I am analyzing school data for a district that is mostly white but with native, black, and multiracial minorities. I'm seeking to determine whether there are statistically significant differences between these students on their ACT scores, but the data is not normal and variances are heterogeneous. I've read that the Kruskall-Wallis is not robust to heterogeneity in variances and that Welsh's ANOVA is not robust unless the data is normal. So what test do I use to analyze the data? I'm not finding a clear answer in other forums or statistics texts I've perused. Recommendations will be greatly appreciated.
Hi,
as far as I know, when you have non-normally distributed data and you want to test for differences between groups, you should go for the Kruskal-Wallis H test, even if you have heterogeneity of variances. The fact that the distributions in your groups do not have the same shape only means that you cannot make inferences about the difference in medians between your groups, but you can proceed and run post-hoc tests (Dunn's Multiple Comparison Test) to study the differences between mean ranks.
You can find more about the assumptions and the interpretation of this test here:
http://www.real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/
https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-statistics.php
You could also consider searching for outliers to eliminate, in order to normalize the distributions and possibly use ANOVA, which has more statistical power.
Good luck with your project.
Hi,
as far as I know, when you have non-normally distributed data and you want to test for differences between groups, you should go for the Kruskal-Wallis H test, even if you have heterogeneity of variances. The fact that the distributions in your groups do not have the same shape only means that you cannot make inferences about the difference in medians between your groups, but you can proceed and run post-hoc tests (Dunn's Multiple Comparison Test) to study the differences between mean ranks.
You can find more about the assumptions and the interpretation of this test here:
http://www.real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/
https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-statistics.php
You could also consider searching for outliers to eliminate, in order to normalize the distributions and possibly use ANOVA, which has more statistical power.
Good luck with your project.
I agree with Emanuele Cassioli , Thanks for this important answer.
Perhaps, use could get use of some of these tips:
https://stats.stackexchange.com/questions/91872/alternatives-to-one-way-anova-for-heteroskedastic-data/91881#91881
Or you could just co,pare medians for multiple groups via median test:
https://www.isixsigma.com/tools-templates/hypothesis-testing/understanding-uses-moods-median-test/
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