Space, Time and Hyperspace statistics

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

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

• n: 182
• Median: 13.0
• Quartile deviation: 2.5
• Range: 22
• Maximum possible: 28
• Male median: 14.0 (n = 164)
• Female median: 11.0 (n = 15)
• Hardness: 0.54
• Resolution: 0.14

Scores by males

n = 164

Scores by females

n = 15

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

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

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

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.

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

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

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

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

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:

• r = -0.05 (n = 146)

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.

Reliability

• Split-half = 0.83
• Cronbach's alpha = 0.96

Error

• Standard error = 1.4 raw score points

Scores by age

Scores by age - within females

Scores by age - within males

Scores by year taken

r_{year taken × median score} = 0.64 (n = 182)

Robustness and overall test quality

• Robustness by month = 0.92
• Quality = 0.77

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.