I've described my typical design with data provided as an example in this question. So, I have 5 dependent groups. The data are in percentages. And I have some very basic questions:

• Is Freeman–Tukey's transformation appropriate (and the most powerful) for percentages? What formula should I use (the one at the bottom of the page or that on the next one: $y=\sqrt{x}+\sqrt{x+1}$)?
• Is it allowed to transform percentages with Box–Cox transformation?
• Is it OK to transform data with different statistics (or use different statistical approaches in general) in similar situations in the same thesis/article?

Thank you in advance