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.