Statistics of unknown and miscellaneous tests

Introduction

This report is about scores reported by candidates either without mention of exactly which test it concerned, or from tests that do not have a field of their own in the database. A test may get its own field when there are more than several scores for it, so the composition of the present field may change over time. The scores are expressed on a scale with a mean of 100 and standard deviation of 15. This grouping of tests has consequences; the correlations of this compound variable with other tests may be lower than in single-test reports. This is so because some tests in this field may yield systematically higher scores than others, or correlate imperfectly with others, which, when combined, reduces or even inverts the correlations that the individual tests may have. Nevertheless, some useful information is retained in this field, hence this report.

Scores on Miscellaneous tests as of 19 August 2026

• n: 465
• Mean: 135.1
• Standard deviation: 14.92
• Male mean: 136.0 (n = 389)
• Female mean: 130.2 (n = 71)
• Unknown sex mean: 133.0 (n = 5)
• Proportion of males among candidates: 0.837
• Resolution: 6.5

Do notice that despite the incongruous grouping of many tests, the shape and range of the distribution closely resemble those of the known high-range distribution.

Scores by males

n = 389

Scores by females

n = 71

Correlation of Miscellaneous tests with other mental ability tests

Weighted mean of correlations: 0.400 (N = 3030)

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.

Remark: As can be expected when grouping a hotchpotch of tests, the correlations with other tests are lower on average than they are for single tests.

Estimated loadings of Miscellaneous tests 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 = 2109

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

Balanced g loading = 0.58

National means for Miscellaneous tests

Total number of countries: 51

For reasons of privacy, only countries with 3 or more candidates are included in this table. Ranking is based on the unrounded means, and then alphabetic.

Correlation of Miscellaneous tests with personal details

Notice: A correlation is generally considered significant if its p value is 0.05 or less.

Do notice that even within this mixture of reported test scores, the negative correlation with disorders (including its approximate size) is firmly established. The same for the surprisingly small size of the correlation with educational level. Both phenomena have been observed for decades in data from high-range tests, and sometimes met with disbelief and resistance from people who insist that persons of high intelligence must be suffering more from psychiatric disorders, and that I.Q. must correlate highly with educational level. It seems though that the highly intelligent suffer less, and that higher education requires only marginally more intelligence.

Correlation with personal details of Miscellaneous tests - within females

Correlation with personal details of Miscellaneous tests - within males

Estimated g factor loadings for restricted ranges

The goal of estimated g factor loadings for restricted ranges 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

The reliability of these reported unknown and miscellaneous test scores can obviously not be computed because there is no actual test and therefore no internal data, but from the g loading it can be surmised that the reliability should be at least .63 (because the g loading can not be higher than the reliability).

Error of measurement

From the estimated reliability it follows that the standard error of measurement of these reported scores is at most 9.1 I.Q. points. That is a large error; it means that if someone quotes a certain I.Q. without identifying the test, that person's true I.Q. is with 95 % confidence within plus or minus 18.2 points from it.

[More statistical reports]