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 4 February 2021

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

0 *
6 *
12 **
17 **
18 *
21 *
22 *
32 *
37 *
38 *
42 *
42.2 *
45 *
48 *
48.5 *
54 **
56.2 *
58 *
59 *
61 **
62 *
63 ***
64 ***
66.2 *
67 *
68 *
69 *
70 **
71 *
72 *
74 **
79 *
80 *
82 *
83 *
85 *
87 *
89 **

Scores by males

n = 46

0 *
12 **
17 **
18 *
21 *
22 *
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 *
72 *
74 *
79 *
80 *
82 *
83 *
85 *
87 *
89 **

Scores by females

n = 3

6 *
68 *
74 *

Correlation of Numerical and spatial sections of The Marathon Test with other tests by I.Q. Tests for the High Range

(Test index) Test name n r
(113) The Piper's Test50.96
(32) Spatial section of The Marathon Test490.96
(31) Numerical section of The Marathon Test490.95
(0) Test of the Beheaded Man160.93
(42) The Marathon Test310.93
(107) The Alchemist Test80.92
(48) Narcissus' last stand90.90
(7) The Final Test70.89
(21) Psychometric Qrosswords90.89
(43) Test For Genius - Revision 201080.89
(114) Dicing with death60.88
(1) Cartoons of Shock90.87
(111) Test For Genius - Revision 201690.86
(36) Reflections In Peroxide120.85
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 2016120.83
(28) The Test To End All Tests120.82
(105) Space, Time, and Hyperspace - Revision 2016120.81
(23) Gliaweb Riddled Intelligence Test - Revision 2011160.79
(40) Reason Behind Multiple-Choice - Revision 2008140.78
(44) Associative LIMIT120.78
(16) Lieshout International Mesospheric Intelligence Test170.78
(87) Cooijmans Intelligence Test - Form 290.77
(47) Psychometrically Activated Grids Acerbate Neuroticism80.76
(110) Cooijmans Intelligence Test 590.74
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude100.74
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 2010120.74
(109) The Bonsai Test - Revision 2016130.74
(2) Cooijmans Intelligence Test - Form 3260.74
(35) Intelligence Quantifier by assessment140.74
(106) Cooijmans Intelligence Test - Form 4150.73
(108) Verbal section of Test For Genius - Revision 201690.73
(3) Qoymans Multiple-Choice #5140.72
(33) Problems In Gentle Slopes of the first degree90.72
(103) Problems In Gentle Slopes of the second degree130.72
(18) The Nemesis Test130.71
(27) Spatial section of Test For Genius - Revision 2004170.71
(30) Verbal section of The Marathon Test310.70
(12) Cooijmans On-Line Test - Two-barrelled version100.70
(10) Genius Association Test120.70
(19) Numerical section of Test For Genius - Revision 2010200.68
(11) Isis Test120.64
(66) Test For Genius - Revision 200480.64
(37) Problems In Gentle Slopes of the third degree80.63
(26) Verbal section of Test For Genius - Revision 2004140.63
(15) Letters40.61
(25) The Sargasso Test150.59
(41) The LAW - Letters And Words40.59
(117) The Hammer Of Test-Hungry - Revision 201360.56
(24) Reason - Revision 2008150.55
(5) Daedalus Test120.44
(29) Words60.27
(104) The Final Test - Revision 201370.27
(80) Qoymans Multiple-Choice #450.25
(46) Labyrinthine LIMIT60.23
(62) Reason Behind Multiple-Choice4-0.09
(82) Reason4-0.35

Weighted average of correlations: 0.751 (N = 716, weighted sum = 537.40)

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 4 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
(211) Culture Fair Numerical Spatial Examination - Final version50.87
(201) Wechsler Adult Intelligence Scales40.77
(231) Mysterium Entrance Exam40.70
(225) Logima Strictica 3670.54
(240) Strict Logic Spatial Exam 4880.37
(234) Strict Logic Sequences Exam I90.30
(242) Unknown and miscellaneous tests180.23
(223) Strict Logic Sequences Exam II4-0.50

Weighted average of correlations: 0.369 (N = 59, weighted sum = 21.75)

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.

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.

Typeng loading of Numerical and spatial sections of The Marathon Test on that type
Verbal1340.82
Numerical690.93
Spatial950.93
Logical310.63
Heterogeneous2340.87

N = 563

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

Balanced g loading = 0.83

National medians for Numerical and spatial sections of The Marathon Test

Country n median score
Japan286.0
Spain477.0
United_Kingdom271.5
Belgium263.0
Germany358.0
India255.5
Finland450.5
Korea_South345.0
Canada239.5
United_States1032.1

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
P.S.I.A. True - Revision 200790.71
P.S.I.A. Ethics factor - Revision 200790.67
P.S.I.A. Orderly - Revision 200790.65
P.S.I.A. Rational - Revision 200790.47
P.S.I.A. Neurotic - Revision 200790.43
P.S.I.A. System factor - Revision 200790.41
Educational level490.37
Cooijmans Inventory of Neo-Marxist Attitudes50.33
P.S.I.A. Introverted - Revision 200790.30
P.S.I.A. Cold - Revision 200790.29
Observed behaviour90.08
Sex490.06
Mother's educational level47-0.00
P.S.I.A. Deviance factor - Revision 20079-0.05
P.S.I.A. Aspergoid - Revision 20079-0.05
P.S.I.A. Just - Revision 20079-0.05
P.S.I.A. Extreme - Revision 20079-0.06
Father's educational level46-0.07
Year of birth49-0.13
Gifted Adult's Inventory of Aspergerisms7-0.16
Disorders (own)48-0.29
Disorders (parents and siblings)48-0.31
P.S.I.A. Cruel - Revision 20079-0.31
P.S.I.A. Antisocial - Revision 20079-0.40
P.S.I.A. Rare - Revision 20079-0.52

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 (716)NaN (0)
200.76 (534)0.73 (108)
340.71 (489)0.74 (170)
480.57 (397)0.83 (302)
620.62 (282)0.83 (379)
690.62 (73)0.85 (561)
760.78 (24)0.86 (631)

Reliability

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.

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).