Normal Order Statistic for Terry-Hoeffding Test

Question

Related to this question:

I am trying to replicate the numbers found in the third column of the table on page 189 from this article (E(V^ri)) in Python by way of the Terry-Hoeffding Normal Scores test. Further explanation is provided on page 184. I am trying to locate Harter, 1961 to include it if needed.

Answer 1

Perhaps without realizing it, you've basically asked the same question twice. Eq. [1] in the paper is $E(V^k)=-E(V^{N+1-k})$. In Table 2 rank $1$ scores $-1$ times what rank $8$ scores, so $N=8$. The code I provided in your other question finds $E(1,\,8)$ to be $1.4236$, the value given to rank $7$, or $-1$ times the value given to rank $1$. In other words, $V(r)=-E(r,\,N)$. (My linked code indents with two spaces at a time, instead of the four used in my other answer.)