Hi everyone, I was wondering if runnig a posthoc test regardeless of a significant interaction might make sense. I have prepared a dataset with obviously invented data but which can help to the discussion
les's suppose to have two factors with two levels each, and that we are interested in a possible interaction of the same factor and that we are measuring a unique response variable
Let's suppose we also find significant interaction and therefore we cannot attribute the differences between groups to a single factor but only to their interaction.
Now, would it be legitimate to explore if one or more means are different from the others and therefore running a posthoc test regardeless of the interactions?
Or would it be possible to run separate one way ANOVAs, one for factor A and one for factor B?
If there is an interaction then you can proceed with posthoc tests to better describe where the effect is, but it needs to be controlled for multiple comparisons (Bonferroni, LSD, etc).... what the interaction tells us is that the response to Factor B (response variable) is different between groups (Factor A). I don't quite understand your graph though... all your response variables are under 1.0... but your data is graphed between 18 and 25? What data is used in the graph?
Using your attached png file for example, if Factor A is Sex (1 = male, 2 = female), Factor B is caffeine dose (100 vs 0 mg) and Response Variable is Test Score then we have the following:
Male w/caffeine = 65.3 (mean)
Male w/o caffeine = 60.33
Female w/ caffeine = 26
Female w/o caffeine = 53.7
Depending on the variability of your data, I could realistically see posthoc analyses suggesting that women's test scores decreased with caffeine consumption, while men's scores were unaffected (or even increased) by caffeine consumption (hence the interaction).
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