Specifying Within-Subjects (Repeated Measures) Univariate and Multivariate Designs - Between-Within Univariate (ANOVA) and Multivariate (MANOVA) Designs

In experimental research, it is very common to administer different treatments to different groups of subjects (between-groups factors), and then to monitor a dependent variable over time or under different circumstances (within-subjects or repeated measures factor). This type of design combines repeated measures factors and between-groups factors into a single design.

For example, a researcher may infect laboratory animals with two types of viruses (between-groups factor 1 with 2 levels) and then administer two different drugs (between-groups factor 2 with 2 levels). Then the researcher may monitor the animals' activity levels 1 day after the drugs were administered, after 2 days, and after 3 days (repeated measures factor Time with 3 levels). The resulting design is 2 x 2 x 3 ANOVA design, where the third factor is a repeated measures factor.

To specify this design, you must separately specify the between-groups part of the design and the within-subjects part of the design. For example, imagine that data were entered into a data file as follows:

	Variable
	1	2	3	4	5
Case 1	1	1	23	34	32
Case 2	1	2	40	43	45
Case 3	2	2	23	24	23
Case 4	2	1	54	34	54
Case 5	1	2	23	24	25
Case 6	2	1	34	23	34
-	-	-	-	-	-
-	-	-	-	-	-
-	-	-	-	-	-

The first two variables (columns) are the independent or grouping variables that uniquely identify to which experimental group the respective case (laboratory animal) "belongs" (to simplify matters, integer codes rather than text labels are shown here). Variables 3 to 5 contain the dependent variables, i.e., the activity measures that were obtained after one, two, and three days. Thus, variable 3 contains the data for the first level of the repeated measures factor, variable 4 contains the data for the second level of the repeated measures factor, and variable 5 contains the data for the third level of the repeated measures factor.

In order to specify the 2 x 2 x 3 between-within design, first select Repeated measures ANOVA as the Type of analysis and Quick specs dialog as the Specification method on the General ANOVA/MANOVA Startup Panel - Quick tab or GLM Startup Panel Quick tab. Next, click the OK button on the General ANOVA/MANOVA (Startup Panel) or GLM (Startup Panel). Then, on the ANOVA/MANOVA Quick Specs - Quick tab or GLM Quick Specs Dialog - Quick tab, click the Variables button and specify Variables 1 and 2 in the Categorical predictors (factors) field, and Variables 3, 4, and 5 in the Dependent variables list field. Next, select the categorical predictors variables codes for the independent variables via the Factor codes button; in this example, the codes 1 and 2 were used to specify with which virus the respective animal had been infected (categorical variable 1), and with which drug it had been treated (categorical variable 2).

The between-groups part of the ANOVA design is now completely specified. Next specify the Repeated measures (within ss) part of the design, that is, click the Within effects button to display the ANOVA Specify Within-Subjects Factor or GLM Specify Within-Subjects Factors dialog and specify one repeated measures factor (you can call it Time) with 3 levels.

In general, you can specify between-within ANOVA designs of any complexity by separately specifying the between-groups part of the design and the within-subjects part of the design. Note that if you have multiple within-subjects (repeated measures) factors, you will need to use the GLM module.

On the ANOVA Results or GLM Results dialog you can select specific effects (options Univariate results and Univ. tests on the GLM and ANOVA Results - Summary tab) and Planned comparisons (option Contrasts for LS means on the GLM and ANOVA Results - Comps tab) in exactly the same manner as in multi-way between-groups designs or in within-subjects designs. Between-groups factors and within-subjects (repeated measures) factors are listed consecutively.