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I used Friedman and Post-hoc Friedman Nemenyi Test.

In this PAPER, page 11, the Critical Difference (CD) equation is different from what has been used in R function, PAGE 14 posthoc.friedman.nemenyi.test.

The only difference is that in R function $q(α)/\sqrt{2}$, while in the paper only $q(α)$.

What is the reason for this difference? and Why?

jeza
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On page 12 of the Demsar paper it says,

where critical values qα are based on the Studentized range statistic divided by [sqrt(2)] (Table 5(a)).

So, they are defining a distribution, with what we usually call a q distribution divided by sqrt(2), and then calling that "q" for the purposes of their paper.

So for example if you look up a table of the Studentized q Range, look up alpha = 0.05, k = 2, and df = infinity, you will get a value of 2.772. Divide this by sqrt(2) and you will get the 1.960 that Demsar lists for "q"0.05, classifiers = 2.

I really don't know why anyone would use this approach in something intended to be read by others.

Sal Mangiafico
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  • you mean that they are the same formulas but with different notations? Also, what do you mean by "I really don't know why anyone would use this approach in something intended to be read by others." and why? – jeza Feb 06 '20 at 13:27
  • how do you know that Demsar is referring to the inf degree of freedom in table 5(a)? – jeza Feb 06 '20 at 13:34
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    1) Yes, as far as I can tell, they are the same formula with different notations. 2) What I mean is that *q* is commonly used to denote the Studentized q distribution. Anyone looking at that formula quickly, would assume that that's what it stands for. It's like saying "I'm going to teach you how to change the tire on a car, but for the purpose of this lecture, I'm going to call the tire "the wheel" and call the lug nuts "the tires". – Sal Mangiafico Feb 06 '20 at 13:44
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    3) With the infinite degrees of freedom, it's just because that's how the values map, like the example of 2.772 and 1.960 in my response. And because that's what's used in the article by Thorsten Pohlert. You might want to double check that all the values given for the "q" distribution in Demsar article map to the standard *q* distribution in the same way. – Sal Mangiafico Feb 06 '20 at 13:45