Statistics of Numbers

© July 2001 Paul Cooijmans

Note: This is a number series test; very unfortunately, criminals are publishing many number series from tests with the answers on the Internet without permission from the tests' authors. It is therefore easy to cheat on such tests, and unwise to accept the tests' scores for admission to IQ societies.

I still score the test because there are people who like taking number series tests, but I do not intend to create new such tests.

I regret this problem especially in the case of this particular test, because it originally was an integral part of my Test For Genius from 1995. After discovering the copyright violation I felt forced to violate the integrity of that extremely beautiful, profound and brilliant creation by removing the numerical subtest. It is sad, but apparently there are people whose dishonesty and desire to help other dishonest persons - cheaters - is so great that they completely disregard intellectual property and the natural necessity to keep test answers secret. Our contempt for them can never be deep enough.

Norms

Numbers consists of 20 number series. Below the scores so far; rounded off to whole numbers for this norming. Numbers is no longer used for admission because of illegal unauthorized answer publication. There may be fraudulent scores among these. I cannot verify fraud and do not accuse anyone, but it is reasonable to assume about 4 of the upper 10 scores might be fraudulent. If so, norms resulting below will be TOO LOW for that range as a direct result (since norms are based on prior scores), so possible culprits punish themselves automatically.

6*
7*
8***
9***** *
10***** ***** **
11***** **
12***** **
13***
14**
15***** **
16***
17**
18*
19*****
20**

Correlation with other tests:

Test # cor
Tests To End All Tests 3 .97
Final Test 10 .94
Ultra Test 4 .93
Test For Genius (short) 21 .87
A-x 10 .83
Mega Test 18 .74
CHART 5 .64
Drenth Number Series 4 .55
CIT 10 .52
Titan Test 9 .5
Cattell Culture Fair 11 .46
Rest 38 .4
Unspecified Mensa Tests 7 .2
Raven APM 15 -.02
Hoeflin Power 6 -.08
W-87 4 -.36

The "Rest" are Nemesis, Chimera Test, Analogies #1, Grail Test, SAT, Concept Mastery, GRE, GMAT, WAIS, LAIT, Stanford-Binet, LSFIT, EIT, IST-70, Thinkfast, CTMM, Drenth Analogies, Quest, NUTE, Wonderlic Personnel Test, ACT, New York High IQ Society Test, Mysterium Entrance.

Used for norming are tests correlating higher than .5. Raw and prior scores are arranged in two columns of numerical order, the highest raw score facing the highest prior IQ (prior scores are if needed converted to an IQ scale with 15 points per standard deviation), etc. For each raw score, the median of the IQs facing it is used to norm that score.

Additional statistics of Numbers - October 2010

© October 2010 Paul Cooijmans

Scores

6 *
7 **
8 *******
9 **************
10 ****************************
11 ************
12 ************
13 *********
14 **********
15 ********
16 *****
17 ****
18 *
19 ******
20 *

Scores by males

n = 114

6 *
7 *
8 ******
9 **************
10 **************************
11 ***********
12 ************
13 ********
14 **********
15 ********
16 *****
17 ****
18 *
19 ******
20 *

Scores by females

n = 6

7 *
8 *
10 **
11 *
13 *

Correlation with other tests by Paul Cooijmans

Test n r
Association and Analogies (French)50.91
Analogies of Long Test For Genius (French)50.90
Short Test For Genius280.87
Long Test For Genius (French)50.86
Intelligence Quantifier by assessment260.79
Association subtest of Long Test For Genius (French)50.79
Reason90.72
Odds140.72
Long Test For Genius (N.L.)120.69
Analogies of Long Test For Genius (N.L.)120.69
Reason Behind Multiple-Choice80.68
Spatial section of Test For Genius - Revision 2004120.67
Analogies #170.66
The Nemesis Test70.66
Isis Test110.66
Cooijmans Intelligence Test - Form 2110.57
Test For Genius - Revision 2004120.57
Space, Time and Hyperspace540.57
Long Test For Genius260.57
Reason Behind Multiple-Choice - Revision 200850.54
Association subtest of Long Test For Genius300.53
Qoymans Multiple-Choice #3140.47
The Final Test250.47
Lieshout International Mesospheric Intelligence Test110.43
Cooijmans Intelligence Test - Form 1190.41
Spatial Insight Test60.40
Analogies of Long Test For Genius300.39
Evens80.38
Genius Association Test160.38
Test of Shock and Awe70.35
The Test To End All Tests120.30
Qoymans Multiple-Choice #550.27
Qoymans Multiple-Choice #4200.26
Qoymans Multiple-Choice #190.24
Cartoons of Shock100.23
Association subtest of Long Test For Genius (N.L.)120.22
Associative LIMIT Test70.21
Bonsai Test130.17
Verbal section of Test For Genius - Revision 2004120.13

Weighted average of correlations: 0.521

Conservatively estimated minimum g loading: 0.72

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 with tests by others

Test n r
Unknown tests160.76
Sigma Test140.71
Nonverbal Cognitive Performance Examination110.69
Chimera High Ability Riddle Test60.64
Mega Test250.60
Titan Test150.59
Drenth number series50.32
Strict Logic Sequences Exam II50.26
Logima Strictica 36140.25
Ultra Test60.22
Cattell Culture Fair180.18
Culture Fair Numerical Spatial Examination - Final version130.18
Raven's Advanced Progressive Matrices (I.Q.)120.17
W-8770.16
Strict Logic Sequences Exam I120.08
Wechsler Adult Intelligence Scales80.06
Raven's Advanced Progressive Matrices (raw)90.02
Mysterium Entrance Exam10-0.01
Hoeflin Power Test6-0.06
Graduate Record Examination5-0.44
Encephalist - R5-0.68
T.R.I.5-0.77

Weighted average of correlations: 0.288

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.

National medians

Country n Median score
Austria215.0
United_Kingdom414.5
Belgium713.0
Canada412.0
Finland612.0
Germany512.0
Greece512.0
Sweden612.0
Brazil311.0
France511.0
Italy210.5
United_States2410.5
Argentina210.0
Japan210.0
Netherlands1410.0
Norway210.0
Singapore29.5
Turkey29.5

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 personal details

Personalia n r
P.S.I.A. True160.72
Observed associative horizon is wide110.49
P.S.I.A. Rare160.47
P.S.I.A. System factor120.37
P.S.I.A. Just160.35
P.S.I.A. Ethics factor270.33
Gifted Adult's Inventory of Aspergerisms110.30
Observed behaviour is good250.28
P.S.I.A. Aspergoid160.28
P.S.I.A. Antisocial160.27
P.S.I.A. Deviance factor270.24
P.S.I.A. Introverted160.23
P.S.I.A. Neurotic160.22
Is male1200.16
Year of birth1070.14
P.S.I.A. Extreme160.11
P.S.I.A. Orderly160.09
Mother's educational level520.07
Father's educational level520.01
P.S.I.A. Rational160.01
Educational level53-0.02
Disorders (own)52-0.12
Disorders (parents and siblings)52-0.21
P.S.I.A. Cruel16-0.24
P.S.I.A. Cold16-0.34

Correlation with personal details - within females

Personalia n r
Observed behaviour is good40.87
Year of birth60.65

Correlation with national I.Q.s

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

Estimated g factor loadings Upward and Downward of specific scores

In parentheses the number of score pairs on which that estimated g factor loading is based. The Upward and Downward values are calculated including the pertinent score itself. It is normal that g factor loadings go down when the range is restricted like this, but careful study of the Upward and Downward columns may reveal possible scores below or above which the test loses validity altogether.

ScoreUpward (n)Downward (n)
6.67 (767)NaN (0)
8.67 (755)-.36 (5)
10.60 (571).50 (239)
12.46 (256).62 (477)
14.40 (92).62 (579)
16.41 (31).66 (697)
18NaN (0).68 (728)
19NaN (0).67 (765)
20NaN (0).67 (767)

Reliability

Error

Scores by age

Age class n Median score
80 to 8417.0
70 to 74110.0
60 to 64212.5
55 to 59511.0
50 to 54810.5
45 to 49512.0
40 to 441310.0
35 to 391213.0
30 to 341011.0
25 to 291712.0
22 to 241010.5
20 or 21714.0
18 or 1949.5
17313.0
16210.5

Scores by age - within females

Age class n Median score
40 to 4438.0
35 to 39212.0
22 to 24110.0

Scores by age - within males

Age class n Median score
80 to 8417.0
70 to 74110.0
60 to 64212.5
55 to 59511.0
50 to 54810.5
45 to 49512.0
40 to 44910.0
35 to 391013.5
30 to 34910.0
25 to 291512.0
22 to 24711.0
20 or 21612.5
18 or 1949.5
17313.0
16210.5

Scores by year taken

Year taken n Median score
1995210.5
19961610.0
1997311.0
19981212.5
19992114.0
2001910.0
2002412.0
2003710.0
20041310.0
20051310.0
2006413.5
2007314.0
2008412.5
2009214.0
2010512.0

ryear taken × median score = 0.41
n = 118

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 (validity of the item in this test) 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, one item was never missed, which, together with the already small number of items, depresses the test's reliability.