Qoymans Multiple-Choice #1 statistics

Introduction

This test was created in 2002 to do something completely different for once. I had always seen multiple-choice tests as inferior (and still do) so I made an extreme one. While the apparently "easy", one-sided verbal test was extremely popular, the data gathered by it was of low quality, and the test had low g loading and reliability. Therefore I later combined it with another test of the same type into a larger test and removed or revised bad items. I also added a "pass" option to each question, which guaranteed half a point. The eventual result is the Qoymans Multiple-Choice #5, which is much better than the earlier ones.

Scores on Qoymans Multiple-Choice #1 as of 12 February 2023

Contents type: Verbal.   Period: 2002-2002

• n: 186
• Median: 26.0
• Quartile deviation: 7.0
• Range: 46
• Maximum possible: 60
• Minimum possible: -60
• Male median: 27.0 (n = 132)
• Female median: 22.0 (n = 45)
• Unknown sex median: 18.0 (n = 9)
• Proportion of males among candidates: 0.710
• Hardness: 0.29
• Resolution: 0.54

Scores by males

n = 132

Scores by females

n = 45

Correlation of Qoymans Multiple-Choice #1 with other mental ability tests

Weighted average of correlations: 0.133 (N = 460, weighted sum = 61)

Estimated g factor loading: 0.36

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 Qoymans Multiple-Choice #1 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 = 279

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

Balanced g loading = 0.41

National medians for Qoymans Multiple-Choice #1

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 with national I.Q.'s of Qoymans Multiple-Choice #1

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

• r = 0.06 (n = 40)

Correlation of Qoymans Multiple-Choice #1 with personal details

Correlation with personal details of Qoymans Multiple-Choice #1 - within females

Correlation with personal details of Qoymans Multiple-Choice #1 - within males

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.

Remark

The below internal statistics are based on a smaller sample because the internal data of this test was not retained for all candidates, which has to do with the circumstance that two different persons were scoring the test in consecutive periods.

Reliability

• Split-half (odd-even) = 0.83
• Split-half (1, 2… 5, 6… vs. 3, 4… 7, 8…) = 0.75
• Cronbach's alpha = 0.77

Error

• Standard error = 4.5 raw score points

Scores by age

N = 69

Scores by age - within females

N = 23

Scores by age - within males

N = 46

Scores by year taken

Robustness and overall test quality

• Robustness by chronological order = 0.69 (r_{raw scores × time-rank} = 0.04)
• Quality = 0.510

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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