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## Does JMP use Bonferroni correction for ANOVA and Krusal-Wallis?

Hi, I am trying to analyze a set of data with ANOVA and a separate set of data with a Kruskal-Wallis test using JMP. For my first set of data, I used an ANOVA and followed up with Tukey's HSD All-Pairs for post-hoc comparisons. Are the p-values that Tukey report lists as significant corrected values? Or do I need to apply the correction myself? Additionally, for a second test (Kruskal-Wallis), are the p-values compared with an adjusted significance level, or do I need to apply my own Bonferroni correction? Thanks!

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Staff

## Re: Does JMP use Bonferroni correction for ANOVA and Krusal-Wallis?

Hi Opnightfall1771,

The Tukey HSD test returns p-values that have been corrected for the number of independent pair-wise comparisons that are possible given the number of factor levels -- so, those p-values may be interpreted directly and require no further corrections.

The Kruskal-Wallis test you mentioned is the generalization of the Wilcoxon (or Mann-Whitney test) to factors with more than 2 levels, however if you are performing pair-wise tests the analyses are just Wilcoxon tests. The results from selecting (in Fit Y by X) Nonparametric > Nonparametric Multiple Comparisons > Wilcoxon Each Pair are not corrected for multiple comparisons. This is simply the nonparametric version of the "Each Pair Student’s t" option. You could use Bonferroni corrections with those p-values, however this will quickly become overly conservative with many factor levels and you would be better off using a more efficient analysis, such as the Steel-Dwass All Pairs (available under Nonparametric Multiple Comparisons), which is the nonparametric equivalent of the Tukey HSD. The p-values returned in that analysis are corrected p-values, just like the p-values generated from running a Tukey HSD.

I hope this helps!

Julian

3 REPLIES 3
Staff

## Re: Does JMP use Bonferroni correction for ANOVA and Krusal-Wallis?

Hi Opnightfall1771,

The Tukey HSD test returns p-values that have been corrected for the number of independent pair-wise comparisons that are possible given the number of factor levels -- so, those p-values may be interpreted directly and require no further corrections.

The Kruskal-Wallis test you mentioned is the generalization of the Wilcoxon (or Mann-Whitney test) to factors with more than 2 levels, however if you are performing pair-wise tests the analyses are just Wilcoxon tests. The results from selecting (in Fit Y by X) Nonparametric > Nonparametric Multiple Comparisons > Wilcoxon Each Pair are not corrected for multiple comparisons. This is simply the nonparametric version of the "Each Pair Student’s t" option. You could use Bonferroni corrections with those p-values, however this will quickly become overly conservative with many factor levels and you would be better off using a more efficient analysis, such as the Steel-Dwass All Pairs (available under Nonparametric Multiple Comparisons), which is the nonparametric equivalent of the Tukey HSD. The p-values returned in that analysis are corrected p-values, just like the p-values generated from running a Tukey HSD.

I hope this helps!

Julian

Community Trekker

## Re: Does JMP use Bonferroni correction for ANOVA and Krusal-Wallis?

Julian,

Thank you so much for the detailed response! This is exactly what I was hoping to learn. Very helpful!

Staff

You're welcome!

Julian