Statistics of Problems In Gentle Slopes of the first degree

© Paul Cooijmans

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

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

4 *
8 *
10 *
16 **
22 *
29 **
31 **
33 *
34 *
37 *
38 **
40 **
41 *
42 *
44 *
46 *****

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

(Test index) Test name n r
(29) Words40.99
(41) The LAW - Letters And Words40.99
(15) Letters40.97
(47) Psychometrically Activated Grids Acerbate Neuroticism60.94
(21) Psychometric Qrosswords60.92
(109) The Bonsai Test - Revision 2016100.92
(37) Problems In Gentle Slopes of the third degree70.91
(1) Cartoons of Shock60.89
(19) Numerical section of Test For Genius - Revision 2010110.87
(7) The Final Test40.87
(5) Daedalus Test70.87
(106) Cooijmans Intelligence Test - Form 490.86
(30) Verbal section of The Marathon Test80.84
(66) Test For Genius - Revision 200460.84
(2) Cooijmans Intelligence Test - Form 3140.83
(36) Reflections In Peroxide90.83
(43) Test For Genius - Revision 201060.82
(0) Test of the Beheaded Man120.82
(44) Associative LIMIT120.81
(42) The Marathon Test80.81
(103) Problems In Gentle Slopes of the second degree110.81
(111) Test For Genius - Revision 201660.80
(48) Narcissus' last stand90.80
(16) Lieshout International Mesospheric Intelligence Test150.79
(114) Dicing with death80.79
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 201660.79
(107) The Alchemist Test70.78
(104) The Final Test - Revision 201360.76
(117) The Hammer Of Test-Hungry - Revision 201350.73
(45) Numerical and spatial sections of The Marathon Test90.72
(32) Spatial section of The Marathon Test90.72
(35) Intelligence Quantifier by assessment100.71
(110) Cooijmans Intelligence Test 580.70
(105) Space, Time, and Hyperspace - Revision 201660.70
(28) The Test To End All Tests100.69
(40) Reason Behind Multiple-Choice - Revision 2008110.69
(31) Numerical section of The Marathon Test90.68
(108) Verbal section of Test For Genius - Revision 201660.67
(12) Cooijmans On-Line Test - Two-barrelled version60.67
(25) The Sargasso Test100.67
(26) Verbal section of Test For Genius - Revision 2004110.67
(18) The Nemesis Test60.66
(68) Numbers40.66
(10) Genius Association Test140.64
(3) Qoymans Multiple-Choice #5110.63
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude90.63
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 201070.59
(24) Reason - Revision 2008110.57
(11) Isis Test100.52
(27) Spatial section of Test For Genius - Revision 2004110.48
(23) Gliaweb Riddled Intelligence Test - Revision 2011100.45
(82) Reason50.31
(62) Reason Behind Multiple-Choice40.25
(80) Qoymans Multiple-Choice #450.24

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

(Test index) Test name n r
(234) Strict Logic Sequences Exam I50.97
(201) Wechsler Adult Intelligence Scales50.91
(239) Titan Test40.84
(242) Unknown and miscellaneous tests100.45

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.

Typeng loading of Problems In Gentle Slopes of the first degree on that type
Verbal930.85
Numerical240.87
Spatial410.82
Logical230.78
Heterogeneous1520.87

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

Country n median score
Canada346.0
United_States931.0

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 Problems In Gentle Slopes of the first degree

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

Correlation of Problems In Gentle Slopes of the first degree with personal details

Personalia n r
Observed associative horizon40.56
Sex250.46
Educational level240.42
P.S.I.A. Orderly - Revision 200790.35
Observed behaviour100.24
P.S.I.A. Antisocial - Revision 200790.18
Father's educational level220.13
P.S.I.A. True - Revision 200790.08
P.S.I.A. Cruel - Revision 200790.04
P.S.I.A. Ethics factor - Revision 200790.04
Mother's educational level22-0.00
Disorders (own)23-0.10
P.S.I.A. Rational - Revision 20079-0.12
P.S.I.A. Rare - Revision 20079-0.15
Gifted Adult's Inventory of Aspergerisms7-0.16
P.S.I.A. Cold - Revision 20079-0.16
P.S.I.A. Extreme - Revision 20079-0.18
P.S.I.A. System factor - Revision 20079-0.21
P.S.I.A. Deviance factor - Revision 20079-0.25
P.S.I.A. Introverted - Revision 20079-0.27
Disorders (parents and siblings)23-0.30
Year of birth24-0.32
P.S.I.A. Aspergoid - Revision 20079-0.39
P.S.I.A. Neurotic - Revision 20079-0.43
P.S.I.A. Just - Revision 20079-0.62
Cooijmans Inventory of Neo-Marxist Attitudes5-0.68

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.

Raw scoreUpward g (N)Downward g (N)
00.86 (438)NaN (0)
240.60 (262)0.83 (50)
30.50.58 (197)0.90 (160)
370.61 (156)0.91 (231)
420.84 (20)0.82 (314)
46NaN (0)0.86 (438)

Reliability

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

Scores by age

Age class n median score
65 to 69138.0
55 to 59146.0
50 to 5414.0
45 to 49331.0
40 to 44538.0
35 to 39227.0
30 to 34129.0
25 to 29437.5
22 to 24244.0
20 or 21337.0
15116.0
13116.0

N = 25

Scores by year taken

Year taken n median score
2006243.0
2008142.0
2009245.0
2010133.0
2011242.0
2012334.0
2013131.0
2014140.0
2015341.0
201614.0
2018212.0
2019129.0
2020322.0
2021234.0

ryear taken × median score = -0.59 (N = 25)

Robustness and overall test quality

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

Verbal0.86
Numerical0.85
Spatial0.89
Logical0.69

Correlations between sections (internal consistency)

Verbal × Numerical0.62
Verbal × Spatial0.65
Verbal × Logical0.49
Numerical × Spatial0.74
Numerical × Logical0.56
Spatial × Logical0.45

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

ScoreProp.# scores (* = 1 score)
00.100 (0.200) *****
10.220 (0.240) *
20.260 (0.280) *
50.300 (0.320) *
80.340 (0.360) *
100.400 (0.440) **
110.720 (1.000) **************

Numerical

ScoreProp.# scores (* = 1 score)
00.040 (0.080) **
20.100 (0.120) *
30.140 (0.160) *
40.220 (0.280) ***
60.340 (0.400) ***
70.460 (0.520) ***
80.540 (0.560) *
90.780 (1.000) ***********

Spatial

ScoreProp.# scores (* = 1 score)
00.120 (0.240) ******
10.280 (0.320) **
40.340 (0.360) *
50.400 (0.440) **
70.460 (0.480) *
80.500 (0.520) *
90.560 (0.600) **
100.620 (0.640) *
110.700 (0.760) ***
120.880 (1.000) ******

Logical

ScoreProp.# scores (* = 1 score)
40.020 (0.040) *
60.060 (0.080) *
80.120 (0.160) **
100.180 (0.200) *
110.240 (0.280) **
130.520 (0.760) ************
140.880 (1.000) ******

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.