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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?

I have this small data set at the moment, but I am interested in the answer for general case. Thanks!

user23709
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  • This will probably be hard to answer in its present state. Can you say more about your data? What are they? Can you paste the histograms or other relevant information in? Also, it may help you to read this classic CV thread: [Is normality testing 'essentially useless'?](http://stats.stackexchange.com/q/2492/7290) – gung - Reinstate Monica Apr 18 '15 at 16:16
  • Description of the data is given in the folloeing link, page 587. https://hoangftu.files.wordpress.com/2014/03/andy-field-discovering-statistics-using-spss-third-edition-2009.pdf SPSS Output is given at this link file:///C:/Users/Goran/Desktop/MVA/MANOVA.htm – user23709 Apr 18 '15 at 16:36
  • In fact, the assumption is about multivariate normality which can't be conducted in SPSS and so the author suggests to check univariate normality which I had done. – user23709 Apr 18 '15 at 17:03

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