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Data set has 2 dependent variables and 1 independent variable with 3 groups. Normality assumption of MANOVA says that variables has to be normally distributed within the groups. My data set has 30 cases (10 in each group) so I took a look at Shapiro-Wilk test statistics. It says that 1st variable is normally distributed within all 3 groups, but the 2nd variable is normally distributed in only 2 groups. At the other side, only one histogram shows normality. Do I have to transform variables so that histograms shows normality or I can trust Shapiro-Wilk statistics? I have in mind that histograms maybe don't look really nice because of the sample size (10 by group) and I am not sure if transformations wold change anything (I tried some transformations and it still looked bad). If I can trust Shapiro-Wilk test statistics, do I need to transform 2nd variable because test is significant for the 3rd group of the 2nd variable?

user23709
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  • When there are only ten observations in each group a test of normality won't be really powerful against most alternatives, and a normal probability plot would be more informative that a histogram. There's also the question of bivariate normality, and testing for that is something I don't know much about. However, this question would probably get better answers at stats.stackexchange.com than here. ${}\qquad{}$ – Michael Hardy Apr 18 '15 at 15:57
  • Thanks! I'll post it there. I have this data set as an example now, but this was actually a question for general case. Thanks anyway! :) – user23709 Apr 18 '15 at 16:00

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