Statistics of Numbers

Introduction

This was a number series test; very unfortunately, criminals are publishing many number series from tests with the answers on the Internet without permission from the tests' authors. It is therefore easy to cheat on such tests, and unwise to accept the tests' scores for admission to I.Q. societies.

I regret this problem especially in the case of this particular test, because originally it was an integral part of my Test For Genius from 1995. After discovering the copyright violation I felt forced to violate the integrity of that extremely beautiful, profound and brilliant creation by removing the numerical subtest. It is sad, but apparently there are people whose dishonesty and desire to help other dishonest persons - cheaters - is so great that they completely disregard intellectual property and the natural necessity to keep test answers secret. Our contempt for them can never be deep enough.

Scores on Numbers as of 13 February 2023

Contents type: Numerical.   Period: 1995-2010

• n: 120
• Median: 11.0
• Quartile deviation: 2.0
• Range: 15
• Maximum possible: 20
• Male median: 11.0 (n = 114)
• Female median: 10.0 (n = 6)
• Proportion of males among candidates: 0.950
• Hardness: 0.40
• Resolution: 0.29

Scores by males

n = 114

Scores by females

n = 6

Correlation of Numbers with other mental ability tests

Weighted average of correlations: 0.399 (N = 980)

Estimated g factor loading: 0.63

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 Numbers 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 = 715

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

Balanced g loading = 0.67

National medians for Numbers

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 with national I.Q.'s of Numbers

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

• r = 0.04 (n = 108)

Correlation of Numbers with personal details

Correlation with personal details of Numbers - within females

Correlation with personal details of Numbers - within males

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.

Reliability

• Split-half (odd-even) = 0.84
• Split-half (1, 2… 5, 6… vs. 3, 4… 7, 8…) = 0.86
• Cronbach's alpha = 0.79

Error

• Standard error = 1.4 raw score points

Scores by age

N = 106

Scores by age - within females

N = 6

Scores by age - within males

N = 100

Scores by year taken

r_{year taken × median score} = 0.41 (N = 118)

Robustness and overall test quality

• Robustness by month = 0.75 (r_{raw scores × months} = -0.12)
• Quality = 0.629

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.

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