# Statistics of Raven's Advanced Progressive Matrices (reported I.Q.'s)

## Introduction

Scores from this test are sometimes reported as "I.Q." with a standard deviation of 24, and sometimes as raw scores out of 36. This report deals with the "I.Q.'s". In a few cases they were reported with an standard deviation of 16 or 15, and those have been converted to 24 as that is the most used scale for this test.

Note that the candidates reporting "I.Q.'s" are not the same individuals as those reporting raw scores (although a few report both so there is a small overlap). So the scores in this report are from a different group than those in the report dealing with R.A.P.M. raw scores.

## Scores on Raven's Advanced Progressive Matrices (I.Q.) as of 16 February 2023

 115 * 120 * 135 * 140 * 148 ********* 149 ***** 151 * 152 * 153 * 154 * 155 * 156 ********************** 157 ** 160 ******** 163 **** 164 * 165 * 171 * 172 *** 174 * 179 * 180 * 187 *

Notice that the two peaks in the distribution correspond to the 98th and 99th centiles, reflecting the fact that many Mensa psychologists used to only report those scores (and/or their corresponding I.Q.'s) when a candidate had qualified, and not the actual precise score, which may have been anywhere above the 99th centile. This probably had to do with the psychologists' intuitive notion that the I.Q.'s from this test were absurdly too high, with far too many scoring over 160 if the norm tables were taken literally. Factors that contributed to this state of affairs were the ridiculous scale with a standard deviation of 24, the outdated norms from the 1960s that were used way into the 1990s, and the strong "Flynn effect" that particularly this test had undergone.

## Scores by males

n = 60

 115 * 120 * 135 * 140 * 148 ****** 149 ***** 151 * 153 * 154 * 155 * 156 ******************** 157 * 160 ******* 163 **** 164 * 165 * 171 * 172 ** 174 * 179 * 180 * 187 *

## Scores by females

n = 8

 148 ** 152 * 156 ** 157 * 160 * 172 *

## Correlation of Raven's Advanced Progressive Matrices (I.Q.) with other mental ability tests

Test name n r
Test For Genius - Revision 200460.81
Verbal section of Test For Genius - Revision 200460.78
Tests by Paul Laurent Miranda (aggregate)50.75
International High IQ Society tests (aggregate)60.74
Cooijmans Intelligence Test - Form 360.71
Titan Test (Ronald K. Hoeflin)40.67
Spatial section of Test For Genius - Revision 200460.65
The Sargasso Test40.62
Strict Logic Sequences Exam II (Jonathan Wai)40.57
Reason - Revision 200850.55
Reason Behind Multiple-Choice - Revision 200850.52
Qoymans Multiple-Choice #550.48
Tests by Ivan Ivec (aggregate)50.46
Culture Fair Numerical Spatial Examination - Final version (Etienne Forsström)60.46
Cartoons of Shock40.43
Tests by Greg Grove (aggregate)50.38
Test of Inductive Reasoning / J.C.T.I. (Xavier Jouve)40.38
Strict Logic Sequences Exam I (Jonathan Wai)80.35
Associative LIMIT70.35
Logima Strictica 36 (Robert Lato)120.27
Epiq Tests (aggregate)50.26
Cooijmans Intelligence Test - Form 290.24
Genius Association Test80.17
Numbers120.17
Sigma Test (Melão Hindemburg)70.15
W-87 (International Society for Philosophical Enquiry)60.13
Unknown and miscellaneous tests250.13
Gliaweb Riddled Intelligence Test (old version)40.11
Qoymans Multiple-Choice #480.08
Short Test For Genius80.07
Cattell Culture Fair150.04
Qoymans Multiple-Choice #25-0.01
Space, Time, and Hyperspace20-0.05
Mega Test (Ronald K. Hoeflin)7-0.06
Cooijmans Intelligence Test - Form 44-0.11
Analogies of Long Test For Genius10-0.11
The Final Test9-0.11
Numerical section of Test For Genius - Revision 20104-0.17
Qoymans Multiple-Choice #19-0.17
Association subtest of Long Test For Genius10-0.21
Strict Logic Spatial Exam 48 (Jonathan Wai)5-0.21
Non-Verbal Cognitive Performance Examination (Xavier Jouve)8-0.23
Lieshout International Mesospheric Intelligence Test8-0.26
Cooijmans Intelligence Test - Form 18-0.42
Long Test For Genius10-0.55
Qoymans Multiple-Choice #39-0.85
Evens4-0.90

Weighted average of correlations: 0.127 (N = 369)

Ranking in above table is based on the unrounded correlations. All available data is present in this table, no tests are left out except for those with less than 4 score pairs. All known pairs are used, including possible floor/ceiling scores or outliers.

The correlation with high-range tests is on the whole very low. This may be caused by factors like a lack of hard enough problems, a few bad items, a few errors in the scoring key (not at all uncommon with psychological tests), inconsistent testing conditions, fraud, or incorrect/incomplete score reporting by psychologists intuitively sensing that the I.Q.'s are enormously too high. It is chilling to consider that this test has been used for admission to I.Q. societies for decades while obviously failing woefully to measure intelligence in the high range.

These are estimated g factor loadings, but against homogeneous tests (containing only particular item types) as opposed to non-compound heterogeneous tests. Although tending to surprise the lay person, it is not uncommon for tests to have high loadings on item types they do not actually contain themselves. Such loadings reflect the empirical fact that most tests for mental abilities measure primarily g, regardless of their contents; that the major part of test score variance is caused by g, and only a minor part by factors germane to particular item types. It is of key importance to understand that this is a fact of nature, a natural phenomenon, and not something that was built into the tests by the test constructors.

Verbal79-0.23
Numerical280.14
Spatial430.12
Logical90.69
Heterogeneous730.36

N = 232

Compound tests have been left out of this table to avoid overlap.

## National means for Raven's Advanced Progressive Matrices (I.Q.)

Country n mean score
United_States3166.67
Finland3162.67
Netherlands5159.60
Belgium10156.80
Greece4153.00
Sweden6149.00

For reasons of privacy, only countries with 3 or more candidates are included in this table. Ranking is based on the unrounded means, and then alphabetic.

## Correlation with national I.Q.'s of Raven's Advanced Progressive Matrices (I.Q.)

Correlation of this test with national average I.Q.'s published by Lynn and Vanhanen:

• r = -0.15 (n = 58)

## Correlation of Raven's Advanced Progressive Matrices (I.Q.) with personal details

Personalia n r
PSIA Rational - Revision 200740.57
Mother's educational level290.30
Father's educational level290.16
Disorders (parents and siblings)300.13
Disorders (own)340.12
Sex680.00
Observed associative horizon7-0.06
PSIA Cruel - Revision 20074-0.14
Observed behaviour8-0.14
Cooijmans Inventory of Neo-Marxist Attitudes5-0.16
Educational level32-0.16
Year of birth62-0.18
PSIA Ethics factor - Revision 20074-0.28
PSIA Antisocial - Revision 20074-0.31
PSIA True - Revision 20074-0.48
PSIA Cold - Revision 20074-0.54
PSIA Extreme - Revision 20074-0.66
PSIA Neurotic - Revision 20074-0.67
PSIA Introverted - Revision 20074-0.73
PSIA Deviance factor - Revision 20074-0.74
PSIA System factor - Revision 20074-0.77
PSIA Aspergoid - Revision 20074-0.82
PSIA Just - Revision 20074-0.88
PSIA Orderly - Revision 20074-0.89
PSIA Rare - Revision 20074-0.94

## Correlation with personal details of Raven's Advanced Progressive Matrices (I.Q.) - within females

Personalia n r
Year of birth60.41

## Correlation with personal details of Raven's Advanced Progressive Matrices (I.Q.) - within males

Personalia n r
PSIA Rational - Revision 200740.57
Mother's educational level280.30
Father's educational level280.17
Disorders (parents and siblings)290.13
Disorders (own)320.11
PSIA Cruel - Revision 20074-0.14
Cooijmans Inventory of Neo-Marxist Attitudes5-0.16
Educational level31-0.17
Year of birth56-0.21
PSIA Ethics factor - Revision 20074-0.28
PSIA Antisocial - Revision 20074-0.31
PSIA True - Revision 20074-0.48
PSIA Cold - Revision 20074-0.54
Observed associative horizon5-0.63
PSIA Extreme - Revision 20074-0.66
PSIA Neurotic - Revision 20074-0.67
Observed behaviour7-0.67
PSIA Introverted - Revision 20074-0.73
PSIA Deviance factor - Revision 20074-0.74
PSIA System factor - Revision 20074-0.77
PSIA Aspergoid - Revision 20074-0.82
PSIA Just - Revision 20074-0.88
PSIA Orderly - Revision 20074-0.89
PSIA Rare - Revision 20074-0.94