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. There exist so many tests that is not doable to give them each a field. The scores are expressed on a scale with a mean of 100 and standard deviation of 16, because that is the scale that was most used years ago when this field was conceived. This grouping of tests has consequences; the correlations with other tests and g loading are lower than in single-test reports. This is so because some tests may yield systematically higher scores than others, which, when combined, reduces or even inverts the correlations that the individual tests may have (such inversion is known as "Simpson's paradox"). Nevertheless, some useful information is retained in this field, hence this report.

Scores on Unknown and miscellaneous tests as of 23 September 2019

• n: 400
• Median: 140.0
• Quartile deviation: 7.5
• Range: 104
• Male median: 141.0 (n = 340)
• Female median: 138.0 (n = 53)
• Resolution: 0.56

Do notice that despite the incongruous grouping of many tests, and taking into account the standard deviation of 16, the shape and range of the distribution closely resemble those of the known high-range distribution.

Scores by males

n = 340

Scores by females

n = 53

Correlation of Unknown and miscellaneous tests with other tests by Paul Cooijmans

Weighted average of correlations: 0.241 (weighted sum: 404.55)

Conservatively estimated minimum g loading: 0.49

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 5 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 much lower on average than they are for single tests. Each test on its own may have a much higher g loading than this.

Correlation of Unknown and miscellaneous tests with tests by others

Weighted average of correlations: 0.352 (weighted sum: 216.64)

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 5 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.

Remark: The fact that the correlations with tests by others are somewhat higher than with tests by Paul Cooijmans may be caused by the circumstance that both the "Unknown and miscellaneous" scores and the "tests by others" scores are self-reported by candidates, and thus subject to the same bias (candidates tend to report their higher scores and withhold the lower ones).

Correlation of Unknown and miscellaneous tests with other tests by Paul Cooijmans - for females

Weighted average of correlations: 0.437

Conservatively estimated minimum g loading among females: 0.66

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 2 score pairs. All known pairs are used, including possible floor/ceiling scores or outliers.

Remark: Just as with single-test reports, the g loading within females is higher than the overall g loading. This is something that needs to be verified further as more data comes in, but it seems that high-range tests measure g better in females than in males.

Estimated loadings of Unknown and 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.

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

Balanced g loading = 0.43

National medians for Unknown and miscellaneous tests

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 Unknown and miscellaneous tests

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

• r = -0.06 (n = 314)

Correlation of Unknown and miscellaneous tests with personal details

Remark: Here, too, the correlations are much lower on the whole than in single-test reports.

Correlation with personal details of Unknown and miscellaneous tests - within females

Remark: The correlations within females are in some respects different from those within males. This suggests that, in general, statistics should be provided and studied within-sex when possible, to prevent the obfuscation of correlations or trends that may occur in sex-combined statistics.

Correlation with personal details of Unknown and miscellaneous tests - within males

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.

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 loadings it can be surmised that the reliability should be at least .5 (because the g loading can not be higher than the reliability). The higher g loading among females suggests a higher reliability for females, like around .7 or more

Error of measurement

From the estimated reliability it follows that the standard error of measurement of these reported scores is at most 9.2 I.Q. points (remember that the scale has a standard deviation of 16 here). 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 18.4 points from it. For females, the error would be at most 7.1 I.Q. points.