# Statistics of unknown and miscellaneous tests

## Introduction

This report is about scores reported by candidates either without mention of exactly which test it concerned, or from tests that do not have a field of their own in the database. There exist so many tests that is not doable to give them each a field. The scores are expressed on a scale with a mean of 100 and standard deviation of 16, because that is the scale that was most used years ago when this field was conceived. This grouping of tests has consequences; the correlations with other tests and g loading are lower than in single-test reports. This is so because some tests may yield systematically higher scores than others, which, when combined, reduces or even inverts the correlations that the individual tests may have (such inversion is known as "Simpson's paradox"). Nevertheless, some useful information is retained in this field, hence this report.

## Scores on Unknown and miscellaneous tests as of 23 September 2019

 80 ** 87 * 95 * 104 * 107 * 110 *** 114 * 115 ** 116 * 117 ** 119 *** 120 *** 122 *** 123 ** 124 * 125 ****** 126 * 127 *** 128 ***** 130 ******* 131 ********* 132 ********** 133 *********************************** 134 ***** 135 *************** 136 *********** 137 ************************ 138 **************** 139 ************ 140 ****************** 141 *********** 142 ************* 143 ********* 144 ******* 145 ******************** 146 ********* 147 ************* 148 **************** 149 ********* 150 *************** 151 *********** 152 ****** 153 ** 154 ****** 155 ******** 156 ****** 157 **** 158 ** 159 ** 160 ***** 162 *** 163 ** 164 *** 165 *** 166 *** 168 * 170 ** 175 * 176 * 183 * 184 **

Do notice that despite the incongruous grouping of many tests, and taking into account the standard deviation of 16, the shape and range of the distribution closely resemble those of the known high-range distribution.

## Scores by males

n = 340

 80 ** 87 * 95 * 107 * 110 * 115 ** 116 * 117 ** 119 ** 120 ** 122 *** 123 ** 124 * 125 ***** 126 * 127 * 128 **** 130 ******* 131 ******** 132 ******** 133 ***************************** 134 ***** 135 ************ 136 ********** 137 ******************** 138 ************ 139 ********** 140 *************** 141 *********** 142 *********** 143 ******* 144 ******* 145 ****************** 146 ******** 147 *********** 148 ************* 149 ******** 150 ************* 151 ******** 152 ****** 153 ** 154 ****** 155 ******** 156 ***** 157 **** 158 ** 159 ** 160 **** 162 * 163 ** 164 *** 165 *** 166 *** 170 ** 175 * 176 * 183 * 184 *

## Scores by females

n = 53

 104 * 110 ** 114 * 119 * 120 * 125 * 127 ** 128 * 131 * 132 * 133 ****** 135 ** 136 * 137 *** 138 **** 139 * 140 ** 142 ** 143 ** 145 ** 146 * 147 ** 148 ** 149 * 150 ** 151 *** 156 * 160 * 162 * 168 * 184 *

## Correlation of Unknown and miscellaneous tests with other tests by Paul Cooijmans

(Test index) Test name n r
(76) Analogies subtest of Long Test For Genius (Netherlandic)50.64
(25) The Sargasso Test220.63
(33) Problems In Gentle Slopes of the first degree70.59
(26) Verbal section of Test For Genius - Revision 2004500.57
(62) Reason Behind Multiple-Choice140.53
(7) The Final Test500.51
(2) Cooijmans Intelligence Test - Form 3480.50
(43) Test For Genius - Revision 2010160.50
(110) Cooijmans Intelligence Test 560.49
(37) Problems In Gentle Slopes of the third degree50.47
(86) Evens140.46
(50) Qoymans Automatic Test #2150.46
(66) Test For Genius - Revision 2004370.44
(79) Association subtest of Long Test For Genius370.44
(54) Test of Shock and Awe100.43
(75) Analogies of Long Test For Genius340.42
(105) Space, Time, and Hyperspace - Revision 2016100.42
(35) Intelligence Quantifier by assessment540.40
(19) Numerical section of Test For Genius - Revision 2010290.40
(0) Test of the Beheaded Man160.39
(103) Problems In Gentle Slopes of the second degree110.39
(29) Words100.38
(10) Genius Association Test540.38
(36) Reflections In Peroxide70.37
(116) Gliaweb Riddled Intelligence Test (old version)180.36
(87) Cooijmans Intelligence Test - Form 2270.35
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 201690.35
(44) Associative LIMIT350.33
(53) Qoymans Multiple-Choice #3520.33
(46) Labyrinthine LIMIT50.31
(109) The Bonsai Test - Revision 201690.30
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 2010220.30
(28) The Test To End All Tests210.28
(32) Spatial section of The Marathon Test140.28
(15) Letters80.27
(11) Isis Test230.27
(51) Qoymans Multiple-Choice #1340.25
(85) Cooijmans Intelligence Test - Form 1220.25
(27) Spatial section of Test For Genius - Revision 2004540.24
(82) Reason140.24
(48) Narcissus' last stand70.23
(72) Qoymans Automatic Test #1150.23
(40) Reason Behind Multiple-Choice - Revision 2008320.22
(52) Qoymans Multiple-Choice #2390.21
(83) KIT Intelligence Test - first attempts60.21
(63) Long Test For Genius280.21
(56) Short Test For Genius260.20
(45) Numerical and spatial sections of The Marathon Test140.17
(108) Verbal section of Test For Genius - Revision 201670.17
(24) Reason - Revision 2008330.16
(3) Qoymans Multiple-Choice #5330.16
(16) Lieshout International Mesospheric Intelligence Test470.13
(23) Gliaweb Riddled Intelligence Test - Revision 2011340.13
(68) Numbers430.12
(18) The Nemesis Test160.11
(65) Long Test For Genius (Netherlandic)50.10
(55) Spatial Insight Test130.10
(80) Qoymans Multiple-Choice #4500.09
(57) Space, Time, and Hyperspace560.07
(31) Numerical section of The Marathon Test140.04
(69) Odds110.04
(73) Qoymans Automatic Test #350.00
(96) A-17 - Early experimental association test in English, 45 items70.00
(12) Cooijmans On-Line Test - Two-barrelled version17-0.01
(8) Female Intelligence Test6-0.01
(41) The LAW - Letters And Words7-0.03
(61) A-10 - Early experimental association test in Netherlandic7-0.03
(5) Daedalus Test11-0.06
(42) The Marathon Test12-0.07
(21) Psychometric Qrosswords9-0.07
(71) Numerical Insight Test6-0.08
(106) Cooijmans Intelligence Test - Form 417-0.08
(30) Verbal section of The Marathon Test13-0.14
(77) Analogies #110-0.19
(74) Cooijmans On-Line Test12-0.20
(1) Cartoons of Shock24-0.21
(104) The Final Test - Revision 20138-0.23
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude9-0.26
(84) Bonsai Test15-0.28
(111) Test For Genius - Revision 20167-0.34
(117) The Hammer Of Test-Hungry - Revision 20138-0.35
(81) Association subtest of Long Test For Genius (Netherlandic)6-0.54
(107) The Alchemist Test8-0.67

Weighted average of correlations: 0.241 (weighted sum: 404.55)

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

Remark: As can be expected when grouping a hotchpotch of tests, the correlations with other tests are much lower on average than they are for single tests. Each test on its own may have a much higher g loading than this.

## Correlation of Unknown and miscellaneous tests with tests by others

(Test index) Test name n r
(228) Miller Analogies Test (raw; old version)60.85
(202) Cattell Verbal50.77
(244) Scholastic Aptitude Test (new)50.76
(239) Titan Test150.64
(226) Logima Strictica 24120.64
(246) Sequentia Numerica Form I130.64
(217) G-test50.59
(229) Mega Test230.58
(245) Stanford-Binet50.56
(238) 916 Test170.56
(214) Epiq Tests90.52
(227) Concep-T70.51
(212) Raven's Advanced Progressive Matrices (raw)110.47
(204) Chimera High Ability Riddle Test120.45
(237) Sigma Test220.43
(213) Encephalist - R80.41
(218) Raven's Advanced Progressive Matrices (I.Q.)160.41
(220) Cattell Culture Fair190.40
(236) International High IQ Society Miscellaneous tests390.40
(234) Strict Logic Sequences Exam I460.39
(205) Cito-toets70.38
(231) Mysterium Entrance Exam380.37
(225) Logima Strictica 36430.31
(211) Culture Fair Numerical Spatial Examination - Final version340.21
(243) Scholastic Aptitude Test (old)150.19
(206) W-87180.13
(224) T.R.I.80.10
(223) Strict Logic Sequences Exam II150.10
(235) Nonverbal Cognitive Performance Examination320.07
(240) Strict Logic Spatial Exam 48150.06
(241) Ultra Test5-0.07
(200) American College Testing program12-0.15
(203) Wechsler Adult Intelligence Scales for Children5-0.30
(230) Omega Contemplative Items Pool6-0.57

Weighted average of correlations: 0.352 (weighted sum: 216.64)

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 5 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.

Remark: The fact that the correlations with tests by others are somewhat higher than with tests by Paul Cooijmans may be caused by the circumstance that both the "Unknown and miscellaneous" scores and the "tests by others" scores are self-reported by candidates, and thus subject to the same bias (candidates tend to report their higher scores and withhold the lower ones).

## Correlation of Unknown and miscellaneous tests with other tests by Paul Cooijmans - for females

(Test index) Test name n r
(8) Female Intelligence Test21.00
(16) Lieshout International Mesospheric Intelligence Test21.00
(28) The Test To End All Tests21.00
(44) Associative LIMIT21.00
(63) Long Test For Genius31.00
(75) Analogies of Long Test For Genius31.00
(79) Association subtest of Long Test For Genius30.98
(53) Qoymans Multiple-Choice #350.86
(7) The Final Test40.71
(57) Space, Time, and Hyperspace40.71
(80) Qoymans Multiple-Choice #440.63
(52) Qoymans Multiple-Choice #260.56
(56) Short Test For Genius40.51
(51) Qoymans Multiple-Choice #160.25
(68) Numbers30.19
(10) Genius Association Test30.19
(50) Qoymans Automatic Test #230.15
(35) Intelligence Quantifier by assessment7-0.02
(2) Cooijmans Intelligence Test - Form 34-0.35
(0) Test of the Beheaded Man2-1.00
(96) A-17 - Early experimental association test in English, 45 items2-1.00

Weighted average of correlations: 0.437

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

Remark: Just as with single-test reports, the g loading within females is higher than the overall g loading. This is something that needs to be verified further as more data comes in, but it seems that high-range tests measure g better in females than in males.

## Estimated loadings of Unknown and miscellaneous tests 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.

Verbal0.53
Numerical0.45
Spatial0.41
Logical0.28
Heterogeneous0.47

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

## National medians for Unknown and miscellaneous tests

Country n median score
Hong_Kong2153.5
Poland3150.0
Korea_South3149.0
Spain6147.5
Brazil3147.0
Greece7146.0
Austria5145.0
United_Kingdom19145.0
Israel2144.5
Japan2144.5
Turkey5144.0
United_States82144.0
Sweden17142.0
Philippines2141.0
Australia11140.0
Malta2139.5
Germany18139.0
Finland10138.5
Switzerland4138.5
France10138.0
Italy4137.5
Romania2137.5
India5137.0
Norway3137.0
South_Africa3136.0
Belgium10135.5
Netherlands33135.0
Denmark5133.0
Mexico3133.0
Singapore3133.0

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 Unknown and miscellaneous tests

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

• r = -0.06 (n = 314)

## Correlation of Unknown and miscellaneous tests with personal details

Personalia n r
Observed associative horizon310.30
P.S.I.A. Cold790.24
P.S.I.A. Rare790.22
Cooijmans Inventory of Neo-Marxist Attitudes230.21
Observed behaviour630.19
P.S.I.A. Aspergoid790.15
P.S.I.A. Orderly790.14
P.S.I.A. Introverted790.13
Educational level2050.13
P.S.I.A. Rational790.13
P.S.I.A. True790.08
P.S.I.A. Cruel790.07
P.S.I.A. System factor630.06
Sex3930.06
P.S.I.A. Deviance factor1010.06
P.S.I.A. Ethics factor1010.02
Father's educational level189-0.01
Mother's educational level194-0.03
Disorders (parents and siblings)201-0.07
P.S.I.A. Extreme79-0.07
Disorders (own)217-0.07
P.S.I.A. Neurotic79-0.07
Year of birth320-0.09
P.S.I.A. Antisocial79-0.10
P.S.I.A. Just79-0.14

Remark: Here, too, the correlations are much lower on the whole than in single-test reports.

## Correlation with personal details of Unknown and miscellaneous tests - within females

Personalia n r
P.S.I.A. Cruel30.97
P.S.I.A. Just30.71
P.S.I.A. Rational30.70
Observed behaviour70.49
P.S.I.A. Cold30.42
P.S.I.A. Orderly30.31
P.S.I.A. Ethics factor50.22
Disorders (parents and siblings)14-0.06
Mother's educational level12-0.09
Father's educational level12-0.14
Disorders (own)16-0.15
Year of birth29-0.20
P.S.I.A. Deviance factor5-0.29
P.S.I.A. Rare3-0.49
Educational level14-0.49
Observed associative horizon5-0.53
P.S.I.A. Antisocial3-0.54
P.S.I.A. Neurotic3-0.63
P.S.I.A. Aspergoid3-0.71
P.S.I.A. True3-0.83
P.S.I.A. Extreme3-0.89
P.S.I.A. Introverted3-0.98

Remark: The correlations within females are in some respects different from those within males. This suggests that, in general, statistics should be provided and studied within-sex when possible, to prevent the obfuscation of correlations or trends that may occur in sex-combined statistics.

## Correlation with personal details of Unknown and miscellaneous tests - within males

Personalia n r
Observed associative horizon260.42
P.S.I.A. Rare760.28
Cooijmans Inventory of Neo-Marxist Attitudes230.21
P.S.I.A. Orderly760.20
P.S.I.A. Cold760.19
P.S.I.A. Aspergoid760.17
Educational level1910.17
Observed behaviour560.15
P.S.I.A. Introverted760.14
P.S.I.A. Deviance factor960.09
P.S.I.A. Rational760.07
P.S.I.A. True760.07
P.S.I.A. System factor610.06
P.S.I.A. Cruel760.05
P.S.I.A. Ethics factor960.01
Father's educational level177-0.00
P.S.I.A. Extreme76-0.02
Mother's educational level182-0.02
P.S.I.A. Neurotic76-0.03
Disorders (own)199-0.06
Disorders (parents and siblings)187-0.07
Year of birth287-0.09
P.S.I.A. Antisocial76-0.10
P.S.I.A. Just76-0.19

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.

I.Q.Upward g (n)Downward g (n)
800.49 (1681)NaN (0)
1250.46 (1631)0.82 (5)
132.50.42 (1530)0.79 (41)
1400.30 (1017)0.40 (635)
147.50.53 (486)0.49 (1047)
1550.38 (119)0.43 (1531)
160-0.21 (15)0.46 (1602)
184NaN (0)0.49 (1681)

## Reliability

The reliability of these reported unknown and miscellaneous test scores can obviously not be computed because there is no actual test and therefore no internal data, but from the g loadings it can be surmised that the reliability should be at least .5 (because the g loading can not be higher than the reliability). The higher g loading among females suggests a higher reliability for females, like around .7 or more

## Error of measurement

From the estimated reliability it follows that the standard error of measurement of these reported scores is at most 9.2 I.Q. points (remember that the scale has a standard deviation of 16 here). That is a large error; it means that if someone quotes a certain I.Q. without identifying the test, that person's true I.Q. is with 95 % confidence within plus or minus 18.4 points from it. For females, the error would be at most 7.1 I.Q. points.