For the latest version of JMP Help, visit JMP.com/help.

There are N observations:
X1, X2,..., XN
H0: median = m
Dj = Xj - m
There are N pairs of observations from two populations:
X1, X2,..., XN and Y1, Y2,..., YN
H0: medianX - Y = 0
Dj = Xj -Yj
Denote the rank or midrank for a difference by Rj. Define the signed rank for as follows:
is the number of signed ranks that equal zero
R+ is the sum of the positive signed ranks
For , exact p-values are calculated.
For N > 20, a Student’s t approximation to the statistic defined below is used. Note that a correction for ties is applied. See Iman (1974) and Lehmann and D’Abrera (2006).
Under the null hypothesis, the mean of W is zero. The variance of W is given by the following:
The last summation in the expression for Var(W) is a correction for ties. The notation di for i > 0 represents the number of values in the ith group of nonzero signed ranks. (If there are no ties for a given signed rank, then di = 1 and the summand is 0.)
The statistic t given by the following has an approximate t distribution with - 1 degrees of freedom:

Help created on 3/19/2020