SPSS syntax for Williams test of two correlations on the same people with one variable in common is taken from here.

================================================ . * File name: Williams1959.sps . * Written by: Bruce Weaver, bwe...@lakeheadu.ca * Date: 15-May-2012. * ================================================ . * 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