# Significant factor in 2-way repeated ANOVA becomes not significant in 3-way repeated ANOVA?

My research design is 2(Ear) x 3(Factor A) x 3(Factor B) with repeated measures on all factors. For 2 way-repeated ANOVA, I used laterality index (normal distribution, calculated from % of responses from both ears) as dependent variable (DV) while Factor A and B are independent variables (IV). I obtained significant main and interaction effects.

However, when I tried 3-way repeated ANOVA using % scores from each ear as DV, factor B becomes not significant. I'm not sure what could be wrong?

1. Is it because the % scores in one of the conditions were not normally distributed with p=0.041? The box plot looks alright but histogram has an inverted bell curve shape. I've tried log, square root and 1/x transformation but didn't work. Is it acceptable to run ANOVA since there's no equivalent non-parametric test in SPSS?

2. Could it be the way I run the test in SPSS? I followed exactly the same way as I did for 2-way repeated ANOVA because I couldn't find any examples similar to my research design. Most examples have a third between subject factor while mine are all within subject factors.

I'd really appreciate any help or suggestions because I'm confused and new with statistics. Many thanks.

Kaye

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Nothing need be wrong. There is no reason this can't happen. A 3 way ANOVA asks a different question than a 2 way ANOVA, and when you ask a different question, you shouldn't be surprised at a different answer. In particular, adding a factor controls for that factor. –  Peter Flom Sep 4 '12 at 0:23
You might use the search feature to look around a bit. Questions about the significance of different factors & changes in the significance as factors are added, etc, have been pretty common. –  gung Sep 4 '12 at 2:32
@PeterFlom I'm just puzzled because the DVs in both analysis are related, as in the laterality index came from the % scores. If adding a factor changes everything, then my concern is if it's valid to run the 3-way ANOVA in the first place considering the lack of normality? perhaps I could justify by saying the p is near to 0.05? –  Kaye Sep 4 '12 at 15:16
@gung. Thanks for your suggestion. I've done a bit of poking around but haven't found what I need. –  Kaye Sep 4 '12 at 15:18
Don't think in terms of p values, think in terms of effect size. Did it change much? But, again, you are asking a different question. –  Peter Flom Sep 4 '12 at 21:46