I've described a typical design for my experiments [in this question][1]. 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][2] 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][3]? Is it OK to transform data using different statistics within a paper? [1]: https://stats.stackexchange.com/questions/11887/what-experimental-design-is-this [2]: https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-21/issue-4/Transformations-Related-to-the-Angular-and-the-Square-Root/10.1214/aoms/1177729756.full [3]: https://stats.stackexchange.com/questions/1601/what-other-normalizing-transformations-are-commonly-used-beyond-the-common-ones