ArticlePDF Available

Spearman's hypothesis on item-level data from Raven's Standard Progressive Matrices: A replication and extension

Authors:
  • Ulster Institute for Social Research

Abstract and Figures

Item-level data from Raven’s Standard Progressive Matrices was compiled for 12 diverse groups from previously published studies. The method of correlated vectors was used on every possible pair of groups with available data (45 comparisons). Depending on exact method chosen, the mean and mean MCV correlation was about .46/51. Only 2/1 of 45 were negative. Spearman’s hypothesis is confirmed for item-level data from the Standard Progressive Matrices.
Content may be subject to copyright.
The Winnower
Published March 22, 2015
Updated November 16, 2015
Spearman’s hypothesis on item-level
data from Raven’s Standard
Progressive Matrices: A replication
and extension
Emil O. W. Kirkegaard, University of Aarhus.
Abstract
Item-level data from Raven’s Standard Progressive Matrices was compiled for 12 diverse groups from
previously published studies. Jensen’s method (method of correlated vectors) was used on every
possible pair of groups with available data (45 comparisons). The mean Jensen coefficient was about .
50. Very few were negative. Spearman’s hypothesis is confirmed for item-level data from the Standard
Progressive Matrices, but interpretation is unclear.
Key words: Raven's Progressive Matrices, IQ, intelligence, Spearman’s hypothesis, method of
correlated vectors, Jensen’s method
1. Introduction and method
Jensen’s method (method of correlated vectors; MCV) is a statistical method invented by Arthur Jensen
(1). The purpose of it is to measure to which degree a latent variable is responsible for an observed
correlation between an aggregate measure and a criteria variable. Jensen had in mind the general factor
of cognitive ability (the g factor) as measured by various IQ tests and their subtests, and criteria
variables such as brain size. The method, however, is applicable to any latent trait (e.g. general
socioeconomic factor (2,3)). When this method is applied to group differences, particularly ethnoracial
ones, it is called Spearman’s hypothesis (SH) because Spearman was the first to note it in his 1927
book (4).
By now, several large studies and meta-analysis of Jensen's method results for group differences have
been published (5–8). These studies generally support the hypothesis. Almost all studies use subtest
loadings instead of item loadings. This is probably because psychologists are reluctant to share their
data (9,10) and as a result there are few open item-level datasets available to use for this purpose,
whereas subtest results are often but not always reported in papers. Furthermore, before the
introduction of modern computers and the internet, it was impractical to share item-level data. There
are advantages and disadvantages to using item-level data over subtest-level data. There are more items
than subtests which means that the vectors will be longer and thus sampling error will be smaller. On
the other hand, items are less reliable and less pure measures which introduces both error and more
non-g ability variance.
The recent study by Nijenhuis et al (5) however, employed item-level data from Raven’s Standard
Progressive Matrices (SPM) and included a diverse set of samples (Libyan, Russian, South African,
Roma from Serbia, Moroccan and Spanish). The authors did not use their collected data to its full
extent, presumably because they were comparing the groups (semi-)manually. To compare all
combinations with a dataset of e.g. 10 groups means that one has to do 45 comparisons.1 However, this
task can easily be overcome with programming skills, and I thus saw a research opportunity.
The authors did not provide the data in the paper despite it being easy to include it in online
supplementary tables. They refused to share the data when contacted. However, the data was available
from the primary studies they cited in most cases. Thus, I collected the data from their data sources.
This resulted in data from 12 samples of which 10 had both difficulty and item-whole correlations data.
Table 1 gives an overview of the datasets:
1 The number of possible sample comparisons is given by the formula for picking 2 out of N without order.
Short name Race Selection N Year Ref
A1 African Undergraduates 173 2000
Rushton and Skuy
2000 (11)
University of the
Witwatersrand and
the Rand Afrikaans
University in
Johannesburg,
South Africa
W1 European Undergraduates 136 2000
Rushton and Skuy
2000
University of the
Witwatersrand and
the Rand Afrikaans
University in
Johannesburg,
South Africa
W2 European Std 7 classes 1056 1992 Owen 1992 (12)
20 schools in the
Pretoria-
Witwatersrand-
Vereeniging (PWV)
area and 10 schools
in the Cape
Peninsula
C1
Colored (African
European) Std 7 classes 778 1992 Owen 1992
20 coloured schools
in the Cape
Peninsula
I1 Indian Std 7 classes 1063 1992 Owen 1992
30 schools selected
at random from the
list of high schools
in and around
Durban
A2 African Std 7 classes 1093 1992 Owen 1992
Three schools in the
PWV area and 25
schools in KwaZulu
(Natal)
A3 African
First year Engineering
students 198 2002
Rushton et al 2002
(13)
First-year students
from the Faculties
of Engineering and
the Built
Environment at the
University of the
Witwatersrand
I2 Indian
First year Engineering
students 58 2002 Rushton et al 2002
First-year students
from the Faculties
of Engineering and
the Built
Environment at the
University of the
Witwatersrand
W3 European First year Engineering
students
86 2002 Rushton et al 2002 First-year students
from the Faculties
of Engineering and
the Built
Environment at the
University of the
Witwatersrand
R1 Roma Adults ages 16 to 66 231 2004.5
Rushton et al 2007
(14)
Three communities
(i.e., Drenovac,
Mirijevo, and
Rakovica) in the
vicinity of Belgrade
W4 European Adults ages 18 to 65 258 2012 Diaz et al 2012 (15)
Mainly from the
city of Valencia
NA1 North African Adults ages 18 to 50 202 2012 Diaz et al 2012
Casablanca,
Marrakech, Meknes
and Tangiers
Table 1: Description of the included studies.
2. Item-whole correlations and item loadings
The data in the papers did usually not contain the actual factor loadings of the items. Instead, they
contained the item-whole correlations. The authors argue that one can use these because of the high
correlation of unweighted means with extracted g-factors (often r=.99, e.g. (16)). Some studies did
provide both loadings and item-whole correlations, yet the authors did not correlate them to see how
good proxies the item-whole correlations are for the loadings. I calculated this for the 4 studies that
included both metrics. Results are shown in Table 2.
Item-whole r / g-loading W2 C1 I1 A2
W2 0.549 0.099 0.327 0.197
C1 0.695 0.9 0.843 0.92
I1 0.616 0.591 0.782 0.686
A2 0.626 0.882 0.799 0.981
Table 2: Correlations of item-whole correlations (rows) and g-loadings of items (columns).
Note: Within sample correlations between item-whole correlations and item factor loadings are in the
diagonal, marked with italic.
As can be seen, the item-whole correlations were not in all cases great proxies for the actual loadings.
To further test this idea, I calculated the item-whole correlations and the factor loadings (first factor,
minimum residuals) in the open Wicherts dataset (N=500ish, Dutch university students, see (9)) tested
on Raven’s Advanced Progressive Matrices. The correlation was .89. Thus, aside from the odd result in
the W2 sample (N=1056), item-whole correlations were a reasonable proxy for the factor loadings.
3. Item difficulties across samples
If two groups are tested on the same test and this test measures the same trait in both groups, then even
if the groups have different mean trait levels, the order of difficulty of the items or subtests should be
similar. Rushton et al (11,13,14) have examined this in previous studies and found it generally to be the
case. Table 3 below shows all the cross-sample correlations of item difficulties.
Sample A1 W1 W2 C1 I1 A2 A3 I2 W3 R1 NA1 W4
A1 1 0.879 0.981 0.962 0.988 0.856 0.956 0.892 0.789 0.892 0.948 0.927
W1 0.879 1 0.926 0.792 0.874 0.652 0.961 0.973 0.945 0.695 0.918 0.946
W2 0.981 0.926 1 0.947 0.984 0.824 0.973 0.923 0.839 0.862 0.96 0.953
C1 0.962 0.792 0.947 1 0.976 0.944 0.89 0.814 0.695 0.952 0.918 0.871
I1 0.988 0.874 0.984 0.976 1 0.88 0.951 0.884 0.788 0.91 0.951 0.924
A2 0.856 0.652 0.824 0.944 0.88 1 0.757 0.682 0.559 0.968 0.823 0.761
A3 0.956 0.961 0.973 0.89 0.951 0.757 1 0.959 0.896 0.802 0.948 0.959
I2 0.892 0.973 0.923 0.814 0.884 0.682 0.959 1 0.924 0.722 0.913 0.92
W3 0.789 0.945 0.839 0.695 0.788 0.559 0.896 0.924 1 0.602 0.876 0.909
R1 0.892 0.695 0.862 0.952 0.91 0.968 0.802 0.722 0.602 1 0.864 0.804
NA1 0.948 0.918 0.96 0.918 0.951 0.823 0.948 0.913 0.876 0.864 1 0.966
W4 0.927 0.946 0.953 0.871 0.924 0.761 0.959 0.92 0.909 0.804 0.966 1
Table 3: Intercorrelations between item difficulties in 12 samples.
The unweighted mean intercorrelation is .88. This is quite remarkable given the diversity of the
samples.
4. Item-whole correlations across samples
Given the above, one might expect similar results for the item-whole correlations. This however is not
so. Results are shown in Table 4.
Sample A1 W1 W2 C1 I1 A2 A3 I2 W3 R1
A1 1 -0.196 0.588 0.578 0.729 0.539 0.267 0.037 -0.302 0.567
W1 -0.196 1 0.165 -0.59 -0.245 -0.683 0.422 0.514 0.546 -0.545
W2 0.588 0.165 1 0.442 0.787 0.292 0.61 0.248 0.023 0.393
C1 0.578 -0.59 0.442 1 0.786 0.942 0.008 -0.249 -0.488 0.779
I1 0.729 -0.245 0.787 0.786 1 0.685 0.424 0.089 -0.325 0.628
A2 0.539 -0.683 0.292 0.942 0.685 1 -0.133 -0.301 -0.52 0.774
A3 0.267 0.422 0.61 0.008 0.424 -0.133 1 0.262 0.372 0.02
I2 0.037 0.514 0.248 -0.249 0.089 -0.301 0.262 1 0.338 -0.207
W3 -0.302 0.546 0.023 -0.488 -0.325 -0.52 0.372 0.338 1 -0.488
R1 0.567 -0.545 0.393 0.779 0.628 0.774 0.02 -0.207 -0.488 1
Table 4: Intercorrelations between item-whole correlations in 10 samples.
Note: The last two samples, NA1 and W4, did not have item-whole correlation data.
The reason for this state of affairs is that the factor loadings/item-whole correlations change when the
group mean trait level changes. For many samples, most of the items were too easy (passing rates at or
very close to 100%). When there is no variation in a variable, one cannot calculate a correlation to
some other variable. This means that for a number of items for multiple samples, there was missing
data for the items. Furthermore, in general, when pass rates move away from .50, the variance in the
items are reduced which then reduces their correlation to the total (or their g-loading when analyzed
with classical test theory approaches). Thus, observed item-wholes/g-loadings are a function of the pass
rate as well as their actual g-loading.
The lack of cross-sample consistency in item-whole correlations may also explain the weak Jensen
coefficients in Diaz et al (15) since they used g-loadings from another study instead of from their own
samples.
5. Spearman’s hypothesis using one static vector of estimated factor
loadings
Some of the samples had rather small sample sizes (I2, N=58, W3, N=86). Thus one might get the idea
to use the item-whole correlations from one or more of the large samples for comparisons involving
other groups. In fact, given the instability of item-whole correlations across sample as can be seen in
Table 4, this is a bad idea. However, for sake of completeness, I calculated the results based on this
method nonetheless. As the best estimate of factor loadings, I averaged the item-whole correlations data
from the four largest samples (W2, C1, I1 and A2).
Using this vector of item-whole correlations, I calculated Jensen's coefficient for every possible sample
comparison. Because there were 12 samples with pass rate data, this number is 66. Jensen's method was
applied by subtracting the lower scoring sample’s item difficulties from the higher scoring sample’s
thus producing a vector of the sample pair difference on each item. I correlated this vector with the
vector of item-whole correlations. The results are shown in Table 5.
Sample A1 W1 W2 C1 I1 A2 A3 I2 W3 R1 NA1 W4
A1 -0.149 0.197 0.422 0.097 0.83 -0.026 -0.116 -0.259 0.797 -0.348 -0.316
W1 -0.149 -0.307 0.066 -0.139 0.469 -0.291 -0.195 -0.401 0.399 0.307 0.057
W2 0.197 -0.307 0.561 0.4 0.865 -0.271 -0.28 -0.377 0.83 -0.355 -0.456
C1 0.422 0.066 0.561 0.534 0.879 0.227 0.11 -0.058 0.641 -0.233 -0.053
I1 0.097 -0.139 0.4 0.534 0.884 -0.021 -0.104 -0.243 0.826 -0.448 -0.287
A2 0.83 0.469 0.865 0.879 0.884 0.655 0.522 0.318 0.199 0.421 0.404
A3 -0.026 -0.291 -0.271 0.227 -0.021 0.655 -0.173 -0.407 0.613 0.434 -0.425
I2 -0.116 -0.195 -0.28 0.11 -0.104 0.522 -0.173 -0.372 0.456 0.331 -0.245
W3 -0.259 -0.401 -0.377 -0.058 -0.243 0.318 -0.407 -0.372 0.233 -0.053 -0.112
R1 0.797 0.399 0.83 0.641 0.826 0.199 0.613 0.456 0.233 0.357 0.316
NA1 -0.348 0.307 -0.355 -0.233 -0.448 0.421 0.434 0.331 -0.053 0.357 -0.026
W4 -0.316 0.057 -0.456 -0.053 -0.287 0.404 -0.425 -0.245 -0.112 0.316 -0.026
Table 5: Jensen's coefficients of group differences across 12 samples using 1 static item-whole
correlations.
As one can see, the results are all over the place. The mean coefficient is .12.
6. Spearman’s hypothesis using a variable vector of estimated factor
loadings
Since item-whole correlations varied from sample to sample, another idea is to use the samples’ item-
whole correlations. I used the unweighted mean of the item-whole correlations for each item (te
Nijenhuis et al (5) used a weighted mean). In some cases, only one sample has item-whole correlations
for some items (because the other sample had no variance on the item, i.e. 100% or 0% got it right). In
these cases, one can choose to use the value from the remaining sample, or one can ignore the item and
use Jensen's method on the remaining items. Not knowing which was the best method, I calculated
results using both methods, they are shown in Table 6 and 7.
Sample A1 W1 W2 C1 I1 A2 A3 I2 W3 R1
A1 0.787 0.388 0.292 0.046 0.7 0.484 0.409 0.368 0.709
W1 0.787 0.799 0.499 0.756 0.515 0.786 0.405 0.604 0.545
W2 0.388 0.799 0.675 0.631 0.852 0.429 0.467 0.504 0.791
C1 0.292 0.499 0.675 0.517 0.88 0.324 0.3 -0.095 0.673
I1 0.046 0.756 0.631 0.517 0.842 0.473 0.397 0.31 0.789
A2 0.7 0.515 0.852 0.88 0.842 0.571 0.428 -0.034 0.217
A3 0.484 0.786 0.429 0.324 0.473 0.571 0.379 0.661 0.64
I2 0.409 0.405 0.467 0.3 0.397 0.428 0.379 0.603 0.44
W3 0.368 0.604 0.504 -0.095 0.31 -0.034 0.661 0.603 0.201
R1 0.709 0.545 0.791 0.673 0.789 0.217 0.64 0.44 0.201
Table 6: Jensen's coefficients of group differences across 10 samples using variable item-whole
correlations, method 1.
Sample A1 W1 W2 C1 I1 A2 A3 I2 W3 R1
A1 0.421 0.397 0.326 0.056 0.717 0.483 0.3 0.147 0.739
W1 0.421 0.72 0.14 0.523 0.178 0.703 0.443 0.65 0.354
W2 0.397 0.72 0.675 0.631 0.852 0.443 0.533 0.502 0.791
C1 0.326 0.14 0.675 0.517 0.88 0.385 0.191 -0.082 0.673
I1 0.056 0.523 0.631 0.517 0.842 0.507 0.403 0.279 0.789
A2 0.717 0.178 0.852 0.88 0.842 0.618 0.303 0.018 0.217
A3 0.483 0.703 0.443 0.385 0.507 0.618 0.418 0.554 0.667
I2 0.3 0.443 0.533 0.191 0.403 0.303 0.418 0.579 0.348
W3 0.147 0.65 0.502 -0.082 0.279 0.018 0.554 0.579 0.078
R1 0.739 0.354 0.791 0.673 0.789 0.217 0.667 0.348 0.078
Table 7: Jensen's coefficients of group differences across 10 samples using variable item-whole
correlations, method 2.
Nearly all results are positive using either method. The results are slightly stronger when ignoring items
where both samples do not have item-whole correlation data. A better way to visualize the results is to
use a histogram with an empirical density curve, as shown in Figure 1 and 2.
Figure 1: Histogram of Jensen's method coefficients using method 1.
The mean result for method 1/2 was .51/.46. Almost all coefficients were positive, only 2/1 was
negative for method 1/2.
For the remainder of the paper, only results using method 1 are used.
7. Mean Jensen's coefficient value by sample and moderator analysis
It is interesting to examine the mean Jensen coefficient by sample. They are shown in Table 8.
Sample mean sd median
A1 0.465 0.235 0.409
W1 0.633 0.151 0.604
W2 0.615 0.175 0.631
C1 0.452 0.286 0.499
I1 0.529 0.257 0.517
A2 0.552 0.312 0.571
A3 0.527 0.149 0.484
I2 0.425 0.081 0.409
W3 0.347 0.278 0.368
R1 0.556 0.226 0.64
Table 8: Mean Jensen's coefficient by sample.
There is no obvious racial pattern. Instead, one might expect the relatively lower result of some
samples to be due to sampling error. Jensen's coefficient is extra sensitive to sampling error. If so, the
mean coefficient should be higher for the larger samples. To see if this was the case, I calculated the
rank-order correlation between sample size and sample mean coefficient, r=.45. Rank-order was used
Figure 2: Histogram of Jensen's method coefficients using method 2.
because the effect of sample size on sampling error is non-linear. Figure 3 shows the scatter plot of this.
One can also examine sample size as a moderating variable as the comparison-level. This increases the
number of datapoints to 45. I used the harmonic mean2 of the 2 samples as the sample size metric.
Figure 4 shows a scatter plot of this.
We can see in the plot that the results from the 6 largest comparisons (harmonic mean sample size>800)
have a mean of .73. For the smaller studies (harmonic mean sample size<800), the results have a mean
of .48. The results from the smaller studies vary more, as expected with their higher sampling error, and
they are on average weaker, as expected from the increased sampling error in the item-whole
2 The harmonic mean is given by the number of numbers divided by the sum of reciprocal values of each number.
Figure 3: Sample size as a moderating variable at the sample mean-
level.
Figure 4: Sample size as a moderator variable at the comparison-
level.
correlation and pass rate difference vectors.
I also examined the group difference size as a moderator variable. I computed this as the difference
between the mean item difficulty by the groups. However, it had a near-zero relationship to the
coefficients (rank-order r=.03).
8. Discussion and conclusion
Spearman’s hypothesis has been decisively confirmed using classical test theory item-level data from
Raven’s Standard Progressive Matrices. The analysis presented here can easily be extended to cover
more datasets, as well as item-level data from other IQ tests. Researchers should compile such data into
open datasets so they can be used for future studies.
It is interesting to note the consistency of results within and across samples that differ in race. Race
differences in general intelligence as measured by the SPM appear to be just like those within races.
Still, the interpretation of the results is contested (5,17,18).
8.1. Limitations
Some authors refused to share data when contacted. They usually required co-authorship to be
willing to share their data. For this reason, the meta-analysis was unnecessarily limited.
Item-level g-loadings were not available for most studies, so instead item-whole correlations
were used as a proxy. These seem to be fairly useful as proxies, but this has not been
extensively tested.
Supplementary material and acknowledgments
R source code and datasets can be found at the Open Science Framework repository
https://osf.io/ef6vb/
References
1. Jensen AR. The g factor: the science of mental ability. Westport, Conn.: Praeger; 1998.
2. Kirkegaard EOW. The international general socioeconomic factor: Factor analyzing international
rankings. Open Differ Psychol [Internet]. 2014 Sep 8 [cited 2014 Oct 13]; Available from:
http://openpsych.net/ODP/2014/09/the-international-general-socioeconomic-factor-factor-
analyzing-international-rankings/
3. Kirkegaard EOW. Crime, income, educational attainment and employment among immigrant
groups in Norway and Finland. Open Differ Psychol [Internet]. 2014 Oct 9 [cited 2014 Oct 13];
Available from: http://openpsych.net/ODP/2014/10/crime-income-educational-attainment-and-
employment-among-immigrant-groups-in-norway-and-finland/
4. Spearman C. The abilities of man. 1927 [cited 2015 Nov 15]; Available from:
http://doi.apa.org/psycinfo/1927-01860-000
5. te Nijenhuis J, Al-Shahomee AA, van den Hoek M, Grigoriev A, Repko J. Spearman’s hypothesis
tested comparing Libyan adults with various other groups of adults on the items of the Standard
Progressive Matrices. Intelligence. 2015 May;50:114–7.
6. te Nijenhuis J, David H, Metzen D, Armstrong EL. Spearman’s hypothesis tested on European
Jews vs non-Jewish Whites and vs Oriental Jews: Two meta-analyses. Intelligence. 2014
May;44:15–8.
7. te Nijenhuis J, van den Hoek M, Armstrong EL. Spearman’s hypothesis and Amerindians: A meta-
analysis. Intelligence. 2015 May;50:87–92.
8. Jensen AR. The nature of the black–white difference on various psychometric tests: Spearman’s
hypothesis. Behav Brain Sci. 1985 Jul;8(02):193.
9. Wicherts JM, Bakker M. Publish (your data) or (let the data) perish! Why not publish your data
too? Intelligence. 2012 Mar;40(2):73–6.
10. Wicherts JM, Borsboom D, Kats J, Molenaar D. The poor availability of psychological research
data for reanalysis. Am Psychol. 2006;61(7):726–8.
11. Rushton JP, Skuy M. Performance on Raven’s Matrices by African and White University Students
in South Africa. Intelligence. 2000;28(4):251–65.
12. Owen K. The suitability of Raven’s Standard Progressive Matrices for various groups in South
Africa. Personal Individ Differ. 1992;13(2):149–59.
13. Rushton JP, Skuy M, Fridjhon P. Jensen Effects among African, Indian, and White engineering
students in South Africa on Raven’s Standard Progressive Matrices. Intelligence. 2002
Sep;30(5):409–23.
14. Rushton JP, Čvorović J, Bons TA. General mental ability in South Asians: Data from three Roma
(Gypsy) communities in Serbia. Intelligence. 2007 Jan;35(1):1–12.
15. Diaz A, Sellami K, Infanzón E, Lanzón T, Lynn R. A comparative study of general intelligence in
Spanish and Moroccan samples. Span J Psychol. 2012 Jul;15(2):526–32.
16. Kirkegaard EOW, Nordbjerg O. Validating a Danish translation of the International Cognitive
Ability Resource sample test and Cognitive Reflection Test in a student sample. Open Differ
Psychol [Internet]. 2015 Jul 31 [cited 2015 Aug 6]; Available from:
http://openpsych.net/ODP/2015/07/validating-a-danish-translation-of-the-international-cognitive-
ability-resource-sample-test-and-cognitive-reflection-test-in-a-student-sample/
17. Raven J. Testing the SpearmanJensen Hypothesis Using the Items of the RPM [Internet]. 2010
[cited 2015 Nov 16]. Available from: http://www.eyeonsociety.co.uk/resources/testingSJHyp.pdf
18. Repko J. Spearman’s hypothesis tested with Raven’s Progressive Matrices: A psychometric meta-
analysis. 2011 [cited 2015 Nov 16]; Available from: http://dare.uva.nl/cgi/arno/show.cgi?
fid=347520
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
We translated the International Cognitive Ability Resource sample test (ICAR16) and the Cognitive Reflection Test (CRT) into Danish. We administered the test online to a student sample (N=72, mean age 17.4). Factor analysis revealed a general factor. The summed score of all test items correlated .42 with GPA. Item difficulties correlated .85 with those reported in the Internet norming sample. Method of correlated vectors analysis showed positive relationships between g-loading of items/subtests and their correlation with GPA (r=.53/.85). Model comparisons revealed that for predicting GPA the CRT did not have incremental validity over the ICAR16, but the evidence was not strong.
Article
Full-text available
I present new predictive analyses for crime, income, educational attainment and employment among immigrant groups in Norway and crime in Finland. Furthermore I show that the Norwegian data contains a strong general socioeconomic factor (S) which is highly predictable from country-level variables (National IQ .59, Islam prevalence -.71, international general socioeconomic factor .72, GDP .55), and correlates highly (.78) with the analogous factor among immigrant groups in Denmark. Analyses of the prediction vectors show very high correlations (generally > ±.9) between predictors which means that the same variables are relatively well or weakly predicted no matter which predictor is used. Using the method of correlated vectors shows that it is the underlying S factor that drives the associations between predictors and socioeconomic traits, not the remaining variance (all correlations near unity).
Article
Full-text available
Many studies have examined the correlations between national IQs and various country-level indexes of well-being. The analyses have been unsystematic and not gathered in one single analysis or dataset. In this paper I gather a large sample of country-level indexes and show that there is a strong general socioeconomic factor (S factor) which is highly correlated (.86-.87) with national cognitive ability using either Lynn and Vanhanen's dataset or Altinok's. Furthermore, the method of correlated vectors shows that the correlations between variable loadings on the S factor and cognitive measurements are .99 in both datasets using both cognitive measurements, indicating that it is the S factor that drives the relationship with national cognitive measurements, not the remaining variance.
Article
Full-text available
Spearman's hypothesis states that differences between groups on the subtests of an IQ battery are a function of the cognitive complexity of these subtests: large differences between groups on high-complex subtests and small differences between groups on low-complex subtests, and it is virtually always confirmed. We test Spearman's hypothesis comparing European Jews with gentile Whites in the US, and European Jews and Oriental Jews in Israel. We carried out two meta-analyses based on, respectively, 4 data points and a total N = 302; 4 data points and a total N = 870. In both meta-analyses Spearman's hypothesis was strongly confirmed with mean rs with values of, respectively, .80 and .87. We conclude that Spearman's hypothesis is not only confirmed when Whites are compared with groups with lower mean IQ scores, but also when Whites are compared with groups with higher mean IQ scores; Spearman's hypothesis appears to be a more robust phenomenon than previously thought.
Article
Full-text available
The aim of this study is to fill a gap in intelligence research by presenting data for the average IQ in Morocco and for a comparable sample in Spain. Adult samples were administered the Raven Standard Progressive Matrices (SPM) (Raven, Court, & Raven, 2001) and scored for the total test and for the three sub-factors of gestalt continuation, verbal-analytical reasoning and visuospatial ability identified by Lynn, Allik, and Irwing (2004). The total test and the three factors have shown satisfactory reliability. Our results for the Moroccan sample show significant relationship between general intelligence factor, gestalt continuation and visuospatial ability with education level and income. Conversely, these variables have been shown to be independent for the Spanish sample. This sample obtained significantly higher scores for the four factors assessed than the Moroccan one. These differences have been found also comparing samples with the same education levels. Finally, the errors percentage for Moroccans has been higher than for Spaniards in all the items, suggesting that the level of difficulty was higher for the Moroccan sample.
Article
Spearman's hypothesis states that differences between groups on the subtests of an IQ battery are a function of the g loadings of these subtests, such that there are small differences between groups on subtests with low g loadings and large differences between groups on subtests with high g loadings, and it is confirmed in the large majority of studies. In this paper, we test Spearman's hypothesis, comparing Amerindians with Whites in the US and Canada. We carried out a meta-analysis based on 25 data points and a total N = 2706 Amerindians. Spearman's hypothesis was strongly confirmed with a mean r with a value of .62. We conclude that Spearman's hypothesis appears to be a more regular phenomenon than previously thought.
Article
This article examines the suitability of the Raven Standard Progressive Matrices Test (SPM) for groups of white, coloured, Indian and black pupils in Standard 7 in South Africa. The four groups show very little difference in test reliabilities, the rank order of item difficulties, item discrimination values, and the loadings of items on the first principal component. Consequently, from a psychometric point of view, the SPM is not culturally biased. However, the test is not culture or ethnic ‘blind’ either. This is revealed by discriminant analysis which shows that the largest proportion of the black and white testees follow the general pattern of their own group. (This tendency is far less evident in the coloured and Indian groups.) The groups also show large mean test score differences, especially between black and white pupils where the differences is nearly 3 SD units. Regarding the nature of these differences, it was found that items which discriminate best within the groups were also the items that showed the largest differences between the groups.It was concluded that, despite the similar properties of the SPM for the various groups, the test is nevertheless unsuitable—on account of the large mean differences—for use as a common test with common norms for black and white pupils in Std 7. In a multicultural society like South Africa, this finding poses serious problems for psychologists who are concerned with the establishment of common tests for all.
Article
Although the black and white populations in the United States differ, on average, by about one standard deviation (equivalent to 15 IQ points) on current IQ tests, they differ by various amounts on different tests. The present study examines the nature of the highly variable black–white difference across diverse tests and indicates the major systematic source of this between-population variation, namely, Spearman's g. Charles Spearman originally suggested in 1927 that the varying magnitude of the mean difference between black and white populations on a variety of mental tests is directly related to the size of the test's loading on g, the general factor common to all complex tests of mental ability. Eleven large-scale studies, each comprising anywhere from 6 to 13 diverse tests, show a significant and substantial correlation between tests' g loadings and the mean black–white difference (expressed in standard score units) on the various tests. Hence, in accord with Spearman's hypothesis, the average black–white difference on diverse mental tests may be interpreted as chiefly a difference in g, rather than as a difference in the more specific sources of test score variance associated with any particular informational content, scholastic knowledge, specific acquired skill, or type of test. The results of recent chronometric studies of relatively simple cognitive tasks suggest that the g factor is related, at least in part, to the speed and efficiency of certain basic information-processing capacities. The consistent relationship of these processing variables to g and to Spearman's hypothesis suggests the hypothesis that the differences between black and white populations in the rate of information processing may account for a part of the average black–white difference on standard IQ tests and their educational and occupational correlates.
Article
Untimed Raven's Standard Progressive Matrices (SPM) were administered to 309 17- to 23-year-old students at the University of the Witwatersrand and the Rand Afrikaans University in Johannesburg, South Africa (173 Africans, 136 Whites; 205 women, 104 men). African students solved an average of 44 of the 60 problems whereas White students solved an average of 54 of the problems (p<.001). By the standards of the 1993 US normative sample, the African university students scored at the 14th percentile and the White university students scored at the 61st percentile (IQ equivalents of 84 and 104, respectively). The African–White differences were found to be greater on those items of the SPM with the highest item–total correlations, indicating a difference in g, or the general factor of intelligence. A small sex difference favoring males was found in both the African and the White samples, but unrelated to g.