Statistics of observed associative horizon

Introduction

To detect possible correlates of associative horizon, scores have been assigned to candidates displaying a markedly narrow associative horizon (scored as 0) and to candidates displaying a markedly wide associative horizon (1). Without claiming that observed associative horizon is exactly the same as actual associative horizon (that would be easy, if one could just observe a mental faculty directly) the following statistics result:

Scores on Observed associative horizon as of 27 January 2023

Contents type: Observation.   

• n: 72
• Mean: 0.53
• Standard deviation: 0.50
• Range: 1.0
• Maximum possible: 1
• Male mean: 0.54 (n = 61)
• Female mean: 0.45 (n = 11)
• Proportion of males among candidates: 0.847

Correlation of Observed associative horizon with other mental ability tests

Weighted average of correlations: 0.389 (N = 559, weighted sum = 217.51)

Conservatively estimated minimum g loading: 0.62

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.

So, observed associative horizon has a loading on general intelligence, not much lower than that of a typical I.Q. test.

Estimated loadings of Observed associative horizon 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 = 387

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

Balanced g loading = 0.61

The fact that the loading on heterogeneous tests is highest also suggests that observed associative horizon is not independent of g.

National means for Observed associative horizon

For reasons of privacy, only countries with 2 or more candidates are included in this table. Ranking is based on the unrounded means, and then alphabetic.

Correlation with national I.Q.'s of Observed associative horizon

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

• r = 0.31 (n = 72)

This is significant and remarkably higher than the correlations normally found with national I.Q.'s.

Correlation of Observed associative horizon with personal details

PSIA Cold and Introverted seem to be the best objective correlates of observed associative horizon. It is remarkable that the correlation with disorders is not negative, which it usually is with I.Q. test scores. While observed associative horizon does correlate positively with g, it seems to differ from g in that it does not correlate negatively with disorders. This concords with the notion that associative horizon is really the disposition for psychosis (but not psychosis itself, it must be stressed; psychosis may be seen as over-inclusive associative horizon).

Correlation with personal details of Observed associative horizon - within females

Here too, the correlation with disorders is positive.

Correlation with personal details of Observed associative horizon - within males

Norming of associative horizon scores to I.Q.

Considering the moderate positive correlation with g, it is meaningful to "norm" the assessments scores of 0 and 1 to protonorms by means of rank equation; I.Q. tests correlating .39 or higher have been used to obtain the below table. Weighted average of correlations: 0.593 (N = 382, weighted sum = 226.44)

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