<?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/WilliamsSPSS/Meng</title><revhistory><revision><revnumber>15</revnumber><date>2021-03-17 09:33:21</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>14</revnumber><date>2021-03-17 09:33:02</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>13</revnumber><date>2021-03-11 14:49:33</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2017-05-09 10:36:30</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2017-05-09 10:35:56</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2017-05-09 10:34:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2017-05-09 10:29:46</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2013-03-08 10:17:17</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>7</revnumber><date>2006-07-18 16:01:04</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>6</revnumber><date>2006-07-18 15:46:50</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>5</revnumber><date>2006-07-18 15:46:04</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>4</revnumber><date>2006-07-17 13:54:36</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>3</revnumber><date>2006-07-17 10:26:17</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>2</revnumber><date>2006-07-12 11:23:15</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision><revision><revnumber>1</revnumber><date>2006-07-12 11:21:21</date><authorinitials>pc0082.mrc-cbu.cam.ac.uk</authorinitials></revision></revhistory></articleinfo><para>Copy and paste the SPSS syntax <emphasis role="strong">in the box below</emphasis> into a SPSS window, select all and click the run arrow key. Amend the spreadsheet data as required. </para><para>This procedure (the Meng et al. test) is an alternate procedure that is said to be superior to Williams’ procedure: See Meng, Rosenthal, &amp; Rubin (1992).  </para><para>The R procedure <ulink url="https://www.rdocumentation.org/packages/cocor/versions/1.1-3/topics/cocor">cocor</ulink> can also evaluate Wiiliams and Meng's tests. </para><screen><![CDATA[* Meng, X, Rosenthal, R and Rubin, D (1992) Comparing Correlated Correlation Coefficients Psychological Bulletin 111 172-175.
* outputs z value and one-tailed p-value: double to get a two-tailed p
]]><![CDATA[
set format f10.5.
DATA LIST free
/r12  r13  r23  n. 
BEGIN DATA
.63 -.03 -.19 15
.59 .31 .71 30
.80 .72 .89 26
END DATA. 
]]><![CDATA[
]]><![CDATA[
]]><![CDATA[
================================.
]]><![CDATA[
* /* Meng's Z test for two correlated
* correlations (r12=r13) having
* n observations with one variable in common ( variable 1)
*
* input columns: r12 r13 r23 n
*
* outputted p-values are one-tailed -
* just double to obtain two-tailed */.
*
*=================================.
]]><![CDATA[
set mexpand off.
set format f10.5.
define !meng (  !pos !tokens(1)
                    / !pos !tokens(1)
                   /  !pos !tokens(1)
                  /   !pos !tokens(1)).
compute #lct1=0.5*ln((1+!1)/(1-!1)).
compute #lct2=0.5*ln((1+!2)/(1-!2)).
compute #f=(1-!3)/( 2*( 1- ( 0.5*(!1*!1+!2*!2) ) ) ).
compute #h=1+ ( 0.5*(!1*!1+!2*!2) ) / ( 1- (0.5*(!1*!1+!2*!2)) )*(1-#f).
compute z=(#lct1-#lct2)*sqrt((!4-3)/(2*(1-!3)*#h)).
if (z le 0) prob_z=cdfnorm(z).
if (z gt 0) prob_z=1-cdfnorm(z).
]]><![CDATA[
FORMAT !1 !2 z prob_z (f9.3).
VARIABLE LABELS !1 'correlation 1' !2 'correlation 2' /z 'z-value' 
/prob_z  '1-tailed p-value'.
EXECUTE.
]]><![CDATA[
REPORT FORMAT=LIST AUTOMATIC ALIGN(CENTER)
  /VARIABLES=!1 !2 z prob_z 
  /TITLE "Meng test of two correlations with one variable in common from same sample".
]]><![CDATA[
!enddefine.
]]><![CDATA[
set mexpand on.
!meng r12 r13 r23 n.
set mprint off.]]></screen><itemizedlist><listitem><para>Multiple invocations of the macro in the same interactive session will produce the following note: </para></listitem></itemizedlist><para>&gt;The macro name specified on the DEFINE command duplicates the name of a previously defined macro.  This instance will take precedence. </para><para>This warning does not indicate a problem and may be ignored. </para><para>The above formula from Meng at al. (1992) is also referred to in Shrout PE and Yip-Bannicq M (2017). </para><para><emphasis role="underline">References</emphasis> </para><para>Meng, Rosenthal, &amp; Rubin (1992) Comparing correlated correlation coefficients. Psychological Bulletin, 111: 172-175. </para><para>Shrout PE and Yip-Bannicq M (2017). Inferences about competing measures based on patterns of binary significance tests are questionable. <emphasis>Psychological Methods</emphasis> <emphasis role="strong">22(1)</emphasis> 84-93. (There are also a few lines of SPSS, R SAS and Mplus syntax in this paper which assesses incremental validity. This compares two competing measures, namely a novel measure with a gold standard measure). </para></article>