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Kolmogorov and Levene

I check Kolmogorov for all data and are >0.05 after for repeated measures anova, for Levene test, 3 of my 4 variables are <0.001. Should I change for non parametric anova?


  • I dont know if the solution will be non parametric or I can do parametric anova?

  • I believe you've already discussed this question and gotten some answers in other threads and forums.


  • I haven't looked at those but I would say: inspect the data for outliers, consider transformations, and assess whether the violation is large enough to matter. Perhaps the bootstrap methodology could be of assistance as well.



  • Yes I check outliers and transformation. Nothing run correctly. My question is if kolgomorv show normality and levene get <0.001 is required to do non parametric statistic?

  • gvt. Again . . .

    Just because the data/residuals are significantly non-normal and the variances are significantly unequal doesn't necessarily mean the violations are large enough to matter. Some judgment is required to make those determinations. It's not unusual to see people report that their analyses violate one or more assumptions while they nevertheless argue that the results are still meaningful because the violations aren't too severe.

    If you're dealing with the kind of data-set you've talked about previously--multiple and possibly interacting factors, with some repeated--measures and some non-repeated-measures factors--there's no standard, widely-accepted 'non-parametric' test for that.

    Alternatively, if you want to deal with just a single, repeated-measures factor there's Friedman's test. However, it needs to be kept in mind that, as a rank-based measure, Friedman's test can tell you only whether the distributions are non-identical. The test can't tell you for example that the medians or means ae significantly different unless you have good reasons to assume that the distributions have identical shapes.

    While there are sophisticated approaches such as permutation testing and bootstrapping, it takes considerable effort and time to figure those out--and even then you'll likely run into disagreements about which is the best specific strategy to use.

    Personally, I would run the repeated-measures ANOVA and acknowledge any assumption-violations. Then to address remaining concerns about the validity of the conclusions, I would follow-up with particular, select, non-parametric tests on the most important pairs of means and/or individual means. I the easiest, most widely acceptable tests would be the Mann-Whitney rank-based test for pairs of non-repeated-measures means, or the Wilcoxon signed rank test for a pair of repeated-measures means or for a single mean.


  • I'd like to add that there are no hard rules in statistics. There are strong recommendations at best :-)


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