Statistics of Letters

© Paul Cooijmans

Scores on Letters as of 10 February 2025

Contents type: Verbal.   Period: 2003-2016

12 *
29 **
30 *
34 *
35 **
36 **
38 **
39 *****
40 ******

Correlation of Letters with other mental ability tests

Test name n r
Problems In Gentle Slopes of the third degree40.99
The LAW - Letters And Words190.98
Problems In Gentle Slopes of the first degree40.97
Words190.95
Verbal section of The Marathon Test60.85
Epiq Tests (aggregate)40.85
Reflections In Peroxide40.84
Numbers40.80
Narcissus' last stand40.77
Test For Genius - Revision 201060.76
Cooijmans On-Line Test - Two-barrelled version40.73
Verbal section of Test For Genius - Revision 200490.72
The Marathon Test50.67
Test of the Beheaded Man50.65
Cartoons of Shock70.63
Verbal section of Test For Genius - Revision 201650.62
Numerical and spatial sections of The Marathon Test40.61
Lieshout International Mesospheric Intelligence Test70.60
Test For Genius - Revision 201650.58
Numerical section of The Marathon Test50.55
Cooijmans Intelligence Test 540.55
Test For Genius - Revision 200440.53
Combined Numerical and Spatial sections of Test For Genius - Revision 201660.53
Associative LIMIT70.51
Numerical section of Test For Genius - Revision 201090.50
The Test To End All Tests80.50
Spatial section of The Marathon Test50.47
The Nemesis Test60.44
Space, Time, and Hyperspace - Revision 201660.43
Isis Test90.42
The Sargasso Test70.40
Genius Association Test110.39
The Bonsai Test - Revision 201660.38
The Final Test70.38
Combined Numerical and Spatial sections of Test For Genius - Revision 201070.34
Cooijmans Intelligence Test - Form 450.30
Cooijmans Intelligence Test - Form 370.29
Qoymans Multiple-Choice #590.27
Reason Behind Multiple-Choice - Revision 200890.26
Spatial section of Test For Genius - Revision 200490.26
The Final Test - Revision 201340.24
Reason - Revision 200890.19
Problems In Gentle Slopes of the second degree40.18
Miscellaneous tests80.03
Gliaweb Riddled Intelligence Test - Revision 20119-0.01
A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude6-0.04
Qoymans Multiple-Choice #44-0.13
Strict Logic Sequences Exam I (Jonathan Wai)5-0.19
Sequentia Numerica Form I (Alexander Herkner)4-0.34
Association subtest of Long Test For Genius5-0.51

Weighted mean of correlations: 0.477 (N = 329)

Estimated g factor loading: 0.69

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 Letters 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 Letters on that type
Verbal1060.77
Numerical230.65
Spatial270.65
Logical90.43
Heterogeneous910.66

N = 256

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

Balanced g loading = 0.63

National medians for Letters

Country n median score
United_States939.0

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 Letters with personal details

Personalia n r
PSIA Orderly - Revision 200740.91
Gifted Adult's Inventory of Aspergerisms80.89
PSIA Rational - Revision 200740.70
Observed behaviour40.67
PSIA Ethics factor - Revision 200740.56
PSIA True - Revision 200740.49
Educational level210.27
PSIA System factor - Revision 200740.20
Disorders (parents and siblings)210.11
Sex220.09
PSIA Just - Revision 200740.07
PSIA Neurotic - Revision 200740.06
Year of birth22-0.10
PSIA Cruel - Revision 20074-0.13
PSIA Aspergoid - Revision 20074-0.14
PSIA Cold - Revision 20074-0.32
Disorders (own)21-0.33
Father's educational level19-0.34
Mother's educational level20-0.48
PSIA Introverted - Revision 20074-0.67
PSIA Extreme - Revision 20074-0.69
PSIA Rare - Revision 20074-0.73
PSIA Deviance factor - Revision 20074-0.77
PSIA Antisocial - Revision 20074-0.84

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 quartile (raw 35.0)0.52 (43)
Below median (raw 38.5)0.64 (174)
Above median (raw 38.5)0.63 (83)
Above 3rd quartile (raw 40.0)NaN (0)

Reliability analysis for Letters

Error

Scores by age for Letters

Age class n Median score
50 to 54234.0
45 to 49339.0
40 to 44234.0
35 to 39239.5
30 to 34140.0
25 to 29436.5
22 to 24140.0
20 or 21438.0
17336.0

N = 22

Scores by year taken for Letters

Year taken n Median scoreprotonorm
2003336.0367
2004232.5355
2005237.0371
2007140.0440
2008140.0440
2010239.5423
2011234.5357
2012138.0376
2013234.0356
2014238.5391
2015437.0371

N = 22

Robustness and overall test quality for Letters

Item analysis

Item statistics are not published as that would help candidates. To detect bad items, answers and comments from candidates are studied, as well as, for each problem, the correlation with total score on the remaining problems (item-rest correlation) and the proportion of candidates getting it wrong (hardness of the item). Possible bad items are revised, replaced, or removed, possibly resulting in a revised version of the test.