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How do I test for differences between two groups on three dependent variables? Is that an ANOVA or multiple t-tests with an adjusted alpha level?

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You need to look into the Multivariate-ANOVA (called MANOVA). I'm not sure about good internet-based resources; the Wikipedia page is here, and the entry in StatSoft's online textbook is here, but neither seem great. For a 'real' textbook that is more or less math-free, Tabachnick & Fidell is the most popular. If you use SPSS, SAS, or Stata, the excellent UCLA statistics help site has some quick tutorials; they can be found here.

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