Is Dunn-Sidak approach in MATLAB multcompare identical to so-called Dunn's test? I've asked the same question elsewhere.

These two articles recommend Dunn's test as non-parametric post hoc multiple comparison test following Kruskal-Wallis test.
How the Dunn method for nonparametric comparisons works
https://www.graphpad.com/guides/prism/7/statistics/stat_how_the_dunn_method_for_nonpar.htm?toc=0
Dunn's test
https://stats.stackexchange.com/tags/dunn-test/info
MATLAB's multcompare function offers a few choices for post hoc tests, including 'dunn-sidak'.
The name suggests that 'dunn-sidak' is Dunn's test mentioned above, but the description here says that it uses t distribution, so I thought that it is unlikely that this approach is used for non-paramatric data.
Is so-called Dunn's test identical to Dunn & Sidák’s Approach used by MATLAB multcompare?
If not, is there a way to run Dunn's test with MATLAB? Perhaps, I need to use R (it has a package dunn.test) or Python instead?
 A: I've got a reply from MathWorks about this. Despite my and others' suspect that 'dunn-sidak' and so called Dunn's test are different (see above comments), their (his) conclusion is that they are the same.
It would be worth comparing the same example data with R and MATLAB and see if they match.

Hello Kouichi,
I am writing in reference to your Technical Support Case ********** regarding 'Is multcompare's 'dunn-sidak' option identical to so-called Dunn's test?'.
I looked at the original Dunn paper and I see equations (4) and (5) defining mean ranks and their variances. Those expressions match the code I see in:


*

*anova1.m - look for the place where 'kruskalwallis' is assigned into a struct field, at line 268 in the latest release

*multcompare.m - look for the case 'kruskalwallis' block


You can open the files by simply typing "edit" in MATLAB. For example:
>> edit anova1.m

Hence, it looks like they are computing the same test statistics. Furthermore, by looking at the R package for this that you mentioned, I see that it offers a variety of multiple comparison approaches:
"none", "bonferroni", "sidak", "holm", "hs", "hochberg", "bh", "by"
which are quite similar to the ones from "multcompare.m"; i.e.:
'tukey-kramer' 'dunn-sidak', 'bonferroni', 'scheffe', 'hsd', 'lsd' (same as 'none')
So I would conclude that you can use "kruskalwallis.m" and "multcompare.m" to carry out Dunn's test.
Having said that, if you find a published example worked out in a book or paper, it may be sensible to try that out in MATLAB and see if it matches the desired test. If you do not know how to, it would be great if you cold provide us with a link and we can see if we duplicate the same test with the existing functions.
Regarding the "Steel-Dwass" test, I will put an enhancement request on your behalf so our development team can consider adding it on a future MATLAB release.
