GRM More Results - Summary Tab

Select the Summary tab of the GRM More Results dialog to access options to display the main results for the current analysis. Depending on the type of design, whether or not there are categorical predictor variables in the design, or whether or not the current analysis is based on stepwise or best subset model building methods, some of the options described below may not be available on the Summary tab.

Element Name Description
All effects/Graphs Click the All effects/Graphs button to display the Table of All Effects dialog. This dialog shows the summary ANOVA (MANOVA) table for all effects; you can then select an effect and produce a spreadsheet or graph of the observed unweighted, observed weighted, and least squares means. Refer also to the description of the options on the Means tab for details concerning the different means computed by STATISTICA, and their standard errors. This option is only available if the current design includes categorical predictor variables.
ANOVA table of all effects Click the ANOVA table of all effects button to display a spreadsheet with the ANOVA (MANOVA) table for all effects. If the design is univariate in nature (involves only a single dependent variable), then the univariate results ANOVA table will be displayed; if the design is multivariate in nature, then the multivariate results MANOVA table will be displayed, showing the statistics as selected in the Multivariate tests  group box (see below). For a discussion of the different types of designs, and how the respective ANOVA/MANOVA tables are computed, see the Introductory overview.
Effect sizes Click the Effect sizes button to display a spreadsheet with the ANOVA (MANOVA) table for all effects and the effect sizes and powers (i.e., Partial eta-squared, Non-centrality, and Observed power). Partial eta-squared is the proportion of the variability in the dependent variables that is explained by the effect. The Non-centrality value is the main statistic used to compute power, and the Power column contains the power values of the significant test on the effect. The ANOVA (MANOVA) table is described above, see ANOVA table of all effects.
Whole model R Click the Whole model R button to display a series of spreadsheets, summarizing the overall fit of the model. For a detailed description of these spreadsheets, please see GRM whole model R results spreadsheets.
Pareto chart of effects Click the Pareto chart of effects button to produce a Pareto chart of the parameter estimates (Regression coefficients, see below), or, optionally, the t-values associated with the parameter estimates if the t-vals check box is selected (see below). The Pareto chart shows the parameter estimates (or t-values) sorted by their absolute size. If you plot the t-values, a vertical line will also be shown to indicate the minimum magnitude of statistically significant parameter estimates, given the current criterion of statistical significance (specified in the Alpha values group box, see below). The Pareto chart is very useful for reviewing a large number of parameters.
t-vals Select the t-vals check box to display the absolute values of the t-values associated with the parameter estimates in the Pareto chart of effects (see above); the Pareto chart will also include a vertical line to indicate the minimum magnitude of statistically significant parameter estimates, given the current criterion of statistical significance (specified in the Alpha values group box, see below).
Univariate results Click the Univariate results button to display a spreadsheet with the standard univariate ANOVA table for each dependent variable.
Descriptive cell statistics Click the Descriptive cell statistics button to display a spreadsheet of the descriptive statistics for each cell in the design; specifically, descriptive statistics are computed for the dependent variables, as well as any continuous predictors (covariates) in the design, for each column of the overparameterized design matrix for categorical effects. Thus, marginal means and standard deviations are available for each categorical effect in the design. Note that for lower-order effects (e.g., main-effects in designs that also contain interactions involving the main effects), the reported means are weighted marginal means, and as such estimates of the weighted population marginal means (for details, see, for example, Milliken and Johnson, 1984, page 132; see also the discussion of means in the description of the options on the Means tab). Least squares means (e.g., see Searle, 1987) can be computed on the Means tab, or via the All effects/Graphs option above; usually, in factorial designs, it is the least squares means that should be reviewed when interpreting significant effects from the ANOVA or MANOVA.
Regression coefficients Click the Regression coefficients button to display a spreadsheet of the current parameter estimates (b), standardized parameter estimates (Beta), their standard errors, significance levels, and related statistics. In complex or incomplete designs, a Comment column may also be shown in the spreadsheet. The cells in this column may either be blank, or contain the designations Biased, Zeroed, or Dropped. Please see the Coefficients option on the GRM Results - Quick tab for detailed information.
Partial corrs and related stats Click the Partial corrs and related stats button to display a spreadsheet with various collinearity statistics, as well as the partial and semi-partial correlations (and related statistics) between the predictor variables (columns in the design matrix) and the dependent (response) variables. Note that matrices of partial and semi-partial correlations among dependent variables (controlling for the effects currently in the model) can be reviewed on the Matrix tab.
Note: Collinearity statistics may possibly be omitted from this spreadsheet if the matrix inversion routine detects numerical round-off problems according to the precision specified by the SDELTA parameter (Sweep Delta and Inverse Delta for matrix inversion and determining estimable functions) on the analysis dialog. To attempt to display the statistics when omitted, try inputting larger values for the DELTA parameters and rerun the analysis. Be aware, though, that you will need to carefully review your results for consistency, as they may be subject to round-off errors.
Design terms Click the Design terms button to display a spreadsheet of all the labels for each column in the design matrix (see GLM Introductory Overview). This spreadsheet is useful in conjunction with the Regression coefficients option (see above) to unambiguously identify how the categorical predictors in the design were coded, that is, how the model was parameterized, and how, consequently, the parameter estimates can be interpreted. The GLM Introductory Overview discusses in detail the overparameterized and sigma-restricted parameterization for categorical predictor variables and effects, and how each parameterization can yield completely different parameter estimates (even though the overall model fit, and ANOVA tables are usually invariant to the method of parameterization). If in the current analysis the categorical predictor variables were coded according to the sigma-restricted parameterization, then this spreadsheet will show the two levels of the respective factors that were contrasted in each column of the design matrix; if the overparameterized model was used, then the spreadsheet will show the relationship of each level of the categorical predictors to the columns in the design matrix (and, hence, the respective parameter estimates).
Estimate If you have not already specified your matrix of coefficients (by clicking on the button (see below)), click the Estimate button to display the Specify Effect to Estimate dialog. In that spreadsheet you can specify a matrix of coefficients; the transpose of this matrix will be post-multiplied by the matrix of parameter estimates or Regression coefficients (see above), to yield a linear combination of parameter estimates that specifies a hypothesis (or simultaneous set of hypotheses) that will be tested. To use the common notation, STATISTICA expects you to specify a matrix of estimable functions L' (L transposed; L is assumed to be a row matrix), for which the sums of squares (and ANOVA or MANOVA tests) will be computed; specifically, the sums of squares (and statistical significance tests) pertain to the hypothesis:

Lb = 0

where L is the transposed matrix of coefficients specified in the Specify Effect to Estimate dialog, and b is the matrix of parameter estimates (Regression coefficients).

The user-defined L matrices are tested for estimability (see Estimability of hypotheses) as well as redundancy (i.e., if a column in L' is a linear function of other columns), and if any of these conditions occur, and error message will be displayed. Refer to the Testing specific hypotheses topic in the GLM Introductory Overview for details concerning the computation of sums of squares for estimable functions of the parameters.

See the Examples section for examples of useful applications of this very flexible tool. Note that custom estimable functions can also be specified in the GRM Analysis Syntax Editor dialog via the ESTIMATE keyword. To review the results for tests of estimable functions specified via GRM (GLM) DESIGN syntax, click on the summary button next to the Estimate button (that button is only available if custom estimable functions were specified via GRM (GLM) DESIGN syntax).

Click this button to display the Specify Effect to Estimate dialog, which allows you to specify custom hypotheses via estimable functions, see Estimate above for details.
Alpha values Use the Alpha values group box to specify Confidence limits and Significance level values. These values are used in all results spreadsheets and graphs whenever a confidence limit is to be computed or a particular result is to be highlighted based its statistical significance.
Confidence limits Enter the value to be used for constructing confidence limits in the respective results spreadsheets or graphs (e.g., spreadsheet of parameter estimates, graph of means) in the Confidence limits field. By default 95% confidence limits will be constructed.
Significance level Enter the value to be used for all spreadsheets and graphs where statistically significant results are to be highlighted (e.g., in the All effects spreadsheet) in the Significance level field. By default all results significant at the p<.05 level will be highlighted.
Model building results The options in the Model building results group box will display summary spreadsheets for the stepwise regression analysis or the best subset regression analysis respectively. Please see Model building results in GRM for further details on these options. Refer also to Model building in GRM in the Introductory Overview for details concerning the available model building procedures.
Multivariate tests In the Multivariate tests group box you can select the specific multivariate test statistics that are to be reported in the respective results spreadsheets. For descriptions of the different multivariate tests statistics, refer to the GLM Introductory Overview. These options are only available if the current design is multivariate in nature, i.e., if there are multiple dependent measures, or a within-subject (repeated measures) design with effects that have more than 2 levels (and hence, multivariate tests for those effects can be computed).

See also GRM - Index.