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Clarification on Tukey-Kramer test in multcompare following the Friedman's Test

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When using multcompare function, Tukey-Kramer is a default post-hoc test performed for the Friedman's test. Given that the most common post hoc test for the Friedman's test is the Nemenyi's test, I wanted to clarify whether:
  • the Tukey-Kramer option is identical to the Nemenyi' test. The previous answer on MathWorks (see [1]) briefly says so, but I wanted to confirm if this is true, and, if so, whether anyone can touch the mathematical equivalence between the two.
It seems the Tukey-Kramer test and Tukey's HSD test is used interchangeably in the multcompare. Further clarification on this point would be helpful, too.
References:

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Shivansh
Shivansh am 18 Dez. 2023
Hi SungJun!
I understand that you want to know about the use of different post-hoc tests in the Friedman’s test with respect to the “multcompare” function in MATLAB.
For your doubts regarding the use of Tukey-Kramer and Tukey HSD test, they are indeed the same, despite being described under different names in various literatures. MATLAB's “multcompare” function provides the option under both names to accommodate this variability in terminology.
Regarding the application of the Tukey-Kramer option after Friedman's test, it is believed that this is equivalent to performing the Nemenyi’s test. There are many literatures where Nemenyi’s test matches the procedure followed in MATLAB.
I also looked at the book by Hochberg and Tamhane on multiple comparison procedures. It seems to be saying that the original Nemenyi idea, perhaps from 1963, was to use a critical value based on a chi-square distribution, but the use of a Tukey-Kramer value is more powerful. There may be a possibility that Nemenyi's name is still attached to the test nowadays even when the Tukey-Kramer value is used.
Hope it helps!

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