In my design, I have 3 binary items for each condition (4 conditions total) meant to measure the same thing. All participants were in all conditions (repeated measures, 12 scores each).
I made a composite score for each participants for each condition (yes, I know, not advisable but this is the way I am doing it so work with me, please). I coded the items such that 0= small and 1= large. I then interpreted the composite score to mean the likelihood of choosing the large item. (With me so far?)
I ran a rANOVA using my 2 IV's as within subjects factors.
The output says that there are 2 main effects and an interaction (I can't post the image but I am basing this off of the table called "multivariate tests" with Wilks' Lambda, which is p<0.05 (as are all the other tests there).
However, when I look at some of the levels (either in the main effects or in the interaction), I see that the confidence interval contains 0.5 (which to me means that we the level does not provide us any more info about how likely it is to choose "large.")
Does the significance in the table I have shown here mean that the effects do exist?
Should I interpret the effect by looking at the individual levels? (i.e. <0.5 means more likely to choose large) and see if the confidence intervals overlap?
What does it mean if the table says a main effect with 2 levels is significant but one of the 2 levels has a confidence interval that contains 0.5?
Thanks so much!