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 posthoc
tests is provided in the Contrast
analysis and posthoc 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 3level
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 userinterface 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 dropdown 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, withinsubject 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 WithinSubject 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 the STATISTICA
Visual Basic function MatrixKroneckerMultiply) 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 threeway 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 threeway interaction effect. Recall
that a threeway interaction effect can be interpreted as a twoway interaction,
modified by the level of a third factor. Suppose further that the original
hypothesis for the study was that a twoway 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 threeway 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 withinsubject (repeated measures) design with effects that have
more than 2 levels (and hence, multivariate tests for those effects can
be computed).
See also GLM  Index.