W-87 statistics

Paul Cooijmans


These are statistics based on the W-87 scores reported by test candidates.

Scores on W-87 (I.S.P.E.) as of 5 July 2022

121 *
129 *
145 **
149 *
150 *********
151 **
152 *
153 *
154 ****
155 **
156 ***
157 ***
159 *
160 **

Correlation of W-87 (I.S.P.E.) with other mental ability tests

(Test index) Test name n r
(241) Ultra Test (Ronald K. Hoeflin)40.86
(79) Association subtest of Long Test For Genius90.46
(229) Mega Test (Ronald K. Hoeflin)140.45
(75) Analogies of Long Test For Genius80.36
(10) Genius Association Test50.35
(239) Titan Test (Ronald K. Hoeflin)50.32
(56) Short Test For Genius50.27
(63) Long Test For Genius80.19
(68) Numbers70.16
(218) Raven's Advanced Progressive Matrices (I.Q.)60.13
(85) Cooijmans Intelligence Test - Form 170.11
(242) Unknown and miscellaneous tests170.09
(87) Cooijmans Intelligence Test - Form 250.08
(7) The Final Test150.07
(231) Tests by Greg Grove (aggregate)4-0.06
(57) Space, Time, and Hyperspace10-0.12
(51) Qoymans Multiple-Choice #14-0.25
(80) Qoymans Multiple-Choice #44-0.27
(211) Culture Fair Numerical Spatial Examination - Final version (Etienne Forsström)7-0.37
(235) Non-Verbal Cognitive Performance Examination (Xavier Jouve)4-0.54
(201) Wechsler Adult Intelligence Scales6-0.64

Weighted average of correlations: 0.108 (N = 154, weighted sum = 16.56)

Conservatively estimated minimum g loading: 0.33

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.

Estimated loadings of W-87 (I.S.P.E.) 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.

Typeng loading of W-87 (I.S.P.E.) on that type

N = 106

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

Balanced g loading = 0.25

National medians for W-87 (I.S.P.E.)

Country n median score

For reasons of privacy, only countries with 2 or more candidates are included in this table. Ranking is based on the medians, and then alphabetic.

Correlation with national I.Q.'s of W-87 (I.S.P.E.)

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

Correlation of W-87 (I.S.P.E.) with personal details

Personalia n r
Father's educational level80.52
Educational level90.28
Mother's educational level80.10
Observed associative horizon7-0.05
Observed behaviour5-0.07
Year of birth30-0.11
Disorders (parents and siblings)8-0.27
Disorders (own)9-0.30

Estimated g factor loadings upward and downward of particular scores

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 both values to be lower than the test's full-range g loading.

Raw scoreUpward g (N)Downward g (N)
1210.33 (154)NaN (0)
1490.28 (123)NaN (0)
1520.49 (52)0.29 (63)
1550.66 (22)0.29 (104)
160NaN (0)0.33 (154)