Statistics of The LAW

Scores on The LAW - Letters And Words as of 11 February 2025

Contents type: Verbal.   Period: 2003-2016

• n: 19
• Median: 75.0
• Quartile deviation: 5.0
• Maximum possible: 80
• Male median: 76.0 (n = 17)
• Female median: 66.0 (n = 2)
• Proportion of males among candidates: 0.895
• Hardness: 0.06
• Resolution: 5.0

Correlation of The LAW - Letters And Words with other mental ability tests

Weighted mean of correlations: 0.485 (N = 291)

Estimated g factor loading: 0.70

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 The LAW - Letters And Words 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 = 227

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

Balanced g loading = 0.70

National medians for The LAW - Letters And Words

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

Correlation of The LAW - Letters And Words with personal details

Estimated g factor loadings for restricted ranges

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 these values to be lower than the test's full-range g loading.

Reliability

• Expanded Spearman-Brown formula: 0.97
• Stratified alpha coefficient: 0.98

These are computed from statistics like subtest reliabilities, subtest variances, and total test variance. This case illustrates excellently how a test with very high reliability can still be a bad, useless test, simply by being too easy and one-sided. To be a good test, high reliability is required but not sufficient, hence the computation of total test quality near the bottom of this report, based on quality of norms, hardness, resolution, validity, reliability, and robustness.

Error of measurement

Standard error = 2.26 raw score points

Correlation between subtests (internal consistency)

• Letters × Words = 0.95

Ideal values for correlations between subtests are around .5, thus being a compromise between the test's ability to yield a "profile" and its ability to provide an indication of general intelligence. With a too high correlation (like .8 or higher) the subtests measure basically the same so there is almost no profile information in them, with a too low correlation (like .2 or lower) the subtests are so different that there is little point in combining them into a measure of general intelligence.

For the correlations of the subtests with total score, see the correlations table above in this report. For statistics per subtest, see the statistical reports of the pertinent subtests.

Robustness and overall test quality for The LAW

• Robustness (score trend by time measured in months) = r_{raw scores × months} = -0.14 (n = 19)
• Quality (new method) = 1.1

[More statistical reports]