# How can I transform my data to achieve homogeneity for a factorial mixed ANOVA?

I'm fairly new to statistics (I'm doing it for my bachelor thesis). I want to do a factorial mixed ANOVA in Jamovi, but not all of my data is homogenous (15 out of 126 measurements are not homogenous). I am able to transform the data with python, but I couldn't find any library that provides a factorial mixed ANOVA.

Experiment design: Subjects dodge virtual objects in virtual reality. I have two groups each with 15 participants. The virtual rotation for group A is amplified (e.g. they turn their head 10° in real space but 15° in virtual space). Group B has no rotation amplification. The groups are the between-subject factor. I measure their greatest turn angle in virtual space (dependent variable), while they try to dodge an incoming object. The 4 independent within-subject factors are form (3 levels), size (2 levels), speed (3 levels) and incoming_angle(7 levels).

I want to find out, if there is a difference in virtual turn angle for each group. I also want to find out, if the greater levels of each factor are causing greater turn angles.

I think because of the experiment design, I really can only go with factorial mixed ANOVA. But none of the assumptions for that method are met (normality of residuals, sphericity, homogeneity of variances).

I tried various transformations (absolute values, raising to higher powers, reciprocal, logarithmic, Box-Cox), but they all fail the assumptions.

My data looks like this:

• Maybe you could tell us what your data represents, and what is your ultimate goal with the analysis? Feb 19 at 20:10
• I'm having trouble determining what your question is. ... If you can run your analysis in Jamovi, that should be a fine software choice. ... The one residual plot you present doesn't look too bad. Do you have a similar plot of residuals vs. predicted values ? ... What do you mean when you say there are 126 tests (for homogeneity ?) ? Feb 19 at 20:19
• @SalMangiafico Yes, the 4 within-subjects factors have 2x3x3x7 levels which make up for 126 measurements per subject. I have 30 subjects, 15 in each group. I think I need to test the homogeneity of variance for all of the 126 measurements, but please correct me if Im wrong. Feb 20 at 21:20
• Look at a plot of residuals vs. predicted values. (And please add to your post.) ... In general, running hypothesis tests (for normality or homogeneity) to determine if a model is appropriate isn't very helpful. ... In this case, I'm not sure how you are running these tests. Feb 20 at 21:45
• @kjetilbhalvorsen Thanks for your reply! I updated the description. Feb 20 at 21:46