Statistics of Letters

Norms

Scores on Letters

Contents type: Verbal.   Period: 2003-present

• n: 22
• Median: 38.5
• Quartile deviation: 2.5
• Range: 28
• Maximum possible: 40
• Male median: 38.5 (n = 20)
• Female median: 34.0 (n = 2)
• Hardness: 0.04
• Resolution: 0.32

Correlation of Letters with other tests by Paul Cooijmans

Weighted average of correlations: 0.562

Conservatively estimated minimum g loading: 0.75

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 Letters with tests by others

Weighted average of correlations: 0.170

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 Letters 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 = 0.72

National medians for Letters

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 Letters

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

• r = -0.05 (n = 22)

Correlation of Letters 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.

Reliability

• Split-half (odd-even) = 0.97
• Split-half (other division) = 0.96
• Cronbach's alpha = 0.95

Error

• Standard error = 1.5 raw score points

Scores by age

Scores by year taken

r_{year taken × median score} = 0.15 (n = 22)

Robustness and overall test quality

• Robustness by chronological rank = 0.79
• Robustness by month = 0.76
• Quality = 0.65

Item analysis

Item statistics are not published as that would help future candidates. To detect bad items, answers and comments from candidates are studied, as well as, for each problem, the correlation with total score and the proportion of candidates getting it wrong (hardness of the item). Possible bad items are removed or revised, resulting in a revised version of the test.

The items of this test perform well in item analysis, which is also expressed in the very high reliability of the test.