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Level II

Wilcoxon signed rank test : Test statistic S

Hello everyone,


I apologize in advance for what must seem like a very obvious question.

When you do a pair analysis of variable in JMP, you can ask the software to perform a Wilcoxon signed rank test which then gives me as a result a test statistics named S.


Question is : What is S?

It does not match the sum of all the ranks because it can be a negative

It does not match the sum of the signed ranks or even the half-sum of the signed ranks (and it would be named W not S)


Can someone please share some light on this issue since the JMP documentation only states how to calculate W but doesn't say a word about S ?


Another question : How do i switch from a one-tail test (which is the one performed) to a two tailed test.


I've included the sample data i use. The sum of the positive ranks is 19 and the sum of the negative ranks is 134.

W should be 62.5. S is 68. What am i missing ?


Best regards,

Level III

Re: Wilcoxon signed rank test : Test statistic S



I am having the same issue as she is. My R+ is 1527, my sample has 76 pairs, and 11 0's. I try plugging my values into that formula and I get . When JMP is returning 581 for S. Please help me I am going nuts. 

S = R+ - 1/4[(N(N+1)-do(do+1)]

S= 1527-1/4[76(76+1)-11(11+1)]


Also how is this calculating M for the sign statistic?


THANK YOU!!!!!!!!!!!!!!


I should mention when adding these in the matched pair test under analyzed I am putting dad height first then height (which is the opposite of how I want it to read out)



Re: Wilcoxon signed rank test : Test statistic S

It looks like you got a response to the same question on a different thread:


I think the key is that the signed ranks for the ties are zero, but then the rest of the signed ranks start at d0+1 (or a midrank associated with that rank, when there are ties), where d0 is the number of ties.

Michael Crotty
Sr Statistical Writer
JMP Development