Statistics of Numerical section of The Marathon Test

© July 2016 Paul Cooijmans

Norms

Scores on Numerical section of The Marathon Test

Contents type: Numerical.   Period: 2005-present

0 *
6 *
8 *
9 *
17 *
23 **
25 *
32 *
34 *
36 ***
37 ***
39 **
40 **
41 ***
42 *
43 *****
44 *

Scores by males

n = 28

0 *
8 *
9 *
17 *
23 **
25 *
32 *
34 *
36 ***
37 ***
39 **
40 **
41 ***
42 *
43 *****

Scores by females

n = 2

6 *
44 *

Correlation of Numerical section of The Marathon Test with other tests by Paul Cooijmans

(Test index) Test name n r
(36) Reflections In Peroxide50.97
(45) Numerical and spatial sections of The Marathon Test270.96
(0) Test of the Beheaded Man70.94
(7) The Final Test60.94
(42) The Marathon Test230.94
(12) Cooijmans On-Line Test - Two-barrelled version50.93
(48) Narcissus' last stand50.91
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude50.88
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 201080.88
(3) Qoymans Multiple-Choice #570.88
(2) Cooijmans Intelligence Test - Form 3120.88
(87) Cooijmans Intelligence Test - Form 280.87
(19) Numerical section of Test For Genius - Revision 201090.87
(27) Spatial section of Test For Genius - Revision 2004130.86
(1) Cartoons of Shock80.85
(43) Test For Genius - Revision 201060.85
(40) Reason Behind Multiple-Choice - Revision 200870.84
(23) Gliaweb Riddled Intelligence Test - Revision 201160.83
(32) Spatial section of The Marathon Test290.83
(25) The Sargasso Test70.83
(28) The Test To End All Tests70.82
(16) Lieshout International Mesospheric Intelligence Test100.79
(26) Verbal section of Test For Genius - Revision 2004120.77
(24) Reason - Revision 200880.71
(44) Associative LIMIT70.69
(5) Daedalus Test50.69
(30) Verbal section of The Marathon Test230.68
(35) Intelligence Quantifier by assessment100.68
(18) The Nemesis Test100.68
(11) Isis Test60.65
(33) Problems In Gentle Slopes of the first degree50.54
(10) Genius Association Test70.44
(29) Words60.36
(66) Test For Genius - Revision 20046-0.31

Weighted average of correlations: 0.788

Conservatively estimated minimum g loading: 0.89

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 section of The Marathon Test with tests by others

(Test index) Test name n r
(234) Strict Logic Sequences Exam I70.36
(240) Strict Logic Spatial Exam 485-0.01
(242) Unknown and miscellaneous tests11-0.10
(225) Logima Strictica 365-0.43

Weighted average of correlations: -0.031

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 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.

Typeg loading of Numerical section of The Marathon Test on that type
Verbal0.84
Numerical0.93
Spatial0.91
Logical0.84
Heterogeneous0.91

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

Balanced g loading = 0.88

National medians for Numerical section of The Marathon Test

Country n median score
Australia241.5
Korea_South239.5
United_Kingdom237.0
Finland336.0
India234.5
Canada226.0
Germany221.5
United_States412.5

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 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
Observed associative horizon31.00
P.S.I.A. True70.83
P.S.I.A. Ethics factor100.70
P.S.I.A. Neurotic70.52
P.S.I.A. Orderly70.46
Educational level290.38
Candidate's self-estimated I.Q.60.36
P.S.I.A. System factor70.35
P.S.I.A. Rational70.24
Sex300.16
P.S.I.A. Cold70.12
Mother's educational level280.03
P.S.I.A. Cruel7-0.01
P.S.I.A. Rare7-0.05
P.S.I.A. Aspergoid7-0.05
P.S.I.A. Introverted7-0.07
P.S.I.A. Just7-0.11
Year of birth30-0.18
P.S.I.A. Extreme7-0.19
P.S.I.A. Antisocial7-0.27
Father's educational level27-0.30
P.S.I.A. Deviance factor10-0.34
Disorders (parents and siblings)29-0.36
Disorders (own)29-0.59
Gifted Adult's Inventory of Aspergerisms3-0.99

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)
00.89 (326)NaN (0)
290.59 (127)0.87 (74)
370.54 (76)0.89 (165)
390.58 (46)0.89 (173)
410.49 (30)0.88 (234)
420.79 (12)0.88 (239)
430.63 (10)0.89 (320)
44NaN (0)0.89 (326)

Reliability

These are very high reliabilities, corresponding to the fact that, in item analysis, all of the items perform excellently.

Error

Scores by age

Age class n median score
55 to 59137.0
50 to 54221.5
45 to 49541.0
40 to 44639.5
35 to 39532.0
30 to 34243.0
25 to 2959.0
22 to 24143.0
20 or 21143.0
18 or 19238.0

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
2016337.0

ryear taken × median score = -0.48 (n = 30)

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.