How to analyze parents' talk when codes are not normal in a mixed design?

This is a but tricky to explain, so I will do my best.

I am trying to analyze coded talk by parents for three different categories of objects. I coded parents labeling of the three different types of objects either as standard labeling, uncertain labeling or labeling of an absent object. The data are the proportion of each type of labels for all labels for that object type. So one column of data is the proportion of standard labeling for object category #1 out of all labeling for category #1.

My main question of interest is how labeling differs depending on object type. This is a within subjects design since all participants had a mixture of the three types of objects.

However, though each family had a mix of the three types of objects I varied the specific objects families have to control for more specific object effects. That varied across participants. I called this different groups "object sets." So this is actually a mixed design.

My plan was to do an repeated measures ANOVA on each type of labeling separately to compare across objects and across object sets (since putting all codes together didn't seem right since they are proportion and so depend on each other). However, the data is not normal. I have tried transformations and removing outliers and none of that helps. I suppose my hypotheses assume it to not by normal. I assume there to be a lot of zeroes for some codes for some objects.

I wondered where to do next. I don't know of a non-parametric version of the mixed ANOVA. Are there other ideas?

Thank you so much for your help!! I am sure I will need to clarify this further, so please do ask me if something is unclear.


TS Contributor
If your sample size is large, ANOVA usually is quite
robust against non-normality. How large is your sample?

With kind regards