Statistics of PIGS of the first degree

© August 2019 Paul Cooijmans

Norms

Scores on Problems In Gentle Slopes of the first degree

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

8 **
16 **
29 **
31 *
33 *
34 *
38 *
40 **
41 *
42 *
44 *
46 *****

Note: Normally, a statistical report is only released after 30 submissions to a test, but with this test it would take too long to wait for that because it is so rarely taken, possibly because of its too low ceiling.

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

(Test index) Test name n r
(112) Combined Numerical and Spatial sections of Test For Genius - Revision 201631.00
(105) Space, Time, and Hyperspace - Revision 201631.00
(68) Numbers31.00
(29) Words40.99
(109) The Bonsai Test - Revision 201640.99
(41) The LAW - Letters And Words40.98
(46) Labyrinthine LIMIT30.97
(104) The Final Test - Revision 201340.97
(114) Dicing with death40.96
(111) Test For Genius - Revision 201630.96
(15) Letters40.96
(47) Psychometrically Activated Grids Acerbate Neuroticism50.95
(21) Psychometric Qrosswords50.93
(5) Daedalus Test60.93
(7) The Final Test30.90
(37) Problems In Gentle Slopes of the third degree40.89
(19) Numerical section of Test For Genius - Revision 201090.88
(1) Cartoons of Shock50.88
(106) Cooijmans Intelligence Test - Form 460.87
(66) Test For Genius - Revision 200460.84
(16) Lieshout International Mesospheric Intelligence Test100.83
(25) The Sargasso Test60.82
(43) Test For Genius - Revision 201060.82
(2) Cooijmans Intelligence Test - Form 3100.81
(30) Verbal section of The Marathon Test60.81
(0) Test of the Beheaded Man80.80
(36) Reflections In Peroxide50.79
(44) Associative LIMIT80.79
(103) Problems In Gentle Slopes of the second degree80.76
(42) The Marathon Test60.75
(40) Reason Behind Multiple-Choice - Revision 200890.74
(35) Intelligence Quantifier by assessment100.73
(48) Narcissus' last stand50.72
(107) The Alchemist Test50.70
(32) Spatial section of The Marathon Test70.69
(26) Verbal section of Test For Genius - Revision 2004110.67
(18) The Nemesis Test50.66
(12) Cooijmans On-Line Test - Two-barrelled version60.66
(28) The Test To End All Tests60.66
(3) Qoymans Multiple-Choice #590.64
(24) Reason - Revision 200890.64
(45) Numerical and spatial sections of The Marathon Test70.63
(10) Genius Association Test80.62
(4) A Paranoiac's Torture: Intelligence Test Utilizing Diabolic Exactitude70.62
(39) Combined Numerical and Spatial sections of Test For Genius - Revision 201070.59
(31) Numerical section of The Marathon Test70.58
(108) Verbal section of Test For Genius - Revision 201630.50
(27) Spatial section of Test For Genius - Revision 2004110.48
(11) Isis Test60.45
(23) Gliaweb Riddled Intelligence Test - Revision 201180.43
(82) Reason50.31
(62) Reason Behind Multiple-Choice40.25
(80) Qoymans Multiple-Choice #440.12

Weighted average of correlations: 0.732

Conservatively estimated minimum g loading: 0.86

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.

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 I31.00
(242) Unknown and miscellaneous tests70.59

Weighted average of correlations: 0.715

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.

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.

Typeg loading of Problems In Gentle Slopes of the first degree on that type
Verbal0.85
Numerical0.89
Spatial0.83
Logical0.80
Heterogeneous0.86

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

Balanced g loading = 0.85

National medians for Problems In Gentle Slopes of the first degree

Country n median score
Canada346.0
United_States531.0

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.

Notice that all Canadian candidates have perfect scores on this test.

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
Educational level190.51
Sex200.48
P.S.I.A. Antisocial80.45
Observed behaviour90.39
Father's educational level170.20
P.S.I.A. Deviance factor100.19
P.S.I.A. Rare80.16
P.S.I.A. Extreme80.15
P.S.I.A. Cruel80.11
P.S.I.A. Rational8-0.00
P.S.I.A. System factor9-0.00
Mother's educational level17-0.01
Gifted Adult's Inventory of Aspergerisms6-0.03
P.S.I.A. Cold8-0.06
P.S.I.A. Aspergoid8-0.08
P.S.I.A. Orderly8-0.09
P.S.I.A. True8-0.14
P.S.I.A. Introverted8-0.17
P.S.I.A. Ethics factor10-0.24
Year of birth19-0.27
P.S.I.A. Neurotic8-0.29
Disorders (own)18-0.32
P.S.I.A. Just8-0.33
Disorders (parents and siblings)18-0.50
Cooijmans Inventory of Neo-Marxist Attitudes3-0.84

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 (320)NaN (0)
310.46 (131)0.93 (147)
390.68 (90)0.93 (173)
46NaN (0)0.86 (320)

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 test whereon several reach the maximum score.

Error

Scores by age

Age class n median score
55 to 59146.0
50 to 5414.0
45 to 49237.5
40 to 44538.0
35 to 39227.0
30 to 34129.0
25 to 29341.0
22 to 24244.0
20 or 21140.0
15116.0
13116.0

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

ryear taken × median score = -0.66 (n = 20)

Remark: Scores have gone down steeply over the years on this test. If this trend continues, it may turn out a good high-range test after all!

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. This test appears to have no bad items.

Correlations of sections with total score

Verbal0.84
Numerical0.91
Spatial0.89
Logic0.66

Correlations between sections

Verbal × Numerical0.68
Verbal × Spatial0.60
Verbal × Logic0.45
Numerical × Spatial0.83
Numerical × Logic0.55
Spatial × Logic0.44

Section histograms

Prop. = proportion of candidates outscored in this section (in parentheses the proportion for any score higher than the current score but lower than the next score in the table).

Verbal

ScoreProp.# scores (* = 1 score)
00.100 (0.200) ****
10.225 (0.250) *
80.275 (0.300) *
100.350 (0.400) **
110.700 (1.000) ************

Numerical

ScoreProp.# scores (* = 1 score)
00.050 (0.100) **
20.125 (0.150) *
30.175 (0.200) *
40.250 (0.300) **
60.350 (0.400) **
70.450 (0.500) **
90.750 (1.000) **********

Spatial

ScoreProp.# scores (* = 1 score)
00.100 (0.200) ****
10.250 (0.300) **
40.325 (0.350) *
70.375 (0.400) *
90.450 (0.500) **
100.525 (0.550) *
110.625 (0.700) ***
120.850 (1.000) ******

Logic

ScoreProp.# scores (* = 1 score)
40.025 (0.050) *
80.100 (0.150) **
100.175 (0.200) *
110.250 (0.300) **
130.500 (0.700) ********
140.850 (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.