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If I am trying to do a two-way ANOVA for a dependent variable with 2 interactions each two factors.

Speed ~ Treatment ( yes or no) * sex (M or F) 

However, my data is not normally distributed which non-parametric test should I do?

  • If you're hoping to find an effect, you really *want* the data not to be Normally distributed! (That is, they ought to clearly reflect their relationships with the explanatory factors.) What matters for computing p-values is the distribution of the *residuals.* Maybe, then, you don't need an alternative to ANOVA. – whuber Feb 24 '22 at 21:23

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