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Clarifications on Dunn-Sidak Approach in multcompare.m

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Hi all,
I am trying to perform the Dunn's test as a non-parametric post hoc multiple comparison test based on the statistical results obtained from the Kruskal-Wallis test.
I want to ask if a 'dunn-sidak' option provided by multcompare.m is actually the Dunn's test. Based on the paper (Dunn, 1964) and other materials, the Dunn's test is known to use z-statistics, but according to the documentation provided here, it seems like 'dunn-sidak' option uses critical values from the t-distribution.
Other software (e.g., R; cf. dunn.test, p.4) explicitly returns z-test statistics from the Dunn test. When I tested with Python, both Python and MATLAB gave equal results for one dataset but different results when conducted using other datasets.
Can anyone clarify whether the Dunn-Sidak approach in MATLAB is actually the Dunn's test and how does t-statistics fit in here?
My question has also been asked in MATLAB Answers and partially discussed in StackExchange, but I feel like it has not been clearly answered, especially for the MATLAB software.
Thank you.
  1 Comment
Scott MacKenzie
Scott MacKenzie on 14 Jul 2021
Presumably the MATLAB documentation you cite on Multiple Comparisons is correct -- the Dunn-Sidak test, as implemented in multcompare, "uses critical values from the t-distribution". It's possible this is mathematically equivalent to the test given in the original source you cite The formula is given, so perhaps you can compare the two sources to find out.

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