Space, Time and Hyperspace statistics

© November 2002 Paul Cooijmans

Norms

Space, Time and Hyperspace, spatial subtest of the long Test For Genius (created 1995), has 28 items. The 110 scores so far:

1*
2*
4*
5***
6**
7***
8***
9****
10***** *
11***** ***** ***** ***
12***** ***
13***** ***
14***** ***
15***** ***** **
16***** ****
17***** *
18***** *
19****
20****
21**
22*

Correlation with other tests

Test # cor
A-x (Early versions of Association test) 4 .96
Long Test For Genius (Dutch) 13 .93
Long TFG (Eng) 51 .92
Nemesis 4 .88
Analogies (Dutch subtest LTFG) 13 .87
Test To End All Tests 6 .83
Short TFG 20 .77
Final Test 19 .77
European IQ Test 4 .76
LTFG (French) 5 .73
Drenth Number Series 4 .73
All the above are used for norming

Cooijmans Intelligence Test 16 .6
Numbers 44 .6
Anlogies (French subtest LTFG) 5 .58
Association (Dutch subtest LTFG) 13 .55
Analogies (Eng subtest LTFG) 52 .53
916 Test 4 .47
Association (Eng subtest LTFG) 51 .45
OCIP 8 .42
Sigma Test 7 .41
Unknown tests 15 .38
ACT 4 .33
Association (French subtest LTFG) 5 .32
Cattell Culture Fair 15 .32
Analogies #1 10 .27
Mega 17 .25
Odds 5 .13
SAT 1 7 .09
Bonsai 5 0
NVCP 4 0
Evens 10 No correlation because all Evens scores are 15
Qoymans Multiple-Choice 2 9 -.02
Logima Strictica 14 -.09
W-87 8 -.1
Daedalus Test 4 -.11
Power Test 8 -.12
Mysterium Entrance Exam 6 -.2
WAIS 7 -.2
Encephalist-R 8 -.23
Qoymans Multiple-Choice 1 14 -.28
Titan 9 -.41
COLT 4 -.56
GRE 4 -.59
Raven APM 15 -.65

All other prior tests have less than 4 scores each.

For norming, tests are used that correlate .73 or higher. 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. Missing scores are interpolated. Scores 23 to 28 are extrapolated.

Additional statistics November 2011

Scores on Space, Time, and Hyperspace

Contents type: Spatial.   Period: 1995-2005

1 *
2 *
3 *
4 **
5 ****
6 ****
7 ****
8 ***
9 *****
10 ***********
11 *************************
12 **************
13 ******************
14 ***************
15 ****************
16 *******************
17 *********
18 *************
19 *******
20 *****
21 ***
22 *
23 *

Scores by males

n = 164

3 *
4 **
5 ***
6 ****
7 ***
8 **
9 *****
10 *******
11 ***********************
12 **************
13 *****************
14 **************
15 **************
16 *******************
17 *******
18 ************
19 *******
20 *****
21 ***
22 *
23 *

Scores by females

n = 15

1 *
2 *
5 *
7 *
8 *
10 **
11 **
13 *
15 **
17 **
18 *

Correlation of Space, Time, and Hyperspace with other tests by Paul Cooijmans

(Test index) Test name n r
(65) Long Test For Genius (Netherlandic)160.94
(63) Long Test For Genius840.93
(35) Intelligence Quantifier by assessment270.87
(76) Analogies subtest of Long Test For Genius (Netherlandic)170.87
(27) Spatial section of Test For Genius - Revision 2004180.85
(55) Spatial Insight Test90.85
(18) The Nemesis Test70.84
(50) Qoymans Automatic Test #260.82
(66) Test For Genius - Revision 2004180.75
(56) Short Test For Genius240.74
(44) Associative LIMIT80.74
(64) Long Test For Genius (French)100.65
(54) Test of Shock and Awe110.65
(85) Cooijmans Intelligence Test - Form 1240.64
(62) Reason Behind Multiple-Choice60.62
(7) The Final Test390.61
(10) Genius Association Test230.58
(68) Numbers540.57
(77) Analogies #1160.54
(75) Analogies of Long Test For Genius860.53
(84) Bonsai Test140.53
(87) Cooijmans Intelligence Test - Form 2130.53
(81) Association subtest of Long Test For Genius (Netherlandic)170.52
(28) The Test To End All Tests170.51
(1) Cartoons of Shock100.49
(79) Association subtest of Long Test For Genius850.48
(90) Analogies subtest of Long Test For Genius (French)100.47
(26) Verbal section of Test For Genius - Revision 2004180.40
(82) Reason70.39
(53) Qoymans Multiple-Choice #3320.36
(60) Association and Analogies (French)100.35
(52) Qoymans Multiple-Choice #2130.30
(11) Isis Test100.28
(80) Qoymans Multiple-Choice #4270.28
(16) Lieshout International Mesospheric Intelligence Test150.15
(91) Association subtest of Long Test For Genius (French)100.14
(72) Qoymans Automatic Test #160.02
(69) Odds7-0.05
(86) Evens12-0.10
(51) Qoymans Multiple-Choice #118-0.16
(74) Cooijmans On-Line Test6-0.18

Weighted average of correlations: 0.554

Conservatively estimated minimum g loading: 0.74

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 Space, Time, and Hyperspace with tests by others

(Test index) Test name n r
(209) Drenth number series50.72
(228) Miller Analogies Test (raw; old version)50.71
(224) T.R.I.100.67
(211) Culture Fair Numerical Spatial Examination - Final version120.62
(230) Omega Contemplative Items Pool110.57
(235) Nonverbal Cognitive Performance Examination300.53
(234) Strict Logic Sequences Exam I180.49
(242) Unknown tests210.45
(239) Titan Test140.44
(219) Graduate Record Examination70.36
(225) Logima Strictica 36320.31
(238) 916 Test100.24
(229) Mega Test180.22
(233) Hoeflin Power Test90.21
(237) Sigma Test220.21
(200) American College Testing program70.21
(243) Scholastic Aptitude Test (old)80.18
(201) Wechsler Adult Intelligence Scales110.02
(231) Mysterium Entrance Exam12-0.05
(220) Cattell Culture Fair24-0.07
(218) Raven's Advanced Progressive Matrices (I.Q.)18-0.09
(206) W-879-0.12
(213) Encephalist - R10-0.17
(212) Raven's Advanced Progressive Matrices (raw)11-0.42
(236) International High IQ Society Miscellaneous tests9-0.42

Weighted average of correlations: 0.239

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 Space, Time, and Hyperspace with other tests by Paul Cooijmans - for females

(Test index) Test name n r
(56) Short Test For Genius21.00
(65) Long Test For Genius (Netherlandic)31.00
(63) Long Test For Genius70.97
(81) Association subtest of Long Test For Genius (Netherlandic)40.95
(35) Intelligence Quantifier by assessment40.95
(76) Analogies subtest of Long Test For Genius (Netherlandic)40.87
(79) Association subtest of Long Test For Genius70.77
(75) Analogies of Long Test For Genius80.69
(68) Numbers50.53
(7) The Final Test30.37

Weighted average of correlations: 0.799

Conservatively estimated minimum g loading: 0.89

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 2 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.

Note: This is one of the rare occasions where these correlations can be computed within females.

Estimated loadings of Space, Time, and Hyperspace 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 Space, Time, and Hyperspace on that type
Verbal0.68
Numerical0.63
Spatial0.77
Logical0.36
Heterogeneous0.77

There is no overlap between the categories in this table as a result of leaving out compound tests.

Balanced g loading = 0.64

National medians for Space, Time, and Hyperspace

Country n median score
Germany518.0
Denmark217.5
Poland217.5
Canada616.5
Australia416.0
Finland1016.0
Slovenia216.0
Norway414.5
Brazil514.0
France1114.0
Greece514.0
Israel214.0
Italy213.5
Japan213.0
Sweden1213.0
United_Kingdom813.0
Netherlands1612.5
Belgium512.0
Turkey211.5
United_States3211.5

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 of Space, Time, and Hyperspace with personal details

Personalia n r
Observed associative horizon120.69
Observed behaviour250.46
P.S.I.A. Rational230.38
P.S.I.A. System factor290.33
Educational level660.27
Year of birth1730.25
P.S.I.A. Cold230.23
P.S.I.A. Just230.20
Sex1790.20
P.S.I.A. Antisocial230.17
Father's educational level540.06
P.S.I.A. Orderly230.04
P.S.I.A. Cruel230.04
P.S.I.A. Ethics factor470.04
P.S.I.A. Introverted230.03
P.S.I.A. Deviance factor470.02
P.S.I.A. Neurotic230.01
P.S.I.A. True23-0.03
P.S.I.A. Aspergoid23-0.03
P.S.I.A. Rare23-0.06
Mother's educational level54-0.08
Disorders (own)64-0.19
Disorders (parents and siblings)64-0.20
Gifted Adult's Inventory of Aspergerisms29-0.30
P.S.I.A. Extreme23-0.33

Correlation with personal details of Space, Time, and Hyperspace - within females

Personalia n r
Observed behaviour50.71
Year of birth140.27
Disorders (own)30.14
Disorders (parents and siblings)30.14
Educational level4-0.37

Correlation with personal details of Space, Time, and Hyperspace - within males

Personalia n r
Observed associative horizon120.69
Observed behaviour200.44
P.S.I.A. Rational220.36
P.S.I.A. System factor280.33
Educational level620.28
P.S.I.A. Cold220.21
Year of birth1580.21
P.S.I.A. Antisocial220.18
P.S.I.A. Just220.18
P.S.I.A. Orderly220.09
Father's educational level520.08
P.S.I.A. Ethics factor450.04
P.S.I.A. Neurotic220.03
P.S.I.A. Introverted220.02
P.S.I.A. Deviance factor450.02
P.S.I.A. Cruel220.01
P.S.I.A. True22-0.00
P.S.I.A. Rare22-0.04
P.S.I.A. Aspergoid22-0.04
Mother's educational level52-0.10
Disorders (own)61-0.21
Disorders (parents and siblings)61-0.21
P.S.I.A. Extreme22-0.31
Gifted Adult's Inventory of Aspergerisms27-0.31

Correlation with national I.Q.s of Space, Time, and Hyperspace

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, so some inevitable depression must be taken into account.

ScoreUpward (n)Downward (n)
00.74 (860)NaN (0)
10.50.63 (661)0.67 (142)
130.63 (474)0.73 (421)
15.50.64 (214)0.72 (573)
180.79 (74)0.70 (786)
28NaN (0)0.74 (860)

Reliability

Error

Scores by age

Age class n median score
70 to 7423.5
60 to 64113.0
55 to 59411.5
50 to 54816.0
45 to 491011.5
40 to 442212.5
35 to 393515.0
30 to 342114.0
25 to 292612.0
22 to 241314.0
20 or 211214.0
18 or 191216.0
17616.0
16310.0

Scores by age - within females

Age class n median score
70 to 7412.0
50 to 54117.0
45 to 49111.0
40 to 4469.0
35 to 39215.0
22 to 2429.0

Scores by age - within males

Age class n median score
70 to 7415.0
60 to 64113.0
55 to 59411.5
50 to 54715.0
45 to 49912.0
40 to 441613.5
35 to 393315.0
30 to 342114.0
25 to 292612.0
22 to 241114.0
20 or 211214.0
18 or 191216.0
17616.0
16310.0

Scores by year taken

Year taken n median score
19961411.0
1997312.0
1998814.5
19991115.0
20001014.0
20012913.0
20024113.0
20033513.0
20042815.5
2005316.0

ryear taken × median score = 0.64 (n = 182)

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.