cancel
Showing results for
Show  only  | Search instead for
Did you mean:
Choose Language Hide Translation Bar
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,

11 REPLIES 11
Level III

## Re: Wilcoxon signed rank test : Test statistic S

Hi,

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)]

S=97

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)

Rachel

Staff

## Re: Wilcoxon signed rank test : Test statistic S

It looks like you got a response to the same question on a different thread: https://community.jmp.com/t5/Discussions/Wilcoxon-Sign-Ranked-Test-JMP-OUT-PUT/td-p/312503

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