Statistics of Psychometric Qrosswords

Scores on Psychometric Qrosswords as of 29 November 2022

Contents type: Verbal.   Period: 2001-present

• n: 25
• Median: 67.0
• Quartile deviation: 8.5
• Range: 80
• Maximum possible: 80
• Male median: 67.0 (n = 24)
• Female median: 5.0 (n = 1)
• Resolution: 0.60

Correlation of Psychometric Qrosswords with other mental ability tests

Weighted average of correlations: 0.723 (N = 502, weighted sum = 363.02)

Conservatively estimated minimum g loading: 0.85

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 Psychometric Qrosswords 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 = 374

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

Balanced g loading = 0.86

National medians for Psychometric Qrosswords

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 Psychometric Qrosswords

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

• r = 0.16 (n = 24)

Correlation of Psychometric Qrosswords 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: The upward g loading from somewhere in the 50s on is low. This seems to be caused by a small number of candidates with (for them) atypical scores on this test and many scores on other tests. As more people take the test, this may either improve, or may turn out to be a real problem.

Reliability

• Split-half (odd-even) = 0.99
• Split-half (1, 2… 5, 6… vs. 3, 4… 7, 8…) = 0.97
• Cronbach's alpha = 0.98

Notice that the very high reliability of this test may be partly due to its being arranged in crosswords, which causes groups of items to be interdependent to some extent.

Error

• Standard error = 2.7 raw score points

Scores by age

N = 25

Scores by year taken

r_{year taken × median score} = -0.18 (N = 25)

Robustness and overall test quality

• Robustness by chronological rank = 0.78
• Robustness by month = 0.77 (r_{raw scores × months} = -0.20)
• Quality = 0.753

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. So far, no bad items have been identified in this test.

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