Does g variance change in adulthood? Testing the age de-differentiation hypothesis across sex

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Does g variance change in adulthood? Testing theage de-differentiation hypothesis across sex

Sergio Escorial*, Manuel Juan-Espinosa, Luis F. Garcıa,Irene Rebollo, Roberto Colom

Departamento de Psicologıa Biologica y de la Salud, Facultad de Psicologıa (Despacho 15),Universidad Autonoma de Madrid, 28049 Madrid Spain

Received 27 December 2001; received in revised form 1 April 2002; accepted 27 April 2002

Abstract

In the last decade, changes in the structure of intelligence across the life-span has become a central topicin the research on human intelligence. One of the main hypotheses that has arisen to account for suchchanges has been the age de-differentiation hypothesis [Balinsky, Genetic Psychology Monographs 23 1941,191]. It predicts an increase in the importance of g, and a decrease in the number and importance of thelower-order abilities from early maturity to senescence. Despite of the research effort to test this hypothesis,no study has ever been conducted controlling by sex. For that purpose, males and females of the Spanishstandardisation sample of the WAIS-III were analysed separately. Results show that the importance of gdoes not change with age irrespective of sex. Thus, the age de-differentiation hypothesis is rejected for bothmales and females. The indifferentiation hypothesis is supported as a more appropriate view of the changesin the structure of intelligence across adulthood.# 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Age de-differentiation hypothesis; Structure of intelligence; Adulthood; Senescence; Sex; g Factor; Indiffer-entiation hypothesis; WAIS-III

1. Introduction

A substantial percentage of variance in human mental ability can be accounted for by a generalintelligence factor (Carroll, 1993; Jensen, 1998; Spearman, 1927). The age-differentiation hypothesis,as coined by Garrett (1946), predicts a decrease in the variance accounted for by g from childhood to

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Personality and Individual Differences 34 (2003) 1525–1532

* Corresponding author. Tel.: +3491-397-51-83; fax: +3491-397-52-15.

E-mail address: [email protected] (S. Escorial).

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adolescence and the corresponding increase in the number and importance of specific factors.Nevertheless, the age de-differentiation hypothesis states that the reverse phenomenon is expectedfrom early maturity to senescence. Therefore, an increase in the importance of g and a decrease inthe number and importance of the remaining abilities are predicted (Balinsky, 1941).

In spite of the age-differentiation hypothesis receiving some support before the sixties (Filella,1960; Garrett, 1946), recent studies have rejected it (Deary, Egan, Gibson, Austin, Brand, &Kellaghan, 1996; Juan-Espinosa, Garcıa, Colom, & Abad, 2000). On the other hand, the age de-differentiation hypothesis shows an equally discussed history (Reinert, 1970), although somestudies have rejected it consistently in the last decade (Bickley, Keith, & Wolfle, 1995; Carroll,1993; Juan-Espinosa, Garcıa, Escorial, Rebollo, Colom, & Abad, in press). Therefore, no changesin the structure of cognitive abilities have been found from childhood to senescence.

Very little has been done to test whether such differentiation patterns remain across sex. Onlythe age-differentiation hypothesis (from childhood to adolescence) has been tested in such a way.Dye and Very (1968), and Very and Iacono (1970) obtained a differentiation effect from childhoodto adolescence in both sexes. However, as far as we know, no study has ever been conducted to testthe role of sex in the changes of the structure of abilities in adulthood (the age de-differentiationhypothesis).

Given that sex differences on g are found to be negligible (Colom, Juan-Espinosa, Abad, &Garcıa, 2000; Jensen, 1998), and that the structure of abilities does not change across sex (Carreta& Ree, 1995), there is no reason to expect a different pattern for males and females. Following theage de-differentiation hypothesis, an increase in the percentage of variance accounted for by g ispredicted for both, males and females.

2. Method

2.1. Participants

The sample comprised two age groups taken from the Spanish standardization sample of theWAIS-III (TEA, 1999). The first age group comprised 316 participants (164 males and 152females) with an age range between 16 and 24 years. The second age group comprised 403 (197males and 206 females) with an age range between 35 and 54 years. Thus, the total sample com-prised 719 participants (361 males and 358 females) with a mean age of 33.09 years (S.D.=12.65).

Both age groups comprised people between early maturity and adulthood, and the likelihood offinding a difference due to age is increasing by the great age difference (more than one decade)between them. On the other hand, there are contradictory evidences regarding the differentiationeffect on senescence. Some studies support it (i.e. Schmidt & Botwinick, 1989), but others do not(i.e. Lindenberger & Baltes, 1997). So, adding participants older than 55 years could hide the realphenomenon. Moreover, taking into account the two age-groups analysed the de-differentiationhypothesis can be clearly tested.

No differences greater than 3% were found between the standardisation sample and the Spanishcensus in variables such as sex, educational level, residence (urban, intermediate, and rural), andgeographic location (Table 1; Seisdedos & Corral, 1999), so the standardisation sample can betaken as representative of the Spanish population.

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2.2. Measures

The Spanish standardisation of the WAIS-III includes 14 subtests (Split-half reliabilities inparenthesis): Vocabulary (0.95), Similarities (0.89), Arithmetic (0.88), Digit Span (0.89), Infor-mation (0.93), Comprehension (0.85), Letter-number series (0.91), Picture Completion (0.91),Coding (Test-retest reliability=0.82), Block design (0.94), Matrices (0.94), Picture Arrangement(0.86), Symbol Search (Test-retest reliability=0.77), and Object Assembly (0.68).

2.3. Analyses

The percentage of variance accounted for by the first unrotated principal component was ana-lysed. According to Jensen and Weng (1994), this is a good estimate of the g factor.

Factor comparisons require the same factor to be extracted for both groups (Cattell, 1978). Thecongruence coefficient (rc) is an index of factor similarity. Two kinds of congruence coefficientswere computed in order to compare the g factor: (1) comparing the age groups within each sex,and (2) comparing each age group across sex.

Table 1Differences between the standardization sample and the Spanish Census in several demographical categories (adapted

from Seisdedos & Corral, 1999)

Variable

Categories Standardizationsample (%)

Spanish Census(1996) (%)

Difference(%)

Sex

Men 48.65 48.97 �0.32 Women 51.35 51.03 0.32

Geographical location

North 25.42 24.72 0.70

Middle

21.84 22.78 �0.94 East 26.22 27.3 �1.08 South 26.52 25.2 1.32

Residence

Urban (>49.999 hab.) 48.14 46.21 1.93

Intermediate (49.999–10.000)

34.77 35.79 �1.02 Rural (<10.000 hab.) 17.09 18 �0.91

Age

16–19 11.91 10.65 1.26

20–24

11.18 11.29 �0.11 25–34 19.87 19.04 0.83 35–54 29.8 28.97 0.83 55–69 17.31 19.72 �2.41

70–94

9.93 11.28 �1.35

Academic Levela

Without studies 21.99 21.5 0.49 First grade 31.56 31.2 0.36

Second grade

38.35 38.9 �0.55 Third grade 8.11 8.3 �0.19

a The subjects were assigned to a given group depending on their achieved educational level. The first two categoriescorrespond approximately to primary and secondary school, respectively. The second grade would be equivalent tohigh school, and people in the college (or that would have finished his/her degree) were classified in the third grade.

S. Escorial et al. / Personality and Individual Differences 34 (2003) 1525–1532 1527

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3. Results

Table 2 shows the means and standard deviations of every subtest and total IQ for each sex andage group. Levene’s test (�=0.05) points out that most of the tests have a larger variance in theoldest group for both sexes. Testing the age de-differentiation hypothesis (or the age and abilitydifferentiation hypotheses) calls for controlling the variance differences across groups (Jensen,1998; Loehlin, 1992). In order to control for these differences in variability, every correlation1 wascorrected for restriction of range (Detterman & Daniel, 1989) using the FSIQ (standardised withrespect to the whole sample) as the explicit selection variable (the mean IQ and the SDs in everyage group are shown in Table 2), following Gulliksen’s formula (1967, p. 149). This correctioncan be considered problematic if changes in the variance were intrinsic to age. Nevertheless, notethat several longitudinal studies (Deary, Whalley, Lemmon, Crawford, & Starr, 2000; Kangas &Bradway, 1971; Schmidt-Scherzer & Thomae, 1983; Tuddenham, Blumenkrantz, & Wilkin, 1968)have shown that there are no changes in variance with age, so the correction for restriction ofrange is appropriate because the differences in variability are not an intrinsic effect of aging at all.Therefore, the corrected matrices were used as input data in the following analyses.

Congruence coefficients are found higher than +0.95. Therefore, the g factor is the same irre-spective of sex and age. This is in strong agreement with other studies that have analysed sexdifferences in g (Colom, et al,. 2000; Jensen, 1998). The percentage of variance accounted for by gwas (Sex and age group in parenthesis): 68.753 (Males/Youngest group), 63.835 (Males/Oldest

Table 2Descriptives (Mean; S.D.=Standard deviation) of the subtests and FSIQ, in each age group

Subtest

Males Females

Youngest

Oldest Youngest Oldest

Mean

S.D. Mean S.D. Mean S.D. Mean S.D.

Vocabulary

42.07 8.73 39.35 12.84 42.70 8.97 36.54 13.14 Similarities 20.46 5.42 17.23 6.39 20.39 5.06 16.52 6.09

Arithmetic

14.48 3.32 13.78 3.80 12.91 3.24 11.23 3.35 Digit span 17.55 3.97 15.35 4.38 16.72 3.74 14.38 4.02 Information 18.23 4.82 18.17 5.67 16.83 4.89 15.62 5.73

Comprehension

19.63 5.22 19.43 5.64 19.27 5.32 18.31 5.59 Letter-number series 11.80 2.69 9.73 3.06 11.35 2.36 9.41 2.93 Picture completion 20.32 3.09 18.92 3.91 20.56 2.58 18.18 4.06

Coding

77.41 16.97 65.80 21.35 79.45 17.03 62.69 22.67 Block design 47.37 10.48 40.38 12.33 46.07 9.96 34.91 11.90 Matrices 19.53 3.99 16.45 5.48 19.11 3.89 14.63 5.49

Picture arrangement

15.66 4.18 13.17 5.03 15.05 3.85 12.29 5.23 Symbol search 36.26 8.46 29.76 10.42 34.97 7.76 28.37 11.05 Object assembly 34.88 8.87 31.12 8.27 34.97 7.59 29.39 9.46 FSIQ 109.63 8.90 102.75 11.53 108.86 7.28 98.93 12.20

1 Uncorrected correlation matrices for males and females are shown in the Appendix.

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group), 66.708 (Females/Youngest group), and 64.361 (Females/Oldest group). The differencesfound among age groups are negligible in both sexes. Note that g explains more variance in theyoungest group, an effect contrary to the predicted one.

Given that g was estimated as the first principal component, it is directly related to the averagecorrelation among all the subtests. A test of the significance of the difference between any of theseaverage correlations can be obtained from Fisher’s Z.2 Average correlations3 were: 0.66 (Males/Youngest group), 0.61 (Males/Oldest group), 0.64 (Females/Youngest group), and 0.62 (Females/Oldest group). No significant (P > 0.05) age or sex differences in the average correlations in thesefour groups were found.

4. Discussion

The age de-differentiation hypothesis does not hold. The importance of g does not change withage in either sex. Moreover, both sexes present the same pattern of negligible differences acrossage. This is in strong agreement with other studies (Bickley et al., 1995; Carroll, 1993; Juan-Espinosa et al., in press). These results are a new piece of evidence against the de-differentiationhypothesis and calls for a change in the theoretical views of the variations in the structure ofcognitive abilities regarding age.

Juan-Espinosa et al. (in press) have proposed the indifferentiation hypothesis. It states that nei-ther the variance accounted for by g nor the main cognitive abilities change along the life span.As the human skeleton, there is a basic structure of intelligence that is already present early inlife. This basic structure does not change at all, although, like the human bones, cognitive abilitiescan grow up and decline at different periods of life (Juan-Espinosa et al., in press). This hypoth-esis should be tested against potential sources of changes in the structure of ability such as sex,social class or educational level. In fact, the present paper supports it since no differences in the gvariance across age groups were found in either sex.

Supporting the indifferentiation hypothesis, a pattern of stability in the structure of abilities inboth sexes is predicted from childhood to adolescence. Nevertheless, nothing can be said aboutthe age-differentiation hypothesis across sexes in the present paper since no childhood or earlyadolescent sample was analysed.

Acknowledgements

This research was supported by a grant funded by the Spanish ‘‘Ministerio de Educacion yCultura’’. Grant No. BSO2000–0043.

2 We thank an anonymous referee for suggesting this interesting analysis.3 Computed after Kaiser’s formula (1968): Average r=(l �1) / (n �1); where l is the eigenvalues of the first prin-

cipal component of the correlation matrix and n is the number of variables represented in the matrix.

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Appendix

Uncorrected correlation matrices for the youngest (top half) and the oldest (bottom half) malesamples

Subtest

1 2 3 4 5 6 7 8 9 10 11 12 13 14 PC1a

(1) Vocabulary

– 0.681 0.491 0.379 0.687 0.687 0.417 0.432 0.413 0.452 0.352 0.479 0.387 0.405 0.900

(2) Similarities

0.640 – 0.470 0.397 0.602 0.626 0.321 0.442 0.394 0.394 0.433 0.478 0.314 0.411 0.879

(3) Arithmetic

0.535 0.509 – 0.434 0.579 0.476 0.468 0.412 0.349 0.445 0.510 0.329 0.330 0.487 0.861

(4) Digit Span

0.418 0.351 0.554 – 0.369 0.273 0.620 0.298 0.256 0.270 0.299 0.299 0.273 0.317 0.746

(5) Information

0.580 0.505 0.595 0.415 – 0.641 0.415 0.414 0.295 0.513 0.410 0.487 0.325 0.488 0.893

(6) Comprehension

0.670 0.653 0.529 0.399 0.534 – 0.358 0.404 0.358 0.391 0.401 0.471 0.324 0.390 0.868

(7) Letter-Number

0.510 0.428 0.635 0.665 0.458 0.469 – 0.273 0.327 0.359 0.285 0.380 0.319 0.384 0.791

(8) Picture completion

0.469 0.496 0.469 0.341 0.501 0.428 0.340 – 0.196 0.332 0.412 0.361 0.321 0.369 0.766

(9) Coding

0.435 0.371 0.434 0.522 0.367 0.371 0.526 0.441 – 0.290 0.245 0.356 0.431 0.328 0.787

(10) Block design

0.446 0.415 0.516 0.354 0.498 0.373 0.378 0.525 0.436 – 0.436 0.495 0.385 0.636 0.850

(11) Matrices

0.567 0.484 0.618 0.420 0.557 0.494 0.520 0.627 0.495 0.611 – 0.389 0.413 0.383 0.799

(12) Picture arrangement

0.473 0.459 0.417 0.403 0.477 0.489 0.465 0.556 0.524 0.537 0.660 – 0.211 0.476 0.825

(13) Symbol search

0.472 0.365 0.488 0.485 0.328 0.348 0.560 0.394 0.686 0.477 0.546 0.495 – 0.338 0.776

(14) Object assembly

0.281 0.272 0.355 0.438 0.253 0.292 0.391 0.418 0.513 0.560 0.507 0.499 0.553 – 0.847

PC1a

0.826 0.775 0.831 0.757 0.783 0.784 0.809 0.778 0.807 0.797 0.871 0.821 0.808 0.727 –

Uncorrected correlation matrices for the youngest (top half) and the oldest (bottom half) femalesamples

Subtest

1 2 3 4 5 6 7 8 9 10 11 12 13 14 PC1a

(1) Vocabulary

– 0.568 0.426 0.323 0.633 0.599 0.370 0.220 0.139 0.188 0.391 0.381 0.266 0.235 0.891

(2) Similarities

0.704 – 0.356 0.279 0.582 0.684 0.264 0.348 0.195 0.138 0.435 0.393 0.200 0.127 0.875

(3) Arithmetic

0.577 0.495 – 0.317 0.394 0.394 0.336 0.265 0.201 0.286 0.363 0.344 0.244 0.210 0.840

(4) Digit Span

0.485 0.463 0.628 – 0.275 0.265 0.626 0.244 0.166 0.194 0.300 0.271 0.123 0.117 0.766

(5) Information

0.696 0.630 0.581 0.517 – 0.578 0.267 0.236 0.126 0.202 0.318 0.414 0.311 0.307 0.882

(6) Comprehension

0.700 0.653 0.526 0.504 0.650 – 0.344 0.260 0.112 0.246 0.363 0.372 0.197 0.217 0.880

(7) Letter-Number

0.545 0.494 0.685 0.734 0.579 0.521 – 0.156 0.142 0.225 0.260 0.296 0.151 0.133 0.772

(8) Picture completion

0.460 0.495 0.423 0.435 0.559 0.436 0.456 – 0.160 0.303 0.303 0.175 0.069 0.170 0.706

(9) Coding

0.554 0.442 0.482 0.501 0.497 0.471 0.611 0.406 – 0.159 0.290 0.126 0.469 0.053 0.768

(10) Block design

0.463 0.474 0.473 0.473 0.536 0.330 0.565 0.460 0.521 – 0.498 0.263 0.207 0.445 0.805

(11) Matrices

0.561 0.533 0.664 0.525 0.563 0.458 0.612 0.558 0.616 0.662 – 0.430 0.223 0.368 0.882

(12) Picture arrangement

0.477 0.416 0.513 0.411 0.574 0.442 0.485 0.507 0.527 0.539 0.626 – 0.225 0.265 0.822

(13) Symbol search

0.435 0.332 0.406 0.389 0.419 0.371 0.537 0.356 0.776 0.485 0.533 0.484 – 0.129 0.780

(14) Object assembly

0.433 0.400 0.377 0.343 0.458 0.315 0.412 0.427 0.470 0.685 0.577 0.545 0.479 – 0.737

PC1a

0.841 0.789 0.812 0.775 0.849 0.776 0.847 0.735 0.830 0.804 0.868 0.791 0.756 0.744 –

a Loadings on the first principal component computed after the corrected for restriction of range correlations.

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