# GLM, GRM, and ANOVA Results - Comps Tab

Contrast Analysis

Select the Comps tab (Comparisons tab) of the GLM Results, GRM Results, or the ANOVA Results dialogs to access options to perform a priori (planned) comparisons between the means in the design. Note that complex a priori hypotheses can also be tested via the Estimate button, on the Summary tab (see the Between effects group box). A discussion of the rationale and applications of planned comparisons and post-hoc tests is provided in the Contrast analysis and post-hoc tests topic in the context of the ANOVA/MANOVA module. Note that these options are only available if the current design contains effects for categorical predictor variables or within subject (repeated measures) effects.

Note: planned (a priori) comparisons (contrast analysis ). A priori planned comparisons are usually performed after an analysis involving effects for categorical predictor variables has yielded significant effects. The purpose of planned comparisons then is to determine whether the pattern of means for the respective effect follows the one that was hypothesized, that is, you compare the specific means for the effect of interest that were hypothesized to be different from each other (e.g., in a 3-level effect Group, you might test whether the mean for level 1 is significantly different from the mean for level 3). STATISTICA GLM provides a convenient user-interface for specifying contrast coefficients; these coefficients are then used to compare the least squares means (see also the Means tab for details) for the respective chosen Effect (see below). Thus, the contrasts for the planned comparisons are applied to the means predicted by the current model; these means are identical to the observed unweighted means in the case of full factorial designs without continuous predictors (covariates).

Note: random effects. The error terms for all planned comparisons will always be computed from the sums of squares residuals. Those error terms may not be appropriate, and when random effects are involved, you should interpret the results of planned comparisons with caution.

Effect. Select the desired effect from all of those effects in the current design in the Effect drop-down box. A priori planned comparisons are performed on the marginal means (least squares, see below) for effects involving only categorical predictor variables.

Planned comparisons of LS means. The options in the Planned comparisons of LS means group box allow you to compute planned comparisons of the least squares means for the current model. The contrast coefficients can be entered Separately for each factor in the current Effect (see above), or Together as a vector simultaneously for all factors (see below). When there are continuous predictors (covariates) in the model, then the least squares means used in the comparison are computed from the covariates at their means (regardless of the selection in the Covariate values group box on the Means tab).

Display least squares means. Click the Display least squares means button to display a spreadsheet with the least squares means for the currently selected Effect; see also the Means tab.

Contrasts for LS means.  Click the Contrasts for LS means button to display the respective contrast specification dialog for the chosen Effect.  If you requested to enter the contrast coefficients Separately for each factor (see below), then the contrast specification dialog will allow you to enter the contrast coefficients for each factor; if you requested to enter the contrast coefficients Together (contrast vector), then the contrast specification dialog will prompt you to enter a matrix (or vector) of contrast coefficients for all levels of the chosen effect (the respective contrast specification dialog will show and label all levels of the respective effect on the dialog).

Depending on the type of Effect that you have selected (e.g., a main effect, within-subject effect, interactions, etc.) and the option buttons you have selected in the Enter contrasts separately or together and/or the Contrasts for dependent variables group boxes various contrast specification dialogs will be displayed. See the Specify Contrasts for This Factor, Specify Contrasts, Contrast for Between Group Factors, Enter Contrasts for this Factor, Repeated Measures, Contrasts for Within-Subject Factors, and Contrasts for Dependent Variables dialogs for further details.

Compute. After you specify your contrasts for least squares (via the Contrasts for LS means button, see above), click the Compute button to display three spreadsheets: the Between contrast coefficients spreadsheet, Contrast estimates spreadsheet, and the Univariate or Multivariate test of significance for planned comparisons spreadsheet.

Enter contrasts separately or together. Use the options in the Enter contrasts separately or together group box to specify how you want to enter the contrasts when you click the Contrasts for LS means button (see above). Select the Separately for each factor option button to enter the contrast coefficients for each factor in the current Effect. Select the Together (contrast vector) option button to enter the contrast coefficients for each cell in the current Effect (combination of factor levels for the factors in the current Effect).

Note that the method of computing the results for the planned comparison is actually identical, regardless of how the contrast coefficients were entered, and any contrast specified via the separately method can also be represented via the together method (but not vice versa). Specifically, when Separately for each factor is selected, the Kronecker Product (see theVisual Basic function) of the specified matrices of contrast coefficients for each factor will be applied to the set of least squares means for the respective chosen Effect.

Note: separately for each factor. This method of specifying contrasts is most convenient when you want to explore interaction effects, for example, to test partial interactions within the levels of other factors. Suppose you had a three-way design with factors A, B, and C, each at 2 levels (so the design is a 2x2x2 between group full factorial design), and you found a significant three-way interaction effect. Recall that a three-way interaction effect can be interpreted as a two-way interaction, modified by the level of a third factor. Suppose further that the original hypothesis for the study was that a two-way interaction effect exists at level 1 of C, but no such effect exists at level 2 of factor C. Entering contrast coefficients Separately for each factor, you could enter the following coefficients:

For factor A: 1 -1

For factor B: 1 -1

For factor C: 1 0

The Kronecker product of these vectors shows which least squares means in the design are compared by this hypothesis:

 Levels, Factor C 1 2 Levels, Factor B 1 2 1 2 Levels, Factor A 1 2 1 2 1 2 1 2 Coefficients 1 -1 -1 1 0 0 0 0

Thus, this hypothesis tests the A by B interaction within level 1 of factor C.

Note: together (contrast vectors). This method of specifying contrasts can be used to compare any set of least squares means in the current Effect. In the table shown above, you could specify directly the contrast vector shown in the row labeled Coefficients. You could also compare any set of least squares means within the three-way interaction. For example:

 Levels, Factor C 1 2 Levels, Factor B 1 2 1 2 Levels, Factor A 1 2 1 2 1 2 1 2 Coefficients 1 0 0 -1 0 1 -1 0

This set of coefficients cannot be set up in terms of main effects and interactions of factors (i.e., via option button Separately for each factor), and could only be specified via the Together option button.

Contrasts for dependent variables. Use the options in the Contrasts for dependent variables group box to determine if you are able to specify a set of contrast matrices for the dependent measures after you click the Contrasts for LS means button (see above). Select the Yes option button if you want to specify a set of contrast matrices for the dependent measures. Select the No option button, if you do not want to. Note that these options are only available if the current design involves multiple dependent variables, or, in case of within subject (repeated measures) designs, multiple dependent measures.

Multivariate tests. Use the options in the Multivariate tests group box to select the specific multivariate tests statistics that are to be reported in the respective results spreadsheets. For a description of the different multivariate tests statistics, refer to the Multivariate designs topic in the 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).