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I am making a pairwise comparison using Dunn's post hoc test with Bonferroni correction. However, I am a bit confused on the interpretation of the adjusted significance on SPSS. I am making 10 pairwise comparisons, and thus my assumption is that the adjusted significance will be 0.005 (0.05/10). However, my question is when seeing the pairwise comparisons table on SPSS do I have to take this calculation that I made into consideration when looking at the adjusted significance? This is an example:

Sample 1 - Sample 2 Sig. Adj. Sig.
1-4 0.000 0.008
1-7 0.000 0.005
4-7 0.895 1.000

According to the table above, my understanding is that observations 1-4 and 4-7 are not significant different as the adj. sig is higher than 0.005 (what I calculated)? Am I wrong? Thank you in advance.

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"Adj. sig" looks like "q values," where instead of adjusting the rejection criterion $\alpha$ by dividing it by the number of comparisons, they multiple the p value by the number of comparisons. (You get incoherent gibberish when doing so, because you end up with "probabilities" greater than 1, but since you would be very far from rejecting with the unadjusted p values anyway, this is tolerated in practice.)

To recap: compare unadjusted p values to $\frac{\alpha}{10}$. This will give the same rejection decisions as comparing adjusted p values of $\alpha$.

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  • $\begingroup$ Hi, thank you for this. I have compared the unadjusted p values and the adjusted p values of alpha - but according to my example above- the unadjusted p value has 2 observations that are significant ( p<0.05), but then when compared with the adjusted significance there is only one observation that is significant as my calculation of Bonferroni indicates me that significance levels over 0.005 are not significant.... This is where it gets me so confused ? Shall I only take into consideration the adjusted significance ? I am doing this to help me select the best categories to predict my problem. $\endgroup$
    – Louise
    Oct 10, 2021 at 14:31
  • $\begingroup$ @Louise Two unadjusted p values are less that $\frac{0.05}{10} = 0.005$. And two of the adjusted p values from the same two tests are less than $0.05$. $\endgroup$
    – Alexis
    Oct 10, 2021 at 15:21

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