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I want to understand if a classroom's quality score differs for classrooms with varying percentages of special ed students.

Percentage of special ed students is a categorical variable, grouped into the following categories: Less than 5%, 5-9%, 10-14%, 15-24%, and 25%+

Classroom quality score is a continuous variable, on a scale of 1 to 7. These data are not normally distributed, so we have generally used non-parametric tests when using these data.

What test would make sense here?

Thanks!

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    $\begingroup$ Welcome to our site. "Looking at a relationship" is a very different kind of activity, with different goals, than either providing a descriptive statistic such as a correlation coefficient or performing hypothesis tests such as the Kruskall-Wallis test. Please, then, edit your post to resolve the apparent contradiction involved in requesting three different things. $\endgroup$
    – whuber ♦
    Commented Sep 6, 2018 at 17:03

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The Kruskal-Wallis test which is an extension of the Mann-Whitney U test for more than two groups would be a suitable choice of test given the information you have given. It tests the null hypothesis that the groups originate from the same population. It is also non-parametric so there is no distribution assumption. It can be implemented in R by kruskal.test.

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