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?