Statistics of Raven's Advanced Progressive Matrices (reported raw scores)

Paul Cooijmans 2006

Scores from this test are sometimes reported as "IQ"s with a standard deviation of 24, and sometimes as raw scores out of 36. This report deals with the raw scores.

Note that the testees reporting raw scores are NOT the same individuals as those reporting "IQ"s (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 RAPM IQs.

Scores so far

# testees: 30
Mean: 33.9
SD: 2.37
Male mean: 33.9
Female mean: - (0 persons)


It is obvious the RAPM is too easy for those taking my tests and there is a ceiling effect.

Correlation with other tests

Mega Test50.83
Qoymans Multiple-Choice #46-0.12
Logima Strictica 364-0.15
Qoymans Multiple-Choice #35-0.24
Test For Genius - Revision 20044-0.31
Space, Time & Hyperspace11-0.42
Association Subtest of LTFG5-0.62

Weighted average of correlations: -0.134

Estimated minimum g loading: -0.37

Ranking in above table is based on the unrounded correlations.

As with the "IQ"s for this test, a negative g loading. This is of course only true for the top of the range, not for the full range of the test. Somewhere there must be a point where the correlation of raw scores with intelligence breaks and becomes negative. This correlation is not yet fully significant, so it may also be the correlation will eventually turn out around zero or slightly positive.

This negative correlation is probably not caused by the ceiling effect alone, because there are a few other tests with similar ceiling effect (Cito-toets and CHART) that nevertheless have a clear positive correlation with prior tests on the whole. Also, the "IQ"s for this test, from another group of testees, show about the same negative correlation, which adds significance to it; the two correlation tables together are as good as significant in pointing to a negative correlation. And a real negative correlation implies that there are bad items that the most intelligent testees consistently answer wrongly.

A negative correlation also means the test, or at least this part of it, cannot be normed the normal way "upward", because the highest raw scores must correspond to lower, not higher, IQs than the preceding ones.

National averages

Country# scoresAverage score

Correlation with personal details

PSIA True60.64
PSIA Aspergoid60.43
PSIA Ethics70.4
Educational level90.34
PSIA Cruel60.16
PSIA Orderly60.04
Father's eduational level90
PSIA Cold6-0.02
PSIA Rare6-0.02
PSIA Rational6-0.02
Year of birth18-0.11
PSIA Extreme6-0.11
PSIA Just6-0.17
Mother's educational level9-0.19
PSIA Neurotic6-0.25
PSIA Deviance7-0.26
PSIA Antisocial6-0.39
PSIA Introverted6-0.61
Disorders (own)9-0.82
Disorders (parents and siblings)9-0.82

Correlation with national IQs

-.2 over 22 pairs.

Required IQs per raw score

It is tempting to norm the top part of this test because there has been controversy and confusion about it in high-IQ circles, but a real norming is not possible at the moment. The normal norming method I use for most other tests (equating ranks of raw and "prior" scores) would result in an "unbroken" norming, either upward or downward, but this test with its negative or zero g loading seems to need a re-entrant norming that goes up and down. Such a norming is only possible with very much data for each raw score, so that each can be normed separately (rather than equating the distributions).

There is not enough data for that, but for informational purposes I provide below a table showing how each raw score corresponds to those testees' IQs on other tests. This is NOT meant as a norming, it does not suffice for that.

The Required IQ (SD=15) is roughly the minimal IQ needed for that raw score; so that would be the norm. The Mean IQ is roughly the mean of the IQs of the testees reporting that score; this will probably be higher than the correct norm because of the ceiling effect. The SE is the standard deviation of their IQs, which more or less serves as the standard error of that raw score.

144Insufficient data

Insufficient data

Insufficient data
156Insufficient data
137Insufficient data