Statistics of Numerical section of The Marathon Test

© Paul Cooijmans

Scores on Numerical section of The Marathon Test as of 8 November 2020

Contents type: Numerical.   Period: 2005-present

0 *
6 *
8 *
9 *
11 *
12 **
17 *
18 *
22 *
23 **
25 *
32 **
33 **
34 *
36 ****
37 ****
38 *
39 ***
40 ***
41 ****
42 *
43 ******
44 *****

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

(Test index) Test name n r
(45) Numerical and spatial sections of The Marathon Test470.95
(21) Psychometric Qrosswords90.94
(42) The Marathon Test310.93
(43) Test For Genius - Revision 201090.90
(7) The Final Test80.90
(48) Narcissus' last stand90.88
(1) Cartoons of Shock90.87
(87) Cooijmans Intelligence Test - Form 290.86
(36) Reflections In Peroxide120.85
(0) Test of the Beheaded Man160.84
(28) The Test To End All Tests120.83
(47) Psychometrically Activated Grids Acerbate Neuroticism80.83
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 2010130.81
(32) Spatial section of The Marathon Test480.81
(107) The Alchemist Test70.80
(114) Dicing with death50.79
(27) Spatial section of Test For Genius - Revision 2004180.79
(40) Reason Behind Multiple-Choice - Revision 2008130.77
(16) Lieshout International Mesospheric Intelligence Test170.76
(2) Cooijmans Intelligence Test - Form 3250.76
(26) Verbal section of Test For Genius - Revision 2004150.76
(66) Test For Genius - Revision 200480.75
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 2016110.73
(23) Gliaweb Riddled Intelligence Test - Revision 2011150.72
(35) Intelligence Quantifier by assessment140.71
(44) Associative LIMIT120.71
(30) Verbal section of The Marathon Test310.70
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude90.70
(111) Test For Genius - Revision 201690.69
(12) Cooijmans On-Line Test - Two-barrelled version100.68
(19) Numerical section of Test For Genius - Revision 2010190.68
(105) Space, Time, and Hyperspace - Revision 2016110.68
(103) Problems In Gentle Slopes of the second degree140.67
(106) Cooijmans Intelligence Test - Form 4140.66
(18) The Nemesis Test130.66
(24) Reason - Revision 2008140.64
(109) The Bonsai Test - Revision 2016110.63
(117) The Hammer Of Test-Hungry - Revision 201360.60
(25) The Sargasso Test150.59
(33) Problems In Gentle Slopes of the first degree80.59
(3) Qoymans Multiple-Choice #5130.57
(10) Genius Association Test120.57
(11) Isis Test110.57
(108) Verbal section of Test For Genius - Revision 201690.53
(46) Labyrinthine LIMIT60.52
(37) Problems In Gentle Slopes of the third degree80.49
(15) Letters40.47
(5) Daedalus Test120.47
(82) Reason40.46
(110) Cooijmans Intelligence Test 580.43
(41) The LAW - Letters And Words40.41
(104) The Final Test - Revision 201370.37
(29) Words60.36
(80) Qoymans Multiple-Choice #450.15
(62) Reason Behind Multiple-Choice4-0.07

Weighted average of correlations: 0.724 (N = 697, weighted sum = 504.85)

Conservatively estimated minimum g loading: 0.85

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 section of The Marathon Test with tests by others

(Test index) Test name n r
(231) Mysterium Entrance Exam40.88
(211) Culture Fair Numerical Spatial Examination - Final version40.85
(238) 916 Test40.78
(225) Logima Strictica 3670.49
(234) Strict Logic Sequences Exam I90.41
(240) Strict Logic Spatial Exam 4880.15
(242) Unknown and miscellaneous tests180.08
(223) Strict Logic Sequences Exam II40.00
(201) Wechsler Adult Intelligence Scales4-0.32

Weighted average of correlations: 0.299 (N = 62, weighted sum = 18.54)

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 section 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 section of The Marathon Test on that type
Verbal1350.80
Numerical190.83
Spatial940.88
Logical300.74
Heterogeneous2190.84

N = 497

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

Balanced g loading = 0.82

National medians for Numerical section of The Marathon Test

Country n median score
Australia241.5
China241.0
Belgium240.5
Germany340.0
Spain239.0
United_Kingdom237.0
Korea_South336.0
India234.5
Finland429.5
Canada226.0
United_States1122.0

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 section of The Marathon Test

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

Correlation of Numerical section of The Marathon Test with personal details

Personalia n r
P.S.I.A. Neurotic - Revision 200770.94
P.S.I.A. True - Revision 200770.83
P.S.I.A. Ethics factor - Revision 200770.74
P.S.I.A. Orderly - Revision 200770.55
P.S.I.A. System factor - Revision 200770.53
P.S.I.A. Rational - Revision 200770.49
Observed behaviour90.49
Educational level480.45
P.S.I.A. Cold - Revision 200770.38
P.S.I.A. Introverted - Revision 200770.26
Cooijmans Inventory of Neo-Marxist Attitudes40.17
P.S.I.A. Just - Revision 200770.10
Mother's educational level460.07
Sex490.05
P.S.I.A. Aspergoid - Revision 20077-0.01
P.S.I.A. Rare - Revision 20077-0.04
Father's educational level45-0.05
P.S.I.A. Deviance factor - Revision 20077-0.06
Year of birth49-0.15
P.S.I.A. Extreme - Revision 20077-0.15
P.S.I.A. Antisocial - Revision 20077-0.18
P.S.I.A. Cruel - Revision 20077-0.23
Gifted Adult's Inventory of Aspergerisms6-0.24
Disorders (parents and siblings)47-0.32
Disorders (own)47-0.45

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)
00.85 (697)NaN (0)
50.84 (680)NaN (0)
130.76 (510)0.49 (121)
210.72 (488)0.54 (142)
290.54 (406)0.68 (241)
330.55 (367)0.81 (358)
370.52 (230)0.82 (445)
390.44 (155)0.82 (476)
420.30 (67)0.83 (540)
44NaN (0)0.85 (697)

The decrease in upward g loading toward the maximum score is probably caused by the fact that the test is a bit too easy and has received multiple perfect and near-perfect scores.

Reliability

Reliability is excellent and reflects the facts that there are no problematic items and the test is long enough. However, this excellent reliability of a too easy test also demonstrates that the reliability coefficient in itself is not a sufficient indicator of test quality.

Error

Scores by age

Age class n median score
65 to 69228.5
55 to 59240.5
50 to 54221.5
45 to 49641.0
40 to 44839.5
35 to 39732.0
30 to 34437.5
25 to 29829.0
22 to 24341.0
20 or 21343.0
18 or 19336.0
17133.0

N = 49

Scores by year taken

Year taken n median score
2005140.0
2006536.0
2007143.0
2008139.0
2009241.0
2010430.0
2011143.0
2012430.5
2013221.5
2014438.5
2015224.5
2016837.5
2017225.5
2018339.0
2019633.0
2020341.0

ryear taken × median score = -0.27 (N = 49)

Robustness and overall test quality

Item analysis

Item statistics are not published as that would help future candidates. To detect bad items, answers and comments from candidates are studied, as well as, for each problem, the correlation with total score and the proportion of candidates getting it wrong (hardness of the item). Possible bad items are removed or revised, resulting in a revised version of the test. No bad items have been found in this test.