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This is for a psychology design.

I have 2 groups, all members of both groups are to be administered all tests.

I think that I want to do a 3x2 factorial ANOVA on the DIFFERENCES in the means of my control vs 'autism' groups. My conceptualization of the design

There are 2 IV's, one with 3 levels (Memory type), and one with 2 levels (Complexity).

My research goal is to determine that: - There is no interaction between the IV's - There is no main effect of memory type (the tests are standardized and I can use standardized scores to avoid issues with the scales' natures) - To establish that there IS a main effect of complexity.

Now, I want to determine these criteria for an autistic population. Specifically, I want to determine that autistic individuals do not vary in performance in terms of memory type, but in fact differ only in terms of memory complexity, without any interaction effects.

I think that I could run this without the Control group, but I also want to simultaneously determine that they perform similar to control on the simple level of complexity, that they do not vary from control depending on the type of memory assessment, and that the main difference is on the complex memory tests. (So basically, t-tests within simple, and across memory types would be non-significant, or with negligible effect sizes, but t-tests within the complex conditions would be significant.)

My questions are: - Can this be done? - Does this have a name? - What tests do I use to analyze this? (Can I just create a new 'difference scores' or 'mean difference' variable [with a pooled SD?] and use one or the other in a basic factorial ANOVA?)

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From what I see, your design actually has three IVs:

  1. Memory Type (V, P, and E, within-subject variable)
  2. Task Complexity (Simple or Complex, between-subject variable)
  3. Participant Type (Control or Autism, between-subject variable)

Thus, I would recommend that you run a 3x2x2 mixed ANOVA, which would enable you to test your hypotheses about the main/interactive effects of Memory Type and Task Complexity, while comparing these effects between your two samples of control v. individuals with autism. Any significant interactions you could follow up by testing simple main effects.

This approach would just use individuals' test scores. In other words, no use of difference scores is needed. Also note that the use of difference scores in analyses--in the way you have proposed at least--is generally discouraged. Peter, Churchhill, & Brown (1993) is a bit of an old reference, but it's a nice review of the issue that holds up pretty well.

References

Peter, J. P., Churchill, G. A., & Brown, T. J. (1993). Caution in the use of difference scores in consumer research. Journal of Consumer Research, 19, 655-662.

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