Correlation between the Wechsler Adult Intelligence Scale and Raven's Progressive Matrices

This page collects information on the correlation between two different IQ tests to answer the question how strongly do different IQ tests correlate with each other?

The two tests chosen to focus on here are the Wechsler Adult Intelligence Scale (WAIS) and Raven's Progressive Matrices (RPM) on the basis that they seem to be the two most well-known tests. The graph below shows the number of page views 10 different Wikipedia articles received in 2018.

Figure Reasoning Test 2.282k
Woodcock-Johnson Tests of Cognitive Abilities 4.723k
Multidimensional Aptitude Battery II 6.44k
Stanford-Binet Intelligence Scales 9.895k
Naglieri Nonverbal Ability Test 13.391k
Peabody Picture Vocabulary Test 22.595k
Otis–Lennon School Ability Test 25.431k
Cattell Culture Fair III 54.332k
Raven's Progressive Matrices 254.434k
Wechsler Adult Intelligence Scale 375.72k

The WAIS and RPM are clearly dominant in terms of interest. And in general these are the two tests people think of when they think of IQ tests, so examining what correlation you should expect from them is useful.

Literature review

A search for articles that reported correlations between WAIS and RPM scores was conducted using Google Scholar. The table below contains the data extracted from them.

Citation	WAIS version	Raven's version	n	r	Sample population
Kizik, 1962	WAIS	SPM	40	0.43	College students
McLeod et. al., 1962	WAIS	SPM	81	0.67	Psychiatric hospital patients
Sydiaha, 1967	WAIS	SPM	40	0.607	Psychiatric hospital patients
Shaw, 1967	WAIS	SPM	83	0.83	Psychiatric hospital patients
Pringle, 1971	WAIS	SPM	63	0.77	Psychiatric hospital patients
McLaurin et. al., 1973	WAIS	SPM	131	0.55	College students
Watson et. al., 1974	WAIS	SPM	120	0.58	Psychiatric hospital patients
Vernon, 1983	WAIS	APM	100	0.72	College students
Burke, 1985	WAIS	SPM	256	0.66	Veterans undergoing treatment and career counseling
Paul, 1986	WAIS	SPM	62	0.69	College students
O'Leary et. al., 1991	WAIS	SPM	105 105 36 25 17 20	.74 .77 .79 .83 .84 .11	Psychiatric hospital patients
Rijsdijk et. al., 2002	WAIS	SPM	388	0.66	Twin study at 18 y.o.

Not that much time was spent, so its possible a much more comprehensive search would find many more articles, but these should be enough to give a reasonable estimate.

Implications

The weighted average of all the correlations found in the literature review between the WAIS and RPM was 0.67.

If we assume that this is the true value and that IQ scores are normally distributed like they are supposed to be, the average expected difference between the two scores an individual would receive if they took both is 9.7 points. And the differences would conform to the distribution graphed below.

0 0.0653902
1 0.0648513
2 0.064229
3 0.0627087
4 0.0612258
5 0.0590905
6 0.0567391
7 0.0541907
8 0.0513536
9 0.048232
10 0.0450676
11 0.0420517
12 0.0387988
13 0.035425
14 0.0322379
15 0.0292238
16 0.02614
17 0.0232983
18 0.0206591
19 0.0182123
20 0.0159595
21 0.0138904
22 0.0119195
23 0.0101392
24 0.0087272
25 0.0073633
26 0.0061311
27 0.0051656
28 0.0042328
29 0.0035229
30 0.0028581
31 0.0023299
32 0.0018719
33 0.0015045
34 0.0011753
35 0.0009222
36 0.0007467
37 0.0005792
38 0.0004488
39 0.0003398
40 0.0002702

This was simulated using the code at two-iq-simulation.py.

Final notes

If you know of any more studies that report a correlation between the WAIS and RPM, please share!