Statistics of Association and Analogies (French)

Introduction

This was the verbal part of a French version of the Test For Genius. It has been taken out of use because there was very little interest in it, and because people would sometimes use it merely to compare it to the English version to gain some kind of advantage when taking the latter, without actually taking the French version itself. For the same reasons, the Netherlandic and German versions have been discontinued.

One's score on this subtest is the sum of one's scores on the respective Association and Analogies subtests, the statistics of which are given separately further down in this report.

Scores on Association and Analogies (French) as of 9 February 2023

Contents type: Verbal.   Period: 1996-2004

• n: 12
• Median: 24.5
• Quartile deviation: 7.0
• Range: 34
• Maximum possible: 70
• Male median: 21.0 (n = 11)
• Female median: 28.0 (n = 1)
• Proportion of males among candidates: 0.917
• Hardness: 0.66
• Resolution: 0.54

Correlation of Association and Analogies (French) with other mental ability tests

Weighted average of correlations: 0.802 (N = 54, weighted sum = 43)

Estimated g factor loading: 0.90

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

Estimated loadings of Association and Analogies (French) 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 = 41

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

Balanced g loading = 0.83

National medians for Association and Analogies (French)

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 Association and Analogies (French)

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

• r = 0.18 (n = 10)

Correlation of Association and Analogies (French) 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

• Reliability = 0.92

Computed from the subtest reliabilities using a form of the Spearman-Brown formula.

Error

• Standard error = 2.7 raw score points

Scores by age

N = 12

Scores by year taken

r_{year taken × median score} = 0.19 (N = 12)

Robustness and overall test quality

• Robustness by month = 0.66 (r_{raw scores × months} = 0.14)
• Quality = 0.697

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.

Statistics of Association

These are separate statistics for the Association section

Scores on Association subtest of Long Test For Genius (French) as of 9 February 2023

Contents type: Verbal.   Period: 1996-2004

• n: 11
• Median: 13.0
• Quartile deviation: 2.5
• Range: 17
• Maximum possible: 31
• Male median: 12.0 (n = 10)
• Female median: 15.0 (n = 1)
• Proportion of males among candidates: 0.909
• Hardness: 0.61
• Resolution: 0.32

Correlation of Association subtest of Long Test For Genius (French) with other mental ability tests

Weighted average of correlations: 0.697 (N = 54, weighted sum = 38)

Estimated g factor loading: 0.83

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

Estimated loadings of Association subtest of Long Test For Genius (French) 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 = 41

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

Balanced g loading = 0.74

National medians for Association subtest of Long Test For Genius (French)

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 Association subtest of Long Test For Genius (French)

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

• r = 0.68 (n = 9)

Correlation of Association subtest of Long Test For Genius (French) 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

• Split-half (odd-even) = 0.86
• Split-half (1, 2… 5, 6… vs. 3, 4… 7, 8…) = 0.83
• Cronbach's alpha = 0.84

Error

• Standard error = 1.8 raw score points

Scores by age

N = 11

Scores by year taken

r_{year taken × median score} = 0.14 (N = 11)

Robustness and overall test quality

• Robustness by month = 0.64 (r_{raw scores × months} = 0.18)
• Quality = 0.624

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.

Statistics of Analogies

These are separate statistics for the Analogies section

Scores on Analogies subtest of Long Test For Genius (French) as of 9 February 2023

Contents type: Verbal.   Period: 1996-2005

• n: 11
• Median: 11.0
• Quartile deviation: 6.0
• Range: 18
• Maximum possible: 39
• Male median: 10.0 (n = 10)
• Female median: 13.0 (n = 1)
• Proportion of males among candidates: 0.909
• Hardness: 0.71
• Resolution: 0.50

Correlation of Analogies subtest of Long Test For Genius (French) with other mental ability tests

Weighted average of correlations: 0.781 (N = 54, weighted sum = 42)

Estimated g factor loading: 0.88

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

Estimated loadings of Analogies subtest of Long Test For Genius (French) 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 = 41

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

Balanced g loading = 0.83

National medians for Analogies subtest of Long Test For Genius (French)

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 Analogies subtest of Long Test For Genius (French)

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

• r = 0.82 (n = 9)

Correlation of Analogies subtest of Long Test For Genius (French) 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

• Split-half (odd-even) = 0.82
• Split-half (1, 2… 5, 6… vs. 3, 4… 7, 8…) = 0.90
• Cronbach's alpha = 0.87

Error

• Standard error = 2.1 raw score points

Scores by age

N = 11

Scores by year taken

r_{year taken × median score} = 0.04 (N = 11)

Robustness and overall test quality

• Robustness by month = 0.71 (r_{raw scores × months} = -0.02)
• Quality = 0.689

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.

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