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I've described a typical design for my experiments in this question. Well, 1-way RM ANOVA assumes a Gaussian distributed vector.
I try $y=\arcsin{\sqrt{x}}$. But for some data it works, for some doesn't... So the next step is to find the most powerful/general statistics. Freeman — Tukey's transformation with $y=\sqrt{x}+\sqrt{x+1}$ is the most powerful and seems to be appropriate in almost all my cases but again it doesn't give normal data sometimes.
What should I do this case? Box — Cox transformation?
Is it OK to transform data using different statistics within 1 thesis/article?

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Do you mean the arcsin(square root(x))? If not, that could be why it didn't work... –  Aaron Jun 21 '11 at 1:57
@Aaron: thank you for the correction. –  stan Jun 22 '11 at 3:24
What do you mean by "But for some data it doesn't work"? In what sense did that transformation not work? Also, what do you mean by "the most powerful statistics"? Powerful in what sense? –  Wolfgang Oct 27 '11 at 1:31
@Wolfgang: thanks for your questions. Let say I have 2 cell types. For cell.type_1 the FT works i.e. it transforms to normality, for the other cell type it doesn't. I meant "powerful" as synonym for "powerful" (i.e. capable to transform "any" to normality) (Correct me please if I'm wrong?). Here I was recommended to use $\beta$ distribution but I can't understand what do I have to do in this case... :( –  stan Oct 27 '11 at 3:23
I see. What you really should be checking is the normality of the residuals after fitting the model, not the normality of the dependent variable itself. See, for example this question, which is quite related. –  Wolfgang Oct 31 '11 at 6:33
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