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Hello,

I am about to do a multigroup analysis as the MICOM analysis confirmed that the data is appropriate for the analysis.
However, I read about the Bonferroni correction in Advanced issues in partial least squares structural equation modeling.

How do I deal with the Bonferroni correction when doing a multigroup analysis between 4 segments?

I am very much looking forward to your help.

Kind regards,
Maria

When you do pairwise group comparisons with 4 groups you have in total 6 comparisons (i.e., 1-2, 1-3, 1-4, 2-3, 2-4, 3-4).

According to Bonferroni you need to achieve a p-value lower than alpha/n, with n being the number of comparisons. In your case (with 6 comparisons), you would need a p-value lower than 0.05/6=0.00833 for an alpha of 0.05.

Bonferroni is usually the most conservative correction method. It thereby avoids type I errors (false positives), but might inflate type II errors (false negatives). But it is also the easiest method to apply.

Thanks for your reply, I really appriciate your comments. However, I might be a bit slow (I am very new to PLS), because I thougt that I should do a multigroup analysis as follows (if four categories):

Compare group 1 with group 2 (p value should be <0,05 or >0,95 if there are significant differences)
Compare group 1 with group 3 (p value should be <0,05 or >0,95 if there are significant differences)
Compare group 1 with group 4 (p value should be <0,05 or >0,95 if there are significant differences)
Compare group 2 with group 3 (p value should be <0,05 or >0,95 if there are significant differences)
Compare group 2 with group 4 (p value should be <0,05 or >0,95 if there are significant differences)
Compare group 3 with group 4 (p value should be <0,05 or >0,95 if there are significant differences)

Have I misunderstood?

Maria

This is not a PLS-specific but general concern. Please search for articles, books, and webpages that address the multiple testing issues. In multiple testing situations, we need to adjust the accepted probability of error level. When using the Bonferroni correction to account for 6 comparisons, the probability of error of 5% changes into 0.83%. In accordance, you need to adjust the considered probability levels (e.g., <0.0083 and >0.9917).

Best
CR

Thanks a lot, this clarified my understanding:)