Statistics of Sigma Test

© January 2020 Paul Cooijmans


These statistics are based on scores on this test as reported by candidates taking I.Q. tests from I.Q. Tests for the High Range.

Scores on Sigma Test as of 22 January 2020

127 *
130 *
133 *
135 *
138 *
139 *
140 *
141 *
142 **
142.7 *
144 **
145 **
145.1 *
146 *
146.2 *
146.5 *
151 *
152 **
153 *
154 **
157 **
158 *****
160 ***
162 *
163 *
164 ****
165 ***
166 ***
166.5 *
166.6 *
167 *
168 **
169 *
171 **
180 *

Remark: These statistics suffer from the fact that the score reports for this test, bizarrely, give an astounding number of widely different "I.Q.'s" for one and the same test administration. Candidates may have reported any one thereof, possibly with an ever so slight bias toward the highest, which explains the ridiculously high median and obvious over-representation of scores in the 150-170 range. Basically, the scores are almost 20 points too high on average.

Correlation of Sigma Test with other tests by I.Q. Tests for the High Range

(Test index) Test name n r
(35) Intelligence Quantifier by assessment40.95
(16) Lieshout International Mesospheric Intelligence Test40.90
(26) Verbal section of Test For Genius - Revision 200460.87
(54) Test of Shock and Awe40.77
(68) Numbers140.71
(66) Test For Genius - Revision 200460.70
(55) Spatial Insight Test50.65
(28) The Test To End All Tests50.64
(86) Evens50.63
(7) The Final Test70.52
(85) Cooijmans Intelligence Test - Form 180.52
(79) Association subtest of Long Test For Genius110.49
(53) Qoymans Multiple-Choice #3140.48
(87) Cooijmans Intelligence Test - Form 240.34
(27) Spatial section of Test For Genius - Revision 200460.29
(51) Qoymans Multiple-Choice #160.27
(63) Long Test For Genius100.22
(57) Space, Time, and Hyperspace220.21
(75) Analogies of Long Test For Genius120.14
(84) Bonsai Test60.08
(80) Qoymans Multiple-Choice #4130.01

Weighted average of correlations: 0.426 (N = 172, weighted sum = 73.21)

Conservatively estimated minimum g loading: 0.65

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 Sigma Test with tests by others

(Test index) Test name n r
(223) Strict Logic Sequences Exam II40.98
(238) 916 Test40.96
(234) Strict Logic Sequences Exam I60.84
(211) Culture Fair Numerical Spatial Examination - Final version60.60
(236) International High IQ Society Miscellaneous tests50.59
(229) Mega Test40.58
(240) Strict Logic Spatial Exam 4840.55
(225) Logima Strictica 36100.53
(242) Unknown and miscellaneous tests270.40
(235) Nonverbal Cognitive Performance Examination110.28
(231) Mysterium Entrance Exam60.26
(218) Raven's Advanced Progressive Matrices (I.Q.)70.15
(220) Cattell Culture Fair5-0.19

Weighted average of correlations: 0.451 (N = 99, weighted sum = 44.70)

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 Sigma 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 Sigma Test on that type

N = 152

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

Balanced g loading = 0.67

National medians for Sigma Test

Country n median score

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 Sigma Test

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

Correlation of Sigma Test with personal details

Personalia n r
Educational level230.25
Mother's educational level210.22
Father's educational level210.05
Disorders (parents and siblings)23-0.05
Year of birth51-0.12
Disorders (own)25-0.13
Observed behaviour6-0.30
Gifted Adult's Inventory of Aspergerisms10-0.56

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)
1250.70 (238)NaN (0)
1380.72 (206)1.00 (6)
1480.69 (132)0.41 (58)
1580.72 (97)0.44 (96)
1680.77 (22)0.59 (212)
180NaN (0)0.70 (238)