GLM, GRM, and ANOVA Results - Comps Tab
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.
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.
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: 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.
See also GLM - Index.