<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/cohenrsq</title><revhistory><revision><revnumber>7</revnumber><date>2015-02-05 10:02:36</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2015-02-05 10:02:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2013-03-08 10:17:36</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>4</revnumber><date>2008-06-24 15:49:54</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2008-06-24 15:44:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2008-06-24 15:43:50</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2008-06-24 15:43:36</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>How do I compare two squared (semi-partial) correlations from the same sample</title><para>Cohen and Cohen (1983) show (Appendix 2) that the comparison of squared semi-partial correlations is equivalent to the comparison of the difference in unstandardised regression coefficients, B. </para><para>Namely for a sample size of N and k predictors of which two have multiple regression estimates, B(1) and B(2): </para><para>[B(1) - B(2)]/Sqrt[V(B(1)) + V(B(2)) - 2COV(B(1),B(2)) ] will follow a t distribution with N-k-1 degrees of freedom under the null hypothesis that the two regression coefficients are equal. </para><para>where V() and COV() represent the variance and covariances of the regression estimates respectively. </para><para>The covariance matrix of the regression coefficients is routinely outputted in most statistical software. In SPSS it may be requested by clicking on the statistics button and the Regression Coefficients:covariance matrix box when running the regression. The diagonal terms pf the covariance matrix represent variances and off-diagonal terms covariances of the regression coefficients. </para><para><emphasis role="underline">Reference</emphasis> </para><para>Cohen J and Cohen P (1983) Applied multiple regression/correlation analysis for the behavioral sciences. Second edition. Lawrence Erlbaum:Hillsdale, NJ. </para></section></article>