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Can I use one way anova for normalized data?

I have trouble knowing the right statistical test that i need to use for my data. I have a group of animals subjected to a task, where each animal is exposed to three or four conditions. The data does not follow a gaussian distribution, so i know that I have to use a non-parametric repeated measure test, that is Friedman test and Dunn's to compare between conditions. Then, i have independent groups of animals tested in the same task. To avoid groups variability I normalized the conditions, setting the control condition (first condition) from each group as 100%. Then, the problem is that if want to compare the change in just one condition between independent groups using the percentages obtained from the normalized data, can I use an one-way anova?
Thanks in Advance