Statistics of combined Numerical and Spatial sections of The Marathon Test

© Paul Cooijmans

Scores on Numerical and spatial sections of The Marathon Test as of 29 May 2023

Contents type: Numerical, spatial.   Period: 2005-present

0 *
2 *
6 *
12 **
17 **
18 *
21 *
22 *
30 *
32 *
37 **
38 *
40 *
42 *
42.2 *
42.5 *
45 *
46 *
46.8 *
48 *
48.5 *
54 ***
55 *
56.2 *
58 *
59 **
61 **
62.2 *
63 ***
64 ***
65.2 *
66.2 *
67 *
68 *
69 *
70 **
71 **
72 *
74 **
75 *
77 *
79 *
80 *
83 *
85 ***
87 *
89 **

Correlation of Numerical and spatial sections of The Marathon Test with other mental ability tests

Test name n r
Tests by Nikolaos Soulios (aggregate)40.97
Laaglandse Aanlegtest - Herziening 201640.97
Epiq Tests (aggregate)40.94
Spatial section of The Marathon Test640.94
Narcissus' last stand150.94
Numerical section of The Marathon Test640.93
Test of the Beheaded Man210.93
The Marathon Test380.93
International High IQ Society tests (aggregate)40.92
916 Test (Laurent Dubois)40.91
De Laatste Test - Herziening 201960.90
Test For Genius - Revision 2016150.90
The Test To End All Tests180.89
The Alchemist Test160.89
Test For Genius - Revision 201080.89
Reflections In Peroxide250.88
The Final Test70.88
Psychometric Qrosswords120.87
A Relaxing Test70.87
Cartoons of Shock100.86
Culture Fair Numerical Spatial Examination - Final version (Etienne Forsström)60.86
Non-Verbal Cognitive Performance Examination (Xavier Jouve)40.86
Tests by Mislav Predavec (aggregate)50.85
Gliaweb Riddled Intelligence Test - Revision 2011260.84
The Piper's Test120.84
The Bonsai Test - Revision 2016210.82
Divine Psychometry90.82
Reason Behind Multiple-Choice - Revision 2008240.82
Tests by Greg Grove (aggregate)60.81
Combined Numerical and Spatial sections of Test For Genius - Revision 2016210.81
Wechsler Adult Intelligence Scales50.80
Lieshout International Mesospheric Intelligence Test290.80
Dicing with death120.80
Associative LIMIT220.78
Spatial section of Test For Genius - Revision 2004220.78
Test For Genius - Revision 2004100.78
Combined Numerical and Spatial sections of Test For Genius - Revision 2010150.78
Qoymans Multiple-Choice #5240.78
Only idiots100.78
Cooijmans Intelligence Test - Form 4220.77
Cooijmans Intelligence Test - Form 3350.77
Space, Time, and Hyperspace - Revision 2016210.77
Verbal section of Test For Genius - Revision 2016150.77
Problems In Gentle Slopes of the second degree220.75
Cooijmans On-Line Test - Two-barrelled version120.75
Psychometrically Activated Grids Acerbate Neuroticism100.73
Logima Strictica 36 (Robert Lato)100.72
Problems In Gentle Slopes of the first degree120.72
Cooijmans Intelligence Test - Form 2100.72
Verbal section of The Marathon Test380.71
The Nemesis Test190.70
The Smell Test40.69
Problems In Gentle Slopes of the third degree190.69
Numerical section of Test For Genius - Revision 2010310.69
A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude200.68
Cooijmans Intelligence Test 5220.68
De Golfstroomtest - Herziening 201960.68
Genius Association Test210.67
Reason - Revision 2008240.65
Logima Strictica 24 (Robert Lato)50.65
The Sargasso Test230.65
Verbal section of Test For Genius - Revision 2004160.64
Miscellaneous tests170.63
Qoymans Multiple-Choice #460.60
Random Feickery40.59
The LAW - Letters And Words40.59
The Hammer Of Test-Hungry - Revision 201360.56
Isis Test160.54
Labyrinthine LIMIT120.50
Daedalus Test190.47
Cattell Culture Fair40.47
Strict Logic Sequences Exam I (Jonathan Wai)110.33
The Final Test - Revision 201370.27
Strict Logic Spatial Exam 48 (Jonathan Wai)90.17
Reason Behind Multiple-Choice4-0.03
Tests by Jason Betts (aggregate)4-0.29
Strict Logic Sequences Exam II (Jonathan Wai)4-0.50
Tests by Ivan Ivec (aggregate)4-0.70

Weighted average of correlations: 0.750 (N = 1191)

Estimated g factor loading: 0.87

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 Numerical and spatial sections of The Marathon Test 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 Numerical and spatial sections of The Marathon Test on that type

N = 914

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

Balanced g loading = 0.84

National medians for Numerical and spatial sections of The Marathon Test

Country n median score

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

Correlation of Numerical and spatial sections of The Marathon Test with personal details

Personalia n r
PSIA True - Revision 2007140.65
PSIA Orderly - Revision 2007140.58
PSIA Rational - Revision 2007140.55
PSIA Ethics factor - Revision 2007140.51
PSIA Neurotic - Revision 2007140.50
Educational level630.48
Observed behaviour90.44
PSIA Introverted - Revision 2007140.41
PSIA System factor - Revision 2007140.39
PSIA Cold - Revision 2007140.27
PSIA Aspergoid - Revision 2007140.22
Cooijmans Inventory of Neo-Marxist Attitudes90.20
PSIA Deviance factor - Revision 2007140.17
PSIA Extreme - Revision 2007140.12
PSIA Just - Revision 2007140.07
Mother's educational level60-0.01
PSIA Rare - Revision 200714-0.06
Father's educational level58-0.08
PSIA Cruel - Revision 200714-0.09
Year of birth64-0.13
PSIA Antisocial - Revision 200714-0.22
Disorders (own)63-0.25
Gifted Adult's Inventory of Aspergerisms12-0.26
Disorders (parents and siblings)62-0.32

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.

Below 1st quartile0.80 (334)
Below median0.82 (622)
Above median0.67 (528)
Above 3rd quartile0.51 (199)


This reliability is computed from the two subtest reliabilities using a form of the Spearman-Brown formula, taking into account the weighting of the spatial score.


Robustness and overall test quality

Further internal statistics

Further internal statistics are reported on subtest level (respectively the Numerical and the Spatial section of The Marathon Test).