Repeated measures ANOVA: Interpreting a significant interaction in SPSS GLM
I have run a repeated measures ANOVA in SPSS using GLM and the results reveal a significant interaction. How can I use GLM to interpret the meaning of the interaction?
Resolving the problem
Before describing how to interpret an interaction, let's review what the presence of an interaction implies. We'll do so in the context of a two-way interaction. A significant two-way interaction means that the effect of one factor depends on the level of another factor, and vice versa. For example, suppose that a researcher is interested in studying the effect of a new medication. To do so, she compares the effects of both the medication and a placebo over time. In this simple model, the finding of a significant Time X Treatment interaction means that the effect of time depends on whether the subject received the new medication or the placebo. Conversely, the interaction also means that the effect of treatment depends on time.
When the initial ANOVA results reveal a significant interaction, follow-up investigation may proceed with the computation of one or more sets of simple effects tests. (Sometimes these sets of follow-up tests are known as tests of simple main effects.) Simple effects tests reveal the degree to which one factor is differentially effective at each level of a second factor.
For example, consider the Time X Treatment interaction introduced in the preceding paragraph. In order to simplify the discussion, let's assume that there were two levels of time, weeks 1 and 2, and two
levels of treatment, placebo and new medication.
One set of simple effects we would probably want to test is the effect of treatment at each time. Let's say we found that the placebo and new medication groups were not significantly different at week 1, but the
new medication group was doing significantly better at week 2. These simple effects tests would support the assertion that the groups were equivalent at the start of the experiment and the new medication resulted in the difference observed at time 2.
The SPSS GLM command syntax for computing the simple main effects of one factor at each level of a second factor is as follows.
/EMMEANS = TABLES(factor1*factor2) COMPARE(factor1)
Consider the hypothetical example, discussed earlier. Let's call the within-subjects effect Time and let's use the eight-letter abbreviation Treatmnt as the name of the between-subjects effect. To run the analysis and get tests for the simple effects of Treatmnt at each level of Time insert the following command syntax into the set of commands generated from the GLM - Repeated Measures dialog box.
/EMMEANS = TABLES(Time*Treatmnt) COMPARE(Treatmnt) ADJ(LSD)
Note that the optional keyword ADJ allows the user to specify anadjustment to the p-values for each set of pairwise comparisons which accompany the tests of simple main effects. The default adjustment is LSD, but users may request Bonferroni (BONF) or Sidak (SIDAK) adjustments.
Note that the EMMEANS subcommand allows specification of simple effects for any type of factors, between or within subjects. Thus if both factors were within-subjects factors (or between-subjects factors) the structure of the EMMEANS subcommand specifications would not change.
Finally, I invite readers who are interested in viewing a fully worked example to run the following command syntax. This brief sample command syntax file reads in a small data set and performs a repeated measures ANOVA with Time and Treatmnt as the within- and between-subjects effects, respectively. Two sets of simple effects tests are produced. The first is the effect of Treatmnt within each level of Time and the second is the effect of Time within each Treatmnt.
*The command syntax begins below.
data list free
/ treatmnt week1 week2 .
0 1 2
0 1 1
0 2 2
0 2 3
1 1 3
1 1 3
1 2 4
1 2 5
end data .
week1 week2 BY treatmnt
/WSFACTOR = time 2 Polynomial
/MEASURE = response
/METHOD = SSTYPE(3)
/PLOT = PROFILE( time*treatmnt )
/PLOT = PROFILE( treatmnt*time)
/EMMEANS = TABLES(treatmnt*time) COMPARE(treatmnt) ADJ(LSD)
/EMMEANS = TABLES(treatmnt*time) COMPARE(time) ADJ(LSD)
/CRITERIA = ALPHA(.05)
/WSDESIGN = time
/DESIGN = treatmnt.