Statistics of Analogies subtest of Long Test For Genius

© Paul Cooijmans May 2003

Norms

Scores so far

Analogies, © 1995, subtest of long Test For Genius (English version), has drawn these scores out of 39 (65 scores):

0*
4*
5*
6***** *
7**
8****
9***** *
10*****
11***
12***** *
13***
14***** *
15***
16****
17****
18***
19***
21*
22**
24*

Remarkably (for high-range tests), the top scorer is a female.

Correlation with other tests:

Test#cor
Bonsai Test40.98
Cattell Culture Fair50.91
Mysterium Entrance Exam50.9
Miller Analogies40.89
Cooijmans Intelligence Test90.84
Final Test180.8
Long Test For Genius570.77
Association Subtest of LTFG630.68
SAT (old)60.62
Unknown tests80.6
Space, Time & Hyperspace580.51
Short Test For Genius100.5
Mega Test120.45
Analogies #170.43
Numbers230.39
WAIS40.37
W8780.36
Encephalist-R40.32
Sigma Test50.2
Qoymans Multiple-Choice100.18
Logima Strictica 3650.16
Qoymans Multiple-Choice #28-0.11
Titan Test5-0.66
GRE4-0.96

Mean correlation: 0.4

Used for norming are tests correlating .77 or higher. Prior scores are converted to the same scale (SD=15) if needed [and in March 2008 converted to protonorms using the initial protonorm formula]. Raw and prior scores are put in columns of numerical order, the highest facing the highest etc. Each raw score is normed at the median of the IQ's facing it. Scores above 24 are extrapolated.

Addition October 2014

© October 2014 Paul Cooijmans

Remark: This was a subtest of the no longer used Long Test For Genius, and most of its problems now occur in the Verbal section of the Test For Genius - Revision 2004.

Scores on Analogies of Long Test For Genius

Contents type: Verbal.   Period: 1995-2004

0 *
4 *
5 **
6 ********
7 **
8 ******
9 *******
10 **********
11 *******
12 *********
13 ********
14 *******
15 ***
16 ******
17 ******
18 ****
19 ******
21 *
22 **
23 *
24 *

Scores by males

n = 90

5 **
6 ********
7 **
8 ******
9 *******
10 ********
11 *******
12 *******
13 *******
14 *******
15 ***
16 ******
17 ******
18 ****
19 ******
21 *
22 **
23 *

Scores by females

n = 8

0 *
4 *
10 **
12 **
13 *
24 *

Correlation of Analogies of Long Test For Genius with other tests by Paul Cooijmans

(Test index) Test name n r
(84) Bonsai Test80.92
(35) Intelligence Quantifier by assessment170.80
(87) Cooijmans Intelligence Test - Form 250.77
(63) Long Test For Genius840.77
(7) The Final Test330.77
(44) Associative LIMIT60.74
(26) Verbal section of Test For Genius - Revision 2004150.74
(85) Cooijmans Intelligence Test - Form 1150.73
(10) Genius Association Test220.71
(66) Test For Genius - Revision 2004150.70
(79) Association subtest of Long Test For Genius930.69
(18) The Nemesis Test60.69
(55) Spatial Insight Test60.68
(54) Test of Shock and Awe80.63
(28) The Test To End All Tests150.59
(1) Cartoons of Shock60.59
(82) Reason50.58
(57) Space, Time, and Hyperspace860.53
(53) Qoymans Multiple-Choice #3230.53
(27) Spatial section of Test For Genius - Revision 2004150.51
(56) Short Test For Genius140.49
(80) Qoymans Multiple-Choice #4150.43
(86) Evens60.41
(74) Cooijmans On-Line Test50.41
(68) Numbers300.39
(77) Analogies #1110.36
(51) Qoymans Multiple-Choice #1120.26
(11) Isis Test90.14
(16) Lieshout International Mesospheric Intelligence Test90.07
(52) Qoymans Multiple-Choice #2100.07

Weighted average of correlations: 0.604

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 5 score pairs. All known pairs are used to obtain the true, honest statistics; correlations have not been artificially inflated by leaving out ceiling scores, outliers or other anomalies.

Correlation of Analogies of Long Test For Genius with tests by others

(Test index) Test name n r
(224) T.R.I.60.78
(238) 916 Test50.75
(239) Titan Test110.75
(228) Miller Analogies Test (raw; old version)60.72
(234) Strict Logic Sequences Exam I90.71
(217) G-test60.69
(231) Mysterium Entrance Exam120.64
(243) Scholastic Aptitude Test (old)60.62
(235) Nonverbal Cognitive Performance Examination170.57
(242) Unknown tests110.50
(229) Mega Test130.46
(201) Wechsler Adult Intelligence Scales50.46
(206) W-8780.36
(213) Encephalist - R60.33
(219) Graduate Record Examination60.24
(220) Cattell Culture Fair100.21
(237) Sigma Test120.14
(225) Logima Strictica 3611-0.08
(218) Raven's Advanced Progressive Matrices (I.Q.)10-0.11
(236) International High IQ Society Miscellaneous tests7-0.26
(211) Culture Fair Numerical Spatial Examination - Final version6-0.28

Weighted average of correlations: 0.389

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 to obtain the true, honest statistics; correlations have not been artificially inflated by leaving out ceiling scores, outliers or other anomalies.

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.

Correlation of Analogies of Long Test For Genius with other tests by Paul Cooijmans - for females

(Test index) Test name n r
(7) The Final Test30.96
(79) Association subtest of Long Test For Genius70.92
(63) Long Test For Genius70.85
(57) Space, Time, and Hyperspace80.69

Weighted average of correlations: 0.835

Conservatively estimated minimum g loading among females: 0.91

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 to obtain the true, honest statistics; correlations have not been artificially inflated by leaving out ceiling scores, outliers or other anomalies.

Estimated loadings of Analogies of Long Test For Genius 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 Analogies of Long Test For Genius on that type
Verbal0.78
Numerical0.63
Spatial0.71
Logical0.70
Heterogeneous0.78

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

Balanced g loading = 0.72

National medians for Analogies of Long Test For Genius

Country n median score
Germany221.0
Brazil314.0
Canada413.0
United_Kingdom913.0
Australia312.0
France212.0
United_States3011.5
Finland511.0
Greece311.0
Israel211.0
Norway211.0
Sweden79.0

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 of Analogies of Long Test For Genius with personal details

Personalia n r
P.S.I.A. Rational130.85
Observed associative horizon130.60
P.S.I.A. Orderly130.55
Observed behaviour150.41
Educational level410.31
P.S.I.A. Ethics factor300.30
P.S.I.A. True130.23
P.S.I.A. Cold130.18
P.S.I.A. System factor200.17
Sex980.11
P.S.I.A. Deviance factor300.03
Disorders (own)40-0.00
Father's educational level32-0.07
P.S.I.A. Introverted13-0.07
Year of birth93-0.11
Disorders (parents and siblings)40-0.14
P.S.I.A. Cruel13-0.17
P.S.I.A. Rare13-0.20
P.S.I.A. Extreme13-0.22
P.S.I.A. Aspergoid13-0.29
P.S.I.A. Neurotic13-0.33
P.S.I.A. Just13-0.38
P.S.I.A. Antisocial13-0.39
Gifted Adult's Inventory of Aspergerisms18-0.43
Mother's educational level32-0.44

Correlation with national I.Q.'s of Analogies of Long Test For Genius

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

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 (604)NaN (0)
8.50.74 (495)0.58 (65)
120.63 (323)0.61 (265)
15.50.32 (127)0.70 (408)
39NaN (0)0.78 (604)

Reliability

Error

Scores by age

Age class n median score
70 to 7428.0
55 to 59212.0
50 to 54914.0
45 to 49613.5
40 to 441613.5
35 to 391713.0
30 to 341113.0
25 to 291312.0
22 to 24410.0
20 or 2139.0
18 or 1938.0
17210.5
16310.0

Scores by age - within females

Age class n median score
70 to 74110.0
50 to 54110.0
40 to 44512.0
35 to 39112.0

Scores by age - within males

Age class n median score
70 to 7416.0
55 to 59212.0
50 to 54814.0
45 to 49613.5
40 to 441115.0
35 to 391613.0
30 to 341113.0
25 to 291312.0
22 to 24410.0
20 or 2139.0
18 or 1938.0
17210.5
16310.0

Scores by year taken

Year taken n median score
1995110.0
199689.0
1998110.0
1999913.0
2000612.0
20011614.5
20022210.5
20031512.0
20041811.0

ryear taken × median score = 0.45 (n = 96)

Remark: The slight increase of scores over the years on this test, expressed in the correlation of .45, may reflect the advent and increase of the Internet as a research tool, which has affected verbal analogies tests more than any other test type.

Robustness and overall test quality

  • Robustness by month = 0.68
  • Quality = 0.64
  • 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 case, the test has been fused with the Association subtest of the Long Test For Genius into the Verbal section of the Test For Genius - Revision 2004.