Statistics of observed associative horizon

© Paul Cooijmans

Introduction

To detect possible correlates of associative horizon, scores have been assigned to candidates displaying a markedly narrow associative horizon (scored as 0) and to candidates displaying a markedly wide associative horizon (1). Without claiming that observed associative horizon is exactly the same as actual associative horizon (that would be easy, if one could just observe a mental faculty directly) the following statistics result:

Scores on Observed associative horizon as of 27 January 2023

Contents type: Observation.   

0 **********************************
1 **************************************

Correlation of Observed associative horizon with other mental ability tests

Test name n r
Cooijmans On-Line Test - Two-barrelled version40.99
A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude70.90
The Alchemist Test40.88
The Nemesis Test80.87
Problems In Gentle Slopes of the second degree40.85
KIT Intelligence Test - first attempts40.83
Analogies #160.83
Cooijmans Intelligence Test - Form 270.81
Cooijmans Intelligence Test - Form 440.80
Numerical section of Test For Genius - Revision 201060.80
California Test of Mental Maturity60.78
Isis Test100.75
Psychometric Qrosswords50.73
Qoymans Multiple-Choice #5100.70
Reason Behind Multiple-Choice - Revision 2008100.67
Cooijmans Intelligence Test - Form 190.65
The Sargasso Test60.62
Titan Test (Ronald K. Hoeflin)90.61
Cartoons of Shock80.61
Analogies of Long Test For Genius130.60
The Final Test180.60
Association subtest of Long Test For Genius160.58
Cooijmans On-Line Test40.58
Problems In Gentle Slopes of the first degree40.56
Unknown and miscellaneous tests370.55
Short Test For Genius140.55
Cooijmans Intelligence Test - Form 390.55
Mega Test (Ronald K. Hoeflin)100.53
Long Test For Genius120.52
Test of the Beheaded Man40.52
Reason Behind Multiple-Choice60.52
Bonsai Test60.51
International High IQ Society tests (aggregate)100.50
Verbal section of Test For Genius - Revision 2004100.48
Lieshout International Mesospheric Intelligence Test90.47
Numbers190.47
Odds40.47
Reason - Revision 2008100.46
Test For Genius - Revision 200480.43
Qoymans Multiple-Choice #4160.41
Gliaweb Riddled Intelligence Test (old version)40.41
Scholastic Aptitude Test (old)70.39
Cooijmans Intelligence Test 550.39
Associative LIMIT40.37
The Test To End All Tests120.35
Spatial section of Test For Genius - Revision 200490.34
Genius Association Test90.24
Space, Time, and Hyperspace180.21
Encephalist - R (Xavier Jouve)40.14
Wechsler Adult Intelligence Scales100.14
Reason80.10
Daedalus Test50.07
Chimera High Ability Riddle Test (Bill Bultas)50.00
Qoymans Multiple-Choice #37-0.02
Qoymans Multiple-Choice #17-0.03
W-87 (International Society for Philosophical Enquiry)7-0.05
Raven's Advanced Progressive Matrices (I.Q.)7-0.06
Graduate Record Examination5-0.12
Non-Verbal Cognitive Performance Examination (Xavier Jouve)6-0.18
Cattell Verbal (also known as Cattell B)5-0.24
Cattell Culture Fair7-0.25
American College Testing program4-0.26
Tests by Greg Grove (aggregate)7-0.26
Culture Fair Numerical Spatial Examination - Final version (Etienne Forsström)8-0.36
Spatial Insight Test4-0.49
Logima Strictica 36 (Robert Lato)4-0.63
Raven's Advanced Progressive Matrices (raw)7-0.68
Words4-0.70
Test of Inductive Reasoning / J.C.T.I. (Xavier Jouve)4-0.80

Weighted average of correlations: 0.389 (N = 559, weighted sum = 217.51)

Conservatively estimated minimum g loading: 0.62

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.

So, observed associative horizon has a loading on general intelligence, not much lower than that of a typical I.Q. test.

Estimated loadings of Observed associative horizon 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 Observed associative horizon on that type
Verbal1380.65
Numerical290.73
Spatial400.48
Logical310.40
Heterogeneous1490.78

N = 387

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

Balanced g loading = 0.61

The fact that the loading on heterogeneous tests is highest also suggests that observed associative horizon is not independent of g.

National means for Observed associative horizon

Country n mean score
United_Kingdom41.00
Netherlands140.64
United_States290.62
Belgium50.60
Canada30.33
Sweden30.33
Germany20.00
Greece30.00

For reasons of privacy, only countries with 2 or more candidates are included in this table. Ranking is based on the unrounded means, and then alphabetic.

Correlation with national I.Q.'s of Observed associative horizon

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

This is significant and remarkably higher than the correlations normally found with national I.Q.'s.

Correlation of Observed associative horizon with personal details

Personalia n r
Observed behaviour450.65
PSIA Cold150.59
PSIA Introverted150.54
PSIA Rare150.39
PSIA Aspergoid150.31
PSIA System factor120.28
PSIA Deviance factor190.27
Disorders (own)460.26
PSIA Introverted - Revision 200760.23
Disorders (parents and siblings)380.18
PSIA Orderly150.18
PSIA True150.18
PSIA Cruel150.15
PSIA Ethics factor190.13
PSIA Extreme150.12
Gifted Adult's Inventory of Aspergerisms130.10
PSIA Antisocial150.06
Sex720.06
PSIA Rational150.06
PSIA Neurotic150.03
Educational level430.02
Mother's educational level36-0.08
Cooijmans Inventory of Neo-Marxist Attitudes9-0.16
PSIA Just15-0.20
Year of birth63-0.24
Father's educational level35-0.24

PSIA Cold and Introverted seem to be the best objective correlates of observed associative horizon. It is remarkable that the correlation with disorders is not negative, which it usually is with I.Q. test scores. While observed associative horizon does correlate positively with g, it seems to differ from g in that it does not correlate negatively with disorders. This concords with the notion that associative horizon is really the disposition for psychosis (but not psychosis itself, it must be stressed; psychosis may be seen as over-inclusive associative horizon).

Correlation with personal details of Observed associative horizon - within females

Personalia n r
Gifted Adult's Inventory of Aspergerisms40.94
Disorders (own)80.77
Disorders (parents and siblings)50.61
Observed behaviour50.17
Father's educational level50.08
Year of birth9-0.06
Educational level6-0.25
Mother's educational level5-0.25

Here too, the correlation with disorders is positive.

Correlation with personal details of Observed associative horizon - within males

Personalia n r
Observed behaviour400.70
PSIA Cold130.57
PSIA Introverted130.47
PSIA Rare130.40
PSIA Aspergoid130.28
PSIA Antisocial130.27
PSIA System factor100.24
PSIA Deviance factor160.20
PSIA Cruel130.19
Disorders (own)380.18
Disorders (parents and siblings)330.16
PSIA Rational130.14
PSIA Orderly130.13
PSIA True130.07
Educational level370.07
PSIA Ethics factor160.05
PSIA Extreme130.02
Mother's educational level31-0.05
Gifted Adult's Inventory of Aspergerisms9-0.06
PSIA Just13-0.09
Cooijmans Inventory of Neo-Marxist Attitudes8-0.22
PSIA Neurotic13-0.27
Father's educational level30-0.27
Year of birth54-0.28

Norming of associative horizon scores to I.Q.

Considering the moderate positive correlation with g, it is meaningful to "norm" the assessments scores of 0 and 1 to protonorms by means of rank equation; I.Q. tests correlating .39 or higher have been used to obtain the below table. Weighted average of correlations: 0.593 (N = 382, weighted sum = 226.44)

A.H.ProtonormI.Q.
0358 (ranging 98-400)132
1487 (402-747)153