Help context ID: 7816*

[CFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_cfi2) = %m() for the %col(1) model.

<a id="t_pratiovalue"></a>
##### PRATIO value

*Help context ID: 7818*

The parsimony ratio, [PRATIO](https://ai-docs.amosdevelopment.com/07-appendices.md#t_pratio2), is %m() for the %col(1) model.

<a id="t_pnfivalue"></a>
##### PNFI value

*Help context ID: 7819*

[PNFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_pnfi2) = %m() for the %col(1) model.

<a id="t_pcfivalue"></a>
##### PCFI value

*Help context ID: 7820*

[PCFI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_pcfi2) = %m() for the %col(1) model.

<a id="t_ncpvalue"></a>
##### NCP value

*Help context ID: 7822*

[NCP](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_ncpncploncphimethods) = %m() for the %col(1) model.

<a id="t_ncplo3"></a>
##### NCPLO

*Help context ID: 7923*

Lower boundary of a two-sided 90 percent confidence interval for the population [NCP](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_ncpncploncphimethods).

<a id="t_ncplovalue"></a>
##### NCPLO value

*Help context ID: 7823*

With approximately 90 percent confidence, the population [NCP](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_ncpncploncphimethods) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_ncphi3"></a>
##### NCPHI

*Help context ID: 7924*

Upper boundary of a two-sided 90 percent confidence interval for the population [NCP](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_ncpncploncphimethods).

<a id="t_ncphivalue"></a>
##### NCPHI value

*Help context ID: 7824*

With approximately 90 percent confidence, the population [NCP](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_ncpncploncphimethods) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_fminvalue"></a>
##### FMIN value

*Help context ID: 7825*

[FMIN](https://ai-docs.amosdevelopment.com/07-appendices.md#t_appendixcmeasuresoffit1) = %m() for the %col(1) model.

<a id="t_f0value"></a>
##### F0 value

*Help context ID: 7826*

[F0](https://ai-docs.amosdevelopment.com/07-appendices.md#t_f02) = %m() for the %col(1) model.

<a id="t_f0lo3"></a>
##### F0LO

*Help context ID: 7927*

Lower boundary of a two-sided 90 percent confidence interval for the population [F0](https://ai-docs.amosdevelopment.com/07-appendices.md#t_f02).

<a id="t_f0lovalue"></a>
##### F0LO value

*Help context ID: 7827*

With approximately 90 percent confidence, the population [F0](https://ai-docs.amosdevelopment.com/07-appendices.md#t_f02) for the $$col(1)$$ model is between $$col(4)$$ and $$col(5)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_f0hi3"></a>
##### F0HI

*Help context ID: 7928*

Upper boundary of a two-sided 90 percent confidence interval for the population [F0](https://ai-docs.amosdevelopment.com/07-appendices.md#t_f02).

<a id="t_f0hivalue"></a>
##### F0HI value

*Help context ID: 7828*

With approximately 90 percent confidence, the population [F0](https://ai-docs.amosdevelopment.com/07-appendices.md#t_f02) for the $$col(1)$$ model is between $$col(4)$$ and $$col(5)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_rmseavalue"></a>
##### RMSEA value

*Help context ID: 7829*

[RMSEA](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rmsea2) = %m() for the %col(1) model.

<a id="t_rmsealo3"></a>
##### RMSEALO

*Help context ID: 7930*

Lower boundary of a two-sided 90 percent confidence interval for the population [RMSEA](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_rmsearmsealormseahimethods).

<a id="t_rmsealovalue"></a>
##### RMSEALO value

*Help context ID: 7830*

With approximately 90 percent confidence, the population [RMSEA](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rmsea2) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_rmseahi3"></a>
##### RMSEAHI

*Help context ID: 7931*

Upper boundary of a two-sided 90 percent confidence interval for the population [RMSEA](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_rmsearmsealormseahimethods).

<a id="t_rmseahivalue"></a>
##### RMSEAHI value

*Help context ID: 7831*

With approximately 90 percent confidence, the population [RMSEA](https://ai-docs.amosdevelopment.com/07-appendices.md#t_rmsea2) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

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##### PCLOSE value

*Help context ID: 7832*

[PCLOSE](https://ai-docs.amosdevelopment.com/05-programming-with-amos-part-2.md#t_pclosemethod) = $$m()$$ for the $$col(1)$$ model. Under the hypothesis of "close fit" (i.e., that RMSEA is no greater than .05 in the population), the probability of getting a sample RMSEA as large as $$col(2)$$ is $$m()$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

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##### AIC value

*Help context ID: 7834*

[AIC](https://ai-docs.amosdevelopment.com/07-appendices.md#t_aic2) = %m() for the %col(1) model.

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##### BCC value

*Help context ID: 7835*

[BCC](https://ai-docs.amosdevelopment.com/07-appendices.md#t_bcc2) = %m() for the %col(1) model.

<a id="t_bicvalue"></a>
##### BIC value

*Help context ID: 7836*

[BIC](https://ai-docs.amosdevelopment.com/07-appendices.md#t_bic2) = %m() for the %col(1) model.

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##### CAIC value

*Help context ID: 7837*

[CAIC](https://ai-docs.amosdevelopment.com/07-appendices.md#t_caic2) = %m() for the %col(1) model.

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##### ECVI value

*Help context ID: 7838*

[ECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ecvi2) = %m() for the %col(1) model.

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##### ECVILO

*Help context ID: 7939*

Lower boundary of a two-sided 90 percent confidence interval for the population [ECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ecvi2).

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##### ECVILO value

*Help context ID: 7839*

With approximately 90 percent confidence, the population [ECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ecvi2) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

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##### ECVIHI

*Help context ID: 7940*

Upper boundary of a two-sided 90 percent confidence interval for the population [ECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ecvi2).

<a id="t_ecvihivalue"></a>
##### ECVIHI value

*Help context ID: 7840*

With approximately 90 percent confidence, the population [ECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_ecvi2) for the $$col(1)$$ model is between $$col(3)$$ and $$col(4)$$. (See [Assumptions](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_assumptions).)

<a id="t_mecvivalue"></a>
##### MECVI value

*Help context ID: 7841*

[MECVI](https://ai-docs.amosdevelopment.com/07-appendices.md#t_mecvi2) = %m() for the %col(1) model.

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##### Hoelter value (significance = .05)

*Help context ID: 7843*

%m() is the largest sample size for which you could accept at the .05 level the hypothesis that the %col(1) model is correct. In other words, if the sample size were any bigger than %m() you would reject the %col(1) model at the .05 level.

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##### Hoelter value (significance = .01)

*Help context ID: 7844*

%m() is the largest sample size for which you could accept at the .01 level the hypothesis that the %col(1) model is correct. In other words, if the sample size were any bigger than %m() you would reject the %col(1) model at the .01 level.

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##### d-separation

*Help context ID: 11980*

The result of a [d-separation](https://ai-docs.amosdevelopment.com/03-amos-graphics-reference-guide-part-2.md#t_d-separation) analysis ([Kline, 2016](https://ai-docs.amosdevelopment.com/08-references.md#t_kline_2005), ch 8, [Pearl, 2009](https://ai-docs.amosdevelopment.com/08-references.md#t_pearl_-j_-_2009_), [Pearl, Glymour and Jewell, 2016](https://ai-docs.amosdevelopment.com/08-references.md#t_pearl_-j__-glymour_-m_-and-jew)).

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##### D-separation description

*Help context ID: 11982*

The model implies that %dsep_description_independence().

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##### D-separation r value

*Help context ID: 11983*

The %dsep_description_correlation() is %m() in the sample. (The model implies that the %dsep_correlation_or_partial_correlation() is zero in the population.)

<a id="t_d-separation-t-value"></a>
##### D-separation t value

*Help context ID: 11984*

%m() is the value of the t statistic given by [Weatherburn (1968, page 256)](https://ai-docs.amosdevelopment.com/08-references.md#t_weatherburn-_1968_) for testing the null hypothesis that the %dsep_correlation_or_partial_correlation() is zero in the population

<a id="t_d-separation-p-value"></a>
##### D-separation p value

*Help context ID: 11985*

%m() is the probability of getting a sample %dsep_correlation_or_partial_correlation() as far from zero as %col(2) ([Weatherburn, 1968, page 256)](https://ai-docs.amosdevelopment.com/08-references.md#t_weatherburn-_1968_). %m() is a two-tailed "p value" for testing the null hypothesis that the %dsep_correlation_or_partial_correlation() is zero in the population.

<a id="t_add-to-version-history"></a>
## Add to version history

*Help context ID: 3316*

Click this button to add the current version of the model to the version history.

<a id="t_cancel-add-to-version-history"></a>
## Do not add to version history

*Help context ID: 3317*

Click this button to save the current version of the model without adding it to the version history.

<a id="t_version-notes"></a>
## Version notes

Enter any notes that you want to associate with this version of the model. Blank lines at the beginning are ignored. The first non-blank line is used as a brief label for the version.