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I am running Kruskal-Wallis tests in SPSS to compare answers to Likert items among 3 (variable 1) and 4 (variable 2) groups. I am not running ANOVAs because assumptions of normality and homoscedasticity are often violated, and because my data is ordinal (totally disagree, disagree, somewhat disagree etc.). Sample sizes are around 50 for variable 1, but range from 17 to 90 for variable 2. My questions are:

  • Is Kruskal-Wallis the appropriate test?
  • Very often, the Kruskal Wallis test gives me a significant result (p < .05) but when I look at the pairwise comparisons (in the SPSS model viewer), the adjusted p-values are not significant (the non-adjusted p values are significant). I'm really confused about how to interpret and report this. Should I use the non-adjusted p values? Or should I use a different post-hoc test (available in SPSS)?

Thank you!

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It is very common to use the Kruskal-Wallis test to test for association between an ordinal and unordered categorical variable, so it might be an appropriate choice in your specific setting.

Global tests are generally more powerful than adjusted pairwise tests (otherwise, they probably would not be used at all). Consequently, it is not worrysome if no pairwise test is significant while the global test is. Just report it like this. It would be ridiculous to report uncorrected p values just because the corrected ones are not significant.

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