FAQ/WilliamsSPSS/Meng - CBU statistics Wiki
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Copy and paste the SPSS syntax in the box below into a SPSS window, select all and click the run arrow key. Amend the spreadsheet data as required.

This procedure (the Meng et al. test) is an alternate procedure that is said to be superior to Williams’ procedure: See Meng, Rosenthal, & Rubin (1992).

The R procedure cocor can also evaluate Wiiliams and Meng's tests.

* 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

set format f10.5.
/r12  r13  r23  n. 
.63 -.03 -.19 15
.59 .31 .71 30
.80 .72 .89 26


* /* 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 */.

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).

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'.

  /VARIABLES=!1 !2 z prob_z 
  /TITLE "Meng test of two correlations with one variable in common from same sample".


set mexpand on.
!meng r12 r13 r23 n.
set mprint off.
  • Multiple invocations of the macro in the same interactive session will produce the following note:

>The macro name specified on the DEFINE command duplicates the name of a previously defined macro. This instance will take precedence.

This warning does not indicate a problem and may be ignored.

The above formula from Meng at al. (1992) is also referred to in Shrout PE and Yip-Bannicq M (2017).


Meng, Rosenthal, & Rubin (1992) Comparing correlated correlation coefficients. Psychological Bulletin, 111: 172-175.

Shrout PE and Yip-Bannicq M (2017). Inferences about competing measures based on patterns of binary significance tests are questionable. Psychological Methods 22(1) 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).

None: FAQ/WilliamsSPSS/Meng (last edited 2021-03-17 09:33:21 by PeterWatson)