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

• n: 69
• Median: 156.0
• Quartile deviation: 5.5
• Range: 73
• Maximum possible: 185
• Male median: 156.0 (n = 60)
• Female median: 156.0 (n = 8)
• Proportion of males among candidates: 0.870
• Hardness: 0.16
• Resolution: 0.48

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 Factors that contributed to this state of affairs were the ridiculous scale with a standard deviation of 24, the outdated norms from the 1960s that were used way into the 1990s, and the strong "Flynn effect" that particularly this test had undergone.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

Scores by females

n = 8

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

Weighted average of correlations: 0.127 (N = 369)

Estimated g factor loading: 0.36

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.

Estimated loadings of Raven's Advanced Progressive Matrices (I.Q.) on particular item types

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.

N = 232

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

Balanced g loading = 0.21

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

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

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

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

Estimated g factor loadings for restricted ranges

In parentheses the number of score pairs on which that estimated g factor loading is based. The goal of this is to verify the hypothesis that g becomes less important, accounts for a smaller proportion of the variance, at higher I.Q. levels. The mere fact of restricting the range like this also depresses the g loading compared to computing it over the test's full range, so it would be normal for these values to be lower than the test's full-range g loading.

[More statistical reports]