Statistics of Culture Fair Numerical Spatial Examination - Final version

Introduction

The scores on this test were provided to me years ago by Etienne Forsström, its constructor. As a result, this sample is complete, and not affected by bias in score reporting by candidates taking tests of mine. There have been several prior versions of this test, and I understand that this final version was formed by leaving out problems from the earlier versions and calculating each candidate's score over the remaining ones. This drastic "pruning" of the test probably explains the block-like shape of the score distribution, with many ceiling and below-threshold scores and no tapering to the high and low end. I do not know if the test has actually been administered in this final form. If so, such would require norms based on those new administrations, because the statistical behaviour of items tends to change when items are placed in a new environment, and norms based on prior versions with more items would likely be too generous for the new administrations.

Scores on Culture Fair Numerical Spatial Examination - Final version

• n: 289
• Median: 9.0
• Quartile deviation: 3.5
• Range: 17
• Maximum possible: 17
• Male median: 9.0 (n = 264)
• Female median: 5.0 (n = 25)
• Resolution: 0.38

Remark: Do notice that the male/female participation and score differences here are highly similar to what is found for other authors' high-range tests. This suggests that these are genuine behavioural sex differences, and not due to bias in tests from any particular author.

Scores by males

n = 264

Scores by females

n = 25

Correlation of Culture Fair Numerical Spatial Examination - Final version with other tests by Paul Cooijmans

Weighted average of correlations: 0.362 (N = 289, weighted sum = 104.53)

Conservatively estimated minimum g loading: 0.60

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 Culture Fair Numerical Spatial Examination - Final version with tests by others

Weighted average of correlations: 0.351 (N = 212, weighted sum = 74.39)

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 Culture Fair Numerical Spatial Examination - Final version 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 = 225

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

Balanced g loading = 0.53

National medians for Culture Fair Numerical Spatial Examination - Final version

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 Culture Fair Numerical Spatial Examination - Final version

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

• r = 0.01 (n = 103)

Correlation of Culture Fair Numerical Spatial Examination - Final version 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.

Remark: For scores of 5 and lower, g loading is negative, meaning that lower scores correspond to higher I.Q.'s there and the norm table would have to be re-entrant. This, together with the fairly low overall g loading and the completeness of the sample (which means that the correlations and g loadings are not affected by bias in score reporting), suggests the presence of a number of items that correlate negatively with total score.

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