SPSS syntax for Williams test of two correlations on the same people with one variable in common is taken from here.
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* File name: Williams1959.sps .
* Written by: Bruce Weaver, bwe...@lakeheadu.ca
* Date: 15-May-2012.
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* SPSS program to compute Williams' (1959) test for
* comparing two correlations with one variable in common.
* The example used here is from Dave Howell's book
* "Statistical Methods for Psychology" (6th Ed., p. 262).
* It assumes the user wants the difference r12 - r13.
* This example reads in only one row of data, but one could
* read in several rows of data, with one test per row.
data list list / r12 r13 r23 (3f5.3) n (f5.0).
begin data
0.80 0.72 0.89 26
end data.
compute #R = (1 - r12**2 - r13**2 - r23**2) +
2*r12*r13*r23.
compute diff = r12 - r13.
compute t = diff *
SQRT( ((n-1)*(1+r23)) /
(2*((n-1)/(n-3))*#R +
((r12+r13)**2/4)*
(1-r23)**3) ).
compute df = n-3.
compute p = cdf.t(abs(t)*-1,df)*2.
formats t p diff (f5.3) / df (f5.0).
list r12 r13 diff t df p. OUTPUT: r12 r13 diff t df p .800 .720 .080 1.361 23 .187 Number of cases read: 1 Number of cases listed: 1