Statistics of combined Numerical and Spatial sections of The Marathon Test

© Paul Cooijmans

(Spatial items are weighted by 3.)

Scores on Numerical and spatial sections of The Marathon Test as of 16 September 2019

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

0 *
6 *
12 **
17 **
21 *
32 *
37 *
38 *
42 *
42.2 *
45 *
48 *
48.5 *
54 **
56.2 *
58 *
59 *
61 **
62 *
63 ***
64 ***
66.2 *
67 *
69 *
70 **
71 *
74 **
76 *
80 *
82 **

Correlation of Numerical and spatial sections of The Marathon Test with other tests by Paul Cooijmans

(Test index) Test name n r
(31) Numerical section of The Marathon Test410.96
(32) Spatial section of The Marathon Test410.95
(111) Test For Genius - Revision 201650.95
(21) Psychometric Qrosswords70.94
(42) The Marathon Test260.92
(0) Test of the Beheaded Man120.91
(7) The Final Test60.91
(48) Narcissus' last stand80.90
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 201660.89
(109) The Bonsai Test - Revision 201660.89
(43) Test For Genius - Revision 201080.89
(36) Reflections In Peroxide100.87
(40) Reason Behind Multiple-Choice - Revision 2008110.86
(1) Cartoons of Shock70.84
(105) Space, Time, and Hyperspace - Revision 201660.84
(28) The Test To End All Tests100.83
(110) Cooijmans Intelligence Test 550.79
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude80.79
(47) Psychometrically Activated Grids Acerbate Neuroticism60.78
(2) Cooijmans Intelligence Test - Form 3200.78
(107) The Alchemist Test50.77
(87) Cooijmans Intelligence Test - Form 280.76
(23) Gliaweb Riddled Intelligence Test - Revision 2011110.76
(3) Qoymans Multiple-Choice #5110.76
(108) Verbal section of Test For Genius - Revision 201650.75
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 2010120.75
(35) Intelligence Quantifier by assessment130.73
(16) Lieshout International Mesospheric Intelligence Test150.72
(103) Problems In Gentle Slopes of the second degree100.72
(18) The Nemesis Test130.71
(26) Verbal section of Test For Genius - Revision 2004130.71
(12) Cooijmans On-Line Test - Two-barrelled version100.70
(19) Numerical section of Test For Genius - Revision 2010160.70
(27) Spatial section of Test For Genius - Revision 2004160.69
(24) Reason - Revision 2008120.68
(44) Associative LIMIT100.68
(25) The Sargasso Test120.65
(30) Verbal section of The Marathon Test260.64
(106) Cooijmans Intelligence Test - Form 4100.63
(33) Problems In Gentle Slopes of the first degree70.63
(10) Genius Association Test100.56
(66) Test For Genius - Revision 200470.55
(37) Problems In Gentle Slopes of the third degree60.49
(117) The Hammer Of Test-Hungry - Revision 201350.47
(5) Daedalus Test100.46
(11) Isis Test90.44
(46) Labyrinthine LIMIT60.23
(104) The Final Test - Revision 201350.09
(29) Words5-0.01

Weighted average of correlations: 0.754 (weighted sum: 412.30)

Conservatively estimated minimum g 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 5 score pairs. All known pairs are used, including possible floor/ceiling scores or outliers.

Correlation of Numerical and spatial sections of The Marathon Test with tests by others

(Test index) Test name n r
(225) Logima Strictica 3660.57
(240) Strict Logic Spatial Exam 4870.24
(242) Unknown and miscellaneous tests130.18
(234) Strict Logic Sequences Exam I80.18

Weighted average of correlations: 0.260 (weighted sum: 8.86)

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 5 score pairs. All known pairs are used, including possible floor/ceiling scores or outliers.

Please be aware that correlations with these external tests are in most cases affected (depressed, typically) by one or more of the following: (1) Little overlap with the object test because of the much lower ceilings and inherent ceiling effects of the tests used in regular psychology; (2) Candidates reporting scores selectively, for instance only the higher ones while withholding lower ones; (3) Candidates reporting, or having been reported by psychometricians, incorrect scores.

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.

Typeg loading of Numerical and spatial sections of The Marathon Test on that type
Verbal0.81
Numerical0.94
Spatial0.92
Logical0.76
Heterogeneous0.86

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

Balanced g loading = 0.86

National medians for Numerical and spatial sections of The Marathon Test

Country n median score
United_Kingdom271.5
Spain269.0
Belgium263.0
Germany358.0
India255.5
Finland450.5
Korea_South345.0
United_States742.2
Canada239.5

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 Numerical and spatial sections of The Marathon Test

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

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

Personalia n r
Cooijmans Inventory of Neo-Marxist Attitudes31.00
Observed associative horizon31.00
P.S.I.A. True90.72
P.S.I.A. Ethics factor120.48
P.S.I.A. Rational90.48
Educational level410.45
P.S.I.A. Neurotic90.41
Observed behaviour80.36
P.S.I.A. System factor90.29
P.S.I.A. Orderly90.27
P.S.I.A. Rare90.22
Mother's educational level390.16
P.S.I.A. Cold90.15
P.S.I.A. Cruel90.13
Sex410.13
P.S.I.A. Just90.06
P.S.I.A. Aspergoid90.03
Father's educational level380.01
P.S.I.A. Introverted9-0.01
P.S.I.A. Deviance factor12-0.08
P.S.I.A. Extreme9-0.08
P.S.I.A. Antisocial9-0.17
Year of birth41-0.18
Disorders (parents and siblings)40-0.31
Gifted Adult's Inventory of Aspergerisms6-0.36
Disorders (own)40-0.41

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)
00.87 (547)NaN (0)
48.50.57 (222)0.89 (219)
610.60 (164)0.89 (256)
73.50.61 (12)0.87 (489)
89NaN (0)0.87 (547)

Reliability

This reliability is computed from the two subtest reliabilities using a form of the Spearman-Brown formula.

Error

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).