Hi
I ran a mixed between-subjects within-subjects ANCOVA in SPSS. I have one between-subject variable (four experimental groups) and one within-subject variable (time1 and time2) and pre-test scores as covariate.
Now I have a significant between-subjects*within subjects interaction effect. Then I checked multiple comparisons table in which for each group, time1 score is compared with time 2 score (I used spss syntax to ask for this).
Now my question is that what a significant between-subject*within-subject interaction means:
1) for some or all between-subject groups (four experimental groups in my study), there is a difference in scores between time1 and time2?
or
2)change of score from time 1 to time 2 is different for at least one between-subject group? (this means that interaction effect is used to show whether increase or decrease in scores from time 1 to time 2 is similar or different among groups).
I think that the second interpretation is more accurate. However, I don't know how I can check whether the change of score from time1 to time2 between different groups is statistically significant.
Thanks.
Only (2) is a valid interpretation. (1) might also happen to be true, but it is not necessarily true (i.e., it is possible that the pre-post difference is different between groups but none of the pre-post differences is significantly different from 0; maybe one group is -1 and another group is 1, and those are significantly different from each other but not from 0). What the interaction shows is (2), not (1).
The easiest way to check the second interpretation would be to calculate the pairwise difference (time2 minus time1) for each group and compare each pair of groups to see which groups are different from which. That would entail performing 12 comparisons, so you will need to correct for multiple comparisons accordingly.
Adding to what Stephen said, see the example in the Technote linked below for info on how to obtain simple main effects via the EMMEANS subcommand with COMPARE key word.
https://www-01.ibm.com/support/docview.wss?uid=swg21475404
HTH.
Dear Stephen Politzer-Ahles
Thanks for your answer.
I still dont know how to examine the differences in change of scores from time 1 to time 2 for each pair of groups.
Attached you can find my pairwise comparisons table and my plot.
AFAIK, SPSS has no easy, straightforward way to get the interaction contrasts Stephen described. I think you have to resort to the sorts of things you'll see in this article by Howell & Lacroix:
http://www.tqmp.org/RegularArticles/vol08-1/p001/p001.pdf
As a quick & dirty work-around, you could use TEMPORARY followed by SELECT IF to run the analysis on only two groups at a time. But by doing this, you would end up with error terms based only on the two groups used for a given model. So it would not be ideal.
I am a long-time SPSS user who has started using Stata a lot more in the last few years. For interaction contrasts of this type, Stata makes life much easier IMO. You can see some examples on this UCLA web-page:
https://stats.idre.ucla.edu/stata/faq/how-can-i-explore-interactions-using-the-contrast-command-stata-12/
I am not a regular useR, but suspect R has similar capabilities.
HTH.
Dear Dr Khajavy
I think running MANOVA possibly best addresses your research questions as you have one independent variable with 4 values and 2 dependent continuous variables. ANCOVA is commonly used when you want to control the pre-test effect as an independent variable.
Best regards
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