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I have $2\times 3$ repeated measures design.

  • 2 conditions(a and b)
  • 3 intensities (low, medium and high).

I am concerned only with the a to b differences at the corresponding intensity. For example I would like to compare:

  • A low and b low
  • A medium and b medium
  • A high and b high.

I am not concerned with comparing A low to A medium to A high as physiologically we know that they are different and it does not answer my research question. I don't care about how the 2 variables interact, but I may be wrong. My inclination is to say the paired T -tests are fine as

Should I perform 3 paired t-tests for the comparisons of interest or a $2\times3$ Repeated measures ANOVA?

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A general strategy is to perform the 2 by 3 repeated measures ANOVA. If you get an interaction effect, then you can go on to perform an analysis of simple effects. An analysis of simple effects involves examining an effect of one factor (e.g., condition) at each level of another factor (e.g., intensity). Thus, if you have an interaction you would be performing both repeated measures ANOVA and the set of paired-samples t-tests. If you don't get an interaction, then the main effect of the focal factor (e.g., condition) would provide a parsimonious hypothesis test.

There are several benefits to this approach. If there are no interaction effects, then main effects provide a parsimonious description of the data. If you are not especially interested in the main effect of intensity,then you don't have to spend much time discussing it. If there is an interaction effect, then you can go on to explore that using analysis of simple effects.

Note also, that another approach is to explicitly model the nature of the interaction. This is particularly interesting where you have a few more levels to intensity. For example, you might posit that there is a linear effect of intensity, and that there is an interaction effect between condition and a linear effect of intensity. Or you could examine an interaction between condition and some non-linear effect of intensity. However, with only three levels of condition, there isn't a lot of information for making such distinctions.

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  • $\begingroup$ Thanks so much for the response. The reason that i asked is that for a few variables there is not a significant interaction term, but if i perform a paired t test the values are highly significant. $\endgroup$ – user28327 Jul 24 '13 at 23:50
  • $\begingroup$ The main effect of condition is then presumably sufficient to answer your research question. $\endgroup$ – Jeromy Anglim Jul 24 '13 at 23:51
  • $\begingroup$ Thanks Jeromy, I suppose the 2x3 it is then and not the paired T test, despite, not being interested in comparing intensity $\endgroup$ – user28327 Jul 25 '13 at 0:03
  • $\begingroup$ The 2 x 3 plot (intensity on x, dv on y, separate lines for condition) of the means should also tell most of the story with the sig tests chipping in to rule out chance as an explanation. $\endgroup$ – Jeromy Anglim Jul 25 '13 at 0:05
  • $\begingroup$ Someone also mentioned that I could perform planned contrasts instead to analyse this data. Do you have any insight into this? $\endgroup$ – user28327 Jul 25 '13 at 0:09

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