Statistics of Sigma Test

Introduction

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

• n: 56
• Median: 158.0
• Quartile deviation: 10.0
• Range: 53
• Male median: 158.0 (n = 55)
• Female median: 145.0 (n = 1)
• Resolution: 0.65

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

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

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.

N = 152

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

Balanced g loading = 0.67

National medians for Sigma Test

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:

• r = -0.01 (n = 50)

Correlation of Sigma Test with personal details

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.

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