Short Test For Genius statistics

© June 1999 Paul Cooijmans

Norms

The TFG (short version), created 1995, revised 1996, contains 43 problems, 3 of which are solved in advance (no, the answers were not filled in accidentally, as several people have stupidly thought over the years). The scores so far obtained (only first attempts are included):

0 **
1 ***
2 ******
3 ********
3.5 *
4 ******
5 **
6 ***
7 ****
8 **
8.5 *
9 *
10 **
11 *
12 **
12.5 *
13.5 *
14 *
15 **
16 *
16.5 *
17 *
21.5 *
25 *
27 *

As a measure of internal consistency, the correlation between odd-item and even-item scores was computed as .84.

The "other" tests (less than 3 scores each) are Nemesis Test, SAT, WAIS, LAIT, Drenth number series, Stanford-Binet, CTMM, Quest, Numbers, Möbius, NUTE, MAT, unspecified tests, California Test of Logical Relations, Collegium Entrance Exam, Cattell B, W-87, Analogies #1, Eight Item Test, Test To End All Tests.

To ensure objectivity and avoid arbitrary decisions, all reported prior scores are used in norming, however weighted by the square of their correlation multiplied by 10. E.g., a correlation of .8 would give a weight of 6, meaning the score pairs from that test would each be used 6 times.

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 and scores 28 to 40 are extrapolated. [March 2008 the IQs were converted to protonorms using the initial protonorm formula.]

The TFG (short version) is no longer in use.

Additional statistics November 2011

Scores on Short Test For Genius

Contents type: Verbal, numerical, spatial.   Period: 1995-2004

0 **
1 ***
2 *********
3 ********
4 **********
5 *****
6 ***
7 ******
8 ***
9 ******
10 *
11 ***
12 **
13 *
13.5 *
14 **
15 **
16 *
17 **
21 *
25 *
27 *

Correlation of Short Test For Genius with other tests by Paul Cooijmans

(Test index) Test name n r
(35) Intelligence Quantifier by assessment150.95
(68) Numbers280.87
(18) The Nemesis Test40.87
(10) Genius Association Test50.85
(77) Analogies #140.83
(51) Qoymans Multiple-Choice #140.83
(11) Isis Test40.81
(76) Analogies subtest of Long Test For Genius (Netherlandic)70.78
(65) Long Test For Genius (Netherlandic)70.74
(57) Space, Time, and Hyperspace240.74
(7) The Final Test210.74
(63) Long Test For Genius120.72
(75) Analogies of Long Test For Genius140.49
(28) The Test To End All Tests60.41
(79) Association subtest of Long Test For Genius140.39
(85) Cooijmans Intelligence Test - Form 1100.38
(84) Bonsai Test50.27
(81) Association subtest of Long Test For Genius (Netherlandic)70.00
(1) Cartoons of Shock4-0.21
(53) Qoymans Multiple-Choice #35-0.57

Weighted average of correlations: 0.625

Conservatively estimated minimum g loading: 0.79

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

Correlation of Short Test For Genius with tests by others

(Test index) Test name n r
(207) Chimera Test50.95
(241) Ultra Test40.89
(239) Titan Test100.76
(228) Miller Analogies Test (raw; old version)40.62
(229) Mega Test150.57
(204) Chimera High Ability Riddle Test100.50
(233) Hoeflin Power Test40.43
(219) Graduate Record Examination60.42
(206) W-8750.27
(218) Raven's Advanced Progressive Matrices (I.Q.)80.07
(242) Unknown tests15-0.09
(220) Cattell Culture Fair8-0.11
(211) Culture Fair Numerical Spatial Examination - Final version4-0.32
(202) Cattell Verbal4-0.97

Weighted average of correlations: 0.302

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 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.

Estimated loadings of Short 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 Short Test For Genius on that type
Verbal0.71
Numerical0.93
Spatial0.86
Heterogeneous0.64

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

Balanced g loading = 0.79

National medians for Short Test For Genius

Country n median score
Finland611.5
Belgium311.0
Australia27.5
Netherlands77.0
Sweden35.0
United_States185.0
United_Kingdom44.5
France54.0

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 Short Test For Genius with personal details

Personalia n r
P.S.I.A. Introverted40.95
P.S.I.A. Aspergoid40.94
P.S.I.A. Rare40.93
P.S.I.A. Rational40.90
Observed behaviour130.78
P.S.I.A. Neurotic40.66
Gifted Adult's Inventory of Aspergerisms40.62
Observed associative horizon110.57
P.S.I.A. System factor50.47
Father's educational level100.44
P.S.I.A. Ethics factor80.40
P.S.I.A. Deviance factor80.39
P.S.I.A. True40.36
P.S.I.A. Cold40.31
Sex730.30
Educational level110.22
Disorders (own)110.20
Mother's educational level100.06
Year of birth610.01
P.S.I.A. Just4-0.04
P.S.I.A. Extreme4-0.16
Disorders (parents and siblings)10-0.38
P.S.I.A. Antisocial4-0.39
P.S.I.A. Orderly4-0.70
P.S.I.A. Cruel4-0.93

Correlation with national I.Q.s of Short 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 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)
00.79 (200)NaN (0)
20.77 (188)0.64 (12)
50.84 (109)0.61 (66)
80.83 (72)0.58 (104)
110.72 (28)0.63 (146)
140.75 (19)0.62 (153)
40NaN (0)0.79 (200)

Reliability

Error

Scores by age

Age class n median score
60 to 6437.0
55 to 59217.5
50 to 5433.0
45 to 4984.0
40 to 4443.0
35 to 3987.5
30 to 34125.0
25 to 29117.0
22 to 2466.0
20 or 2134.0
18 or 1927.0
1718.0
1514.0

Scores by age - within females

Age class n median score
45 to 4923.0
40 to 4421.0
25 to 2914.0

Scores by age - within males

Age class n median score
60 to 6437.0
55 to 59217.5
50 to 5433.0
45 to 4964.5
40 to 4428.0
35 to 3987.5
30 to 34125.0
25 to 29108.0
22 to 2466.0
20 or 2134.0
18 or 1927.0
1718.0
1514.0

Scores by year taken

Year taken n median score
199562.5
1996184.0
1997117.0
1998186.0
199997.0
200026.5
200124.5
2002211.5
200335.0
200426.5

ryear taken × median score = 0.46 (n = 73)

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.