Wilcoxon Sign Ranked Test - JMP OUT PUT

[#1]

 Hi, 

So I am doing Wilcoxon Sign Ranked test and I am not understanding what JMP is doing for where it says test statistic. I understand its using the "Pratt method" and this is the formula 

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

but could you expand on this a little further as I am not getting the same thing as what JMP is gettting.

where my values are :

R+ is 1527,

my sample has 76 pairs,

and 11 0's.

I try plugging my values into that formula and I get is but JMP is returning 581 for S. Please help me I am going nuts. 

S = 581 does not = 1527-1/4[76(76+1)-11(11+1)]

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). Data attached

Rachel

@Mark_Bailey 

[#2 · Accepted solution]

I've done the calculations in a JMP table (attached).

Following the calculation steps in the online documentation:

https://www.jmp.com/support/help/en/15.2/index.shtml#page/jmp/wilcoxon-signed-rank-test.shtml

I get S = -581 (same as JMP)

And for R+ I get 849; plug that into the R+ formula using d0=11, you also arrive at -581.

[#3]

@David_Burnham wow thank you so much for putting that together for me and showing me!. I greatly appreciate this!! 

I finally saw where I was going wrong, my error was with R+!

Curious if you could answer another question for me?

Can you explain to me what the highlighted part of the the variance formula is? I can not wrap my head around the term di.

Thank you,

Rachel

[#4]

The principle is that the presence of ties will have the effect of reducing the variance, so an adjustment is required by an amount that is a function of the proportions of the observations that are tied at each tie point. However, I'm not familiar with the details of the calculation or the theoretical basis of it.