Statistics of Problems In Gentle Slopes of the second degree

© Paul Cooijmans

Scores on Problems In Gentle Slopes of the second degree as of 10 October 2019

Contents type: Numerical, spatial.   Period: 2013-present

3 **
6 *
7 *
9 *
9.5 *
10 ***
10.5 *
12 **
13 *
14 *
14.5 *
16 *
16.5 *
17 *
18 **
19.5 *
21 **
26 *
31.5 *

Correlation of Problems In Gentle Slopes of the second degree with other tests by Paul Cooijmans

(Test index) Test name n r
(114) Dicing with death40.92
(107) The Alchemist Test90.92
(47) Psychometrically Activated Grids Acerbate Neuroticism60.92
(111) Test For Genius - Revision 201670.88
(0) Test of the Beheaded Man100.87
(18) The Nemesis Test80.83
(1) Cartoons of Shock80.82
(36) Reflections In Peroxide90.82
(66) Test For Genius - Revision 200450.82
(105) Space, Time, and Hyperspace - Revision 201680.80
(33) Problems In Gentle Slopes of the first degree90.80
(42) The Marathon Test60.80
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 201680.80
(7) The Final Test50.79
(106) Cooijmans Intelligence Test - Form 4140.77
(21) Psychometric Qrosswords60.77
(2) Cooijmans Intelligence Test - Form 3190.76
(104) The Final Test - Revision 201390.75
(45) Numerical and spatial sections of The Marathon Test110.73
(109) The Bonsai Test - Revision 2016100.72
(43) Test For Genius - Revision 2010110.70
(32) Spatial section of The Marathon Test120.69
(31) Numerical section of The Marathon Test120.67
(11) Isis Test90.67
(44) Associative LIMIT130.67
(48) Narcissus' last stand70.67
(35) Intelligence Quantifier by assessment110.66
(19) Numerical section of Test For Genius - Revision 2010170.65
(26) Verbal section of Test For Genius - Revision 2004140.64
(5) Daedalus Test100.63
(108) Verbal section of Test For Genius - Revision 201670.61
(16) Lieshout International Mesospheric Intelligence Test160.61
(117) The Hammer Of Test-Hungry - Revision 201390.57
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 2010120.55
(46) Labyrinthine LIMIT60.54
(23) Gliaweb Riddled Intelligence Test - Revision 2011110.53
(37) Problems In Gentle Slopes of the third degree90.49
(10) Genius Association Test130.49
(30) Verbal section of The Marathon Test80.48
(25) The Sargasso Test110.44
(110) Cooijmans Intelligence Test 560.42
(3) Qoymans Multiple-Choice #5120.42
(28) The Test To End All Tests70.39
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude100.37
(27) Spatial section of Test For Genius - Revision 2004140.36
(12) Cooijmans On-Line Test - Two-barrelled version100.36
(40) Reason Behind Multiple-Choice - Revision 2008120.31
(15) Letters40.18
(24) Reason - Revision 2008120.18
(41) The LAW - Letters And Words40.12
(29) Words40.08
(68) Numbers4-0.28

Weighted average of correlations: 0.610 (N = 488, weighted sum = 297.53)

Conservatively estimated minimum g loading: 0.78

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 second degree with tests by others

(Test index) Test name n r
(234) Strict Logic Sequences Exam I60.92
(242) Unknown and miscellaneous tests110.39
(240) Strict Logic Spatial Exam 484-0.25

Weighted average of correlations: 0.417 (N = 21, weighted sum = 8.75)

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 second 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 second degree on that type
Verbal960.71
Numerical330.74
Spatial500.77
Logical250.67
Heterogeneous1690.82

N = 373

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

Balanced g loading = 0.74

National medians for Problems In Gentle Slopes of the second degree

Country n median score
Spain316.0
Canada214.3
South_Africa210.8
Italy210.5
United_States410.0

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 second degree

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

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

Personalia n r
Cooijmans Inventory of Neo-Marxist Attitudes31.00
Observed associative horizon30.84
P.S.I.A. Cold70.67
P.S.I.A. Neurotic70.59
P.S.I.A. Aspergoid70.59
P.S.I.A. Just70.56
P.S.I.A. Rare70.52
P.S.I.A. Rational70.50
P.S.I.A. Introverted70.47
P.S.I.A. True70.46
P.S.I.A. Extreme70.43
P.S.I.A. Orderly70.42
P.S.I.A. Deviance factor80.40
P.S.I.A. System factor80.38
Sex250.34
P.S.I.A. Ethics factor80.33
Educational level250.26
Observed behaviour90.25
Disorders (parents and siblings)240.13
Gifted Adult's Inventory of Aspergerisms50.01
Year of birth25-0.06
Father's educational level23-0.15
Mother's educational level23-0.21
P.S.I.A. Antisocial7-0.24
P.S.I.A. Cruel7-0.28
Disorders (own)24-0.37

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)
00.78 (488)NaN (0)
90.61 (364)0.79 (67)
130.65 (113)0.78 (301)
150.75 (38)0.76 (358)
170.95 (4)0.75 (385)
40NaN (0)0.78 (488)

As in many of these reports, the downward g loading is more consistent than the upward g loading. This phenomenon should really be discussed in the report The differentiation hypothesis of g tested, but it is compatible with there being a higher g loading in the bottom half of the test's range than in the upper half, the halves being separated by the median (in this case, the bottom half has .78, the upper half .65).

Reliability

This reliability is sufficient for a standalone test, meaning that the test's length and item quality have been projected correctly. A too low reliability would mean that the test contained bad items and/or was too short. Remarks like this are in these reports for the purpose of education.

Error

Scores by age

Age class n median score
65 to 69116.5
50 to 5413.0
45 to 49112.0
40 to 44415.5
35 to 39214.5
30 to 34313.0
25 to 29616.3
22 to 24310.0
20 or 21118.0
18 or 1919.5
1628.8

N = 25

Scores by year taken

Year taken n median score
201326.0
2014815.8
201559.5
2016218.0
201713.0
2018110.0
2019615.3

ryear taken × median score = 0.14 (N = 25)

Robustness and overall test quality

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. In this test, no bad items have been found so far.

Correlations of sections with total score

Numerical0.77
Spatial0.94

Correlations between sections

Numerical × Spatial0.51

This correlation between test sections is ideal as it constitutes a near-perfect balance between internal consistency (higher correlation is more consistent) and differentiation between ability types (lower correlation is greater differentiation).

Section histograms

Prop. = proportion of candidates outscored in this section.

Numerical

ScoreProp.# scores (* = 1 score)
30.040 (0.080) **
50.100 (0.120) *
60.180 (0.240) ***
70.360 (0.480) ******
80.520 (0.560) **
8.50.620 (0.680) ***
9.50.720 (0.760) **
100.800 (0.840) **
110.860 (0.880) *
120.920 (0.960) **
140.980 (1.000) *

Spatial

ScoreProp.# scores (* = 1 score)
00.080 (0.160) ****
0.50.180 (0.200) *
10.220 (0.240) *
20.280 (0.320) **
30.340 (0.360) *
40.380 (0.400) *
4.50.420 (0.440) *
50.480 (0.520) **
60.580 (0.640) ***
70.660 (0.680) *
90.700 (0.720) *
100.740 (0.760) *
110.820 (0.880) ***
130.900 (0.920) *
140.940 (0.960) *
17.50.980 (1.000) *