Proper analysis for group differences in proportion scores

Hello all,

I am running analyses looking at group differences in the proportion of time kids were distressed in a task.

I have a task that has been broken up in to 10s time slices and kids receive a score of 1 in each slice they evince distress. To create my outcome variable, I am dividing the number of slices in which they received a 1 by the total number of slices. This is necessary because the total number of slices varies by kid, so I can't just look at the total number of 1s they received overall.

This gives me a "distress proportion" score, that ranges from 0.0 - 1.0.

My question: I had planned to run an ANOVA on this to examine group differences (3 groups). It was non-normal (many 0.0s) and has many outliers (according to SPSS, because distress was infrequent, kids who were very distressed are "outliers") so I switched from ANOVA to Kruskall Wallis and found that the distributions were the same and that the median scores did not significantly differ from each other.

My question: was this the proper analysis? I am not interested in distress v. non distress, so logistic regression doesn't work, which is what I've come across most in searching for an answer to this. I've yet to find a better analysis for non-normal distribution scores, but thought I'd check on here to make sure!

Thank you, all! :)