Statistics of Problems In Gentle Slopes of the first degree

Scores on Problems In Gentle Slopes of the first degree as of 15 May 2021

Contents type: Verbal, numerical, spatial, logical.   Period: 2006-present

• n: 25
• Median: 37.0
• Quartile deviation: 6.5
• Range: 43
• Maximum possible: 46
• Male median: 37.5 (n = 24)
• Female median: 4.0 (n = 1)
• Resolution: 0.52

Correlation of Problems In Gentle Slopes of the first degree with other tests by I.Q. Tests for the High Range

Weighted average of correlations: 0.730 (N = 438, weighted sum = 319.86)

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.

Correlation of Problems In Gentle Slopes of the first degree with tests by others

Weighted average of correlations: 0.720 (N = 24, weighted sum = 17.28)

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 Problems In Gentle Slopes of the first degree 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 = 333

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

Balanced g loading = 0.84

National medians for Problems In Gentle Slopes of the first degree

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 Problems In Gentle Slopes of the first degree

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

• r = -0.12 (n = 24)

Correlation of Problems In Gentle Slopes of the first degree 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) = 0.99
• Split-half (other division) = 0.99
• Cronbach's alpha = 0.97

Note: Near-perfect reliability is obviously no guarantee for a satisfactory high-range test. In fact, a more difficult test whereon no one reaches the ceiling is likely to have a lower reliability coefficient than a too easy test like this one, whereon several reach the maximum score.

Error

• Standard error = 2.2 raw score points

Scores by age

N = 25

Scores by year taken

r_{year taken × median score} = -0.59 (N = 25)

Robustness and overall test quality

• Robustness by chronological rank = 0.88
• Robustness by month = 0.88 (r_{raw scores × months} = -0.56)
• Quality = 0.729

It is remarkable that scores on this test have dropped so steeply over time. Possibly, potential high scorers lost interest in the test because of its low ceiling.

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. This test appears to have no bad items.

Correlations of sections with total score

Correlations between sections (internal consistency)

Section histograms

Prop. = proportion of candidates outscored in this section. In parentheses the proportion outscored for any possible scores higher than the present score but lower than the next-higher score in the table.

Verbal

Numerical

Spatial

Logical

Remark: On the whole, the slopes are too gentle, and too many reach the maximum scores. As a result, the test is too easy for its purpose. This test illustrates well the fact that a test with very high reliability, validity, and robustness may still be unsatisfactory by simply being too easy.

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