Mental Rotation .as a Mediator for Sex-related Differences

in Visualization

ANA R. DELGADO GERARDO PRIETO

Universidad de Salamanca, Spain

This study was designed to analyze whether Mental Rotation (MR) played a role as a mediating variable for sex-related differences in Visualization (VZ). Two psychometric tests measuring MR and VZ were applied to a representative sample of 309 males and 390 females in their last year of high school. Three non-zero correlations between sex and MR, sex and VZ, and MR and VZ were found, and the effect of sex on VZ was eliminated when MR was introduced as a covariable. When three subgroups of different VZ ability were made by dividing up the VZ distribution by the first and third quartiles, sex-differences were only found for the high-scorers group, for which previous results were replicated. Results clearly indicate that MR is a plausible mediator variable for sex differences in VZ when such differences do exist. Theoretical, methodological and practical con- sequences of these results are discussed.

Sex-related differences in spatial abilities have been consistently reported ever since Mac- coby and Jacklin (1974) published their classical review of the scientific literature. A meta- analysis by Hyde (1981) on the same literature showed that the median effect size was .45, accounting for only 4.3 % of the variance, and so it was suggested that sex had a minimal influence on spatial test scores. Subsequent meta-analyses explained this result by using a different rationale: classifying tests by means of psychometric criteria into categories showing near-homogeneous effect sizes showed that these were large and significant when mental rotation tests were used (d = .73), but failed to reach significance (d = .13) for the spatial visualization grouping (Linn & Petersen, 1985); a third type of tests, grouped under the denomination of spatial perception, showed medium effect sizes (d = .44).

Voyer, Voyer, and Bryden (1995) have examined the magnitude of sex differences in various measures of spatial performance taking into account not only the separate effect sizes for each test but also some critical variables which could be affecting them. Results from this meta-analysis (which included only published studies carried out on at least five

Direct all correspondence to: Ana R. Delgado, Facultad de Psicologia, Avda. de la Merced 109-135, 37005 Salamanca, Spain <adelgado@gugu.usal.es>

INTELLIGENCE 24(3): 405-416

ISSN: 0160-2896

Copyright 0 1997 by Ablex Publishing Corporation

All rights of reproduction in any form reserved.

405

406 DELGADO AND PRIETO

different samples of participants) clearly show that sex differences are most compelling for mental rotation tests. They are large-although less consistent-for the spatial perception category, and small, or nonsignificant, and heterogeneous for spatial visualization tests. Their claim that some spatial visualization tests actualZy show significant sex differences is of particular interest, as is their tentative explanation of this fact. The explanation was pre- viously suggested by Linn and Petersen (1985), that spatial visualization tests showing significant sex differences are those tests which have an important mental rotation component.

Findings of sex-differences in spatial aptitude-especially when operationalized by three-dimensional mental rotation tests-are large (Halpem, 1992) and stable over time (Masters & Sanders, 1993). Moreover, this difference has been reported when the task is solved under unspeeded conditions (Resnick, 1993; Delgado & Prieto, 1996). An illustra- tion of the substantive significance of these differences can be found in Casey, Nuttall, Pezaris, and Benbow (199.Q who found mental rotation skills to be mediators for sex- related differences in math aptitude among diverse samples.

Until recently, meta-analytic literature was generally based on data collected from short and selected samples. Some effort was made to improve the representativeness of the samples by combining the evidence from test norming samples (Feingold, 1988), but only recently have we had access to a study carried out on mental test data from six large-scale surveys on representative samples of adolescents and young adults in the United States. Results indicate that average sex differences are generally small but stable (Hedges & Nowel, 1995). In the Project Talent sample, for example, the effect size d was .13 for spa- tial ability and .12 for mathematics. However, size effects associated with vocational aptitude scales were very large for the same sample (e.g., d= .83 for the mechanical reason- ing test). We mention these particular effect sizes because, as will be seen, they can all be related in some way to sex differences in mental rotation.

Our principal concern at the moment is not, then, the search for sex differences in spa- tial abilities, because we believe that there is enough evidence of that, but rather the classification, the analysis and, when possible, the explanation of at least some of these dif- ferences. We will summarize the impact of some specific methodological recommenda- tions that have been made in the last ten years to guide researchers in the areas of spatial abilities and sex-related differences.

Caplan, MacPherson, and Tobin (1985) criticized the weak evidence of construct validity of the so-called spatial ability and concluded that it was inappropriate to ask about sex differences until spatial abilities were adequately divided up and labelled. It seems that a great amount of work has been devoted to this and, as a result, considerable agreement exists with respect to the classification of spatial abilities when measured by means of psy- chometric tests. Carroll (1993) re-analyzed 230 sets of data found in the factor-analytic literature and, using previously established factor names, classified spatial tests according to five factors: Visuulization (VZ), tests reflecting processes of apprehending, encoding and mentally manipulating spatial forms, with the exception of relatively simple speeded tests; Sputial Relations (SR), relatively simple speeded tests with mental rotation as the common element; and Closure Speed (CS), Closure Flexibility (CF) and Perceptual Speed (P), which are related to the search for spatial forms, under different instructions, despite a distracting context. This psychometric classification is in many respects a replication of the reanalysis conducted by Lohman (1979), who considered CS and CF as minor factors and

SEX DIFFERENCES IN MENTAL ROTATION 407

urged recognition of three basic spatial ability factors: VZ, SR, and Spatial Orientation (SO). In practice, it is often difficult to distinguish the third factor from the first, so that a schematical representation of Spatial Aptitude has been proposed with only two factors ordered in a speed/power continuum and a simple/complex processing dimension: SR tests are classified as speeded and simple-with three-dimensional mental rotation as the least speeded and least simple type of test in this half of the continuum-while VZ tests occupy the other end, with Surface Development tests illustrating maximum power and complexity (Pellegrino, Alderton, & Shute, 1984). A judgmental analysis of the tasks demonstrates that the three categories used by Linn and Petersen (1985), and subsequently by many other authors, correspond reasonably well with the factors found by Carroll (1993). Mental rota- tion and spatial visualization are similar to SR and VZ, respectively, while spatial perception tasks resemble tests loading on CS, CF and P.

Although names and interpretations of factors are sometimes ambiguous or indetermi- nate, focusing on the nature of the tasks without regard to their names can help to avoid confusion. For example, the Project Talent test of visual ability, whose results have been reanalyzed by Hedges and Nowell (1995) is a Surface Development task. This task consis- tently loads on the VZ factor-in fact it is typically used as marker-not on SR, and so it is not surprising that the effect size for sex is small. Despite its name, the Project Talent mechanical reasoning test has high loadings on X&---and only secondary loadings on the Mecanical Knowledge (MK) factor-suggesting that, regardless of an individual’s experi- ence with mechanical objects, it is tapping a basic ability in spatial visualization (Carroll, 1993). The nature of the task -requiring the subjects to comprehend and make decisions about the movements, operations and processes of simple machines such as geartrains- seems to be related to mental rotation, especially if the test has been applied under speeded conditions. Therefore the fact that the test does not load in SR could be attributed to the cri- teria for the extraction of factors and/or the design of the dataset that do not yield a separate SR factor.

Both judgmental and empirical analyses of the sources of difficulty in the existing tests, and a generative approach to the construction of new tests are helping to solve the problem from the point of view of the stimuli (Bejar, 1993; Embretson, 1993). But what about the characteristics of the sample? A source of confusion that is more difficult to deal with is the fact that test takers apparently can arrive at answers by a variety of different strategies. This leads to wide fluctuations in factor loadings. Subjects can even employ dif- ferent strategies for different items within the same test (Kyllonen, Lohman, & Woltz, 1984). This is partly as a function of their level of aptitude in dealing with the tasks (Snow & Lohman, 1989). And there is still a puzzling question: If that people solve tasks differ- ently depending on their ability patterns, should we say that a person solving a Surface Development task by using a strategy other than a “spatial” one is not actually solving a visual-spatial aptitude test, even if the task has been performed reasonably quickly and accurately? Taking the argument to its extreme form, should we say that the MR factor is irrelevant to the samples not using this strategy in the same sense that a factor of Spanish vocabulary knowledge is irrelevant to those not speaking Spanish? (Does it mean that the score in visual-spatial aptitude for this sample is nought?) It should be noted that these problems are not specific to the visual-spatial aptitude but have been reported for other aptitudinal constructs such as language comprehension (MacLeod, Hunt, & Mathews, 1978) and, more recently, sillogistic reasoning (Ford, 1995). Simple answers to these prob-

408 DELGADO AND PRIETO

lems cannot be expected. In part because there are some built-in definitional problems that will not be solved empirically. A classical psychometric point of view, requires defining which conditions affect the relationships between the relevant variables as a first step.

With respect to investigation in the area of sex-related differences, concern about the over-reliance on tests of statistical significance led to recommendations to provide evi- dence of practical significance (Denmark et al., 1988; Halpem, 1992), which seem to have been followed by most researchers. Not only are effect sizes usually provided for readers, but interest has also grown and reached the tail areas of the distributions (Hedges & Fried- man, 1993). Feingold (1995) has clearly shown how sex differences in variability may combine with sex differences in central tendency to produce tail ratios that are not deriv- able from effect sizes. Following the data from the above example (Hedges & Nowell, 1995; Project Talent sample), and given a normal score distribution in which the sex effect size is small but the male/female variance ratio (VR) is slightly higher than one (visual ability: d= .13; VR=1.27), the sex ratio is 1.86 for scores in the top 10% and reaches 2.33 in the top 5% of the overall distribution. For large effect sizes (mechanical reasoning: d = .83; VR=1.45), the disproportion increases dramatically and the sex ratio reaches 11 in the top 5%, meaning that, if a cutoff for selection were set at this percentile point, only one- twelfth of the selected subjects would be female. A detailed account of the effects of the interaction between mean differences and variance ratios on the tails of the distributions, and their consequences for job assignment policies can be found in Hunt (1995).

Finally, we would like to make a comment on the report of the Ad Hoc Committee on Nonsexist Research, which was developed to identify some of the ways that gender bias can affect research at each of its stages. At the stage corresponding to Methods, the follow- ing problem was identified: gender is confounded with other participant variables. The suggested correction is simple: before asserting that differences in groups are due to gen- der, other major explanatory factors must be controlled for (Denmark et al., 1988). For example, Rosenthal (1988) proposed a series of statistical tests in order to consider a vari- able as a possible mediator for sex differences in mathematical reasoning scores. It is necessary to have three non-zero correlations: sex and mathematics score, sex and media- tor and mediator and mathematics score. Then, the effect of sex on the mathematics score can be examined after partialling out the effect of the mediator. If the partial r approaches zero, then the mediator could be considered as a plausible explanatory variable; if not, we can only qualify it as a useful predictor. This is exactly the procedure followed by Casey et al. (1995) to show that mental rotation skills are mediators for sex-related differences in mathematics scores.

Of course, the fact that the sex difference disappears when the mediator is statistically removed does not mean that the difference was not real-obviously, it was! We can still be interested in finding another major explanatory factor which is closer in the causal chain, so that we can explore the intermediate steps, in the pathway leading from sex differences to differences in a particular performance. Apart from the theoretical relevance, there is an obvious advantage in finding that a certain skill is a mediator for human sex differences in a certain performance: biological sex can not be manipulated in order to improve that par- ticular performance; however, finding a mediating variable which can be manipulated might serve to design training programs. In addition, if it happens that the same variable can be shown to be a mediator for sex differences on various critical performances, then an effort should be made to focus on that specific variable in order to find its links both with

SEX DIFFERENCES IN MENTAL ROTATION 409

performance and with sex-e.g., Thomas and Kail (1991) proposed an X-linked genetic hypothesis to explain sex differences in mental rotation. Following this line of reasoning, our hypothesis is that mental rotation skills are mediators for the sex-related differences in visualization scores. If this hypothesis is true, sex differences in visualization should be eliminated when mental rotation is covaried out. It must be shown that this would be true whatever the level of ability.

PARTICIPANTS, MATERIALS, AND PROCEDURE

Participants

This research was conducted in nine Spanish high schools. It is part of a broader study, of which some results can be found in Delgado and Prieto (1996), this sample being a sub- sample. Three hundred and nine males and three hundred and ninety females in their last year of high school participated. At this point in their education, all the students have a gen- eral background in math and science. Reward in terms of confidential feedback was given to those participants who asked for it. The mean age was 18.35 years (SD=.99, range= 17- 22). The disproportion in number of males/females is due to the actual disproportion of the population in schools. It was presumed that all levels of spatial aptitude-as well as an ample range in general aptitude with the probable exception of the lowest end of the distri- bution-would be represented, given that no other selection was carried out and most of the Spanish adolescent population is enrolled in high school. The sex-related differential dropout rate in the population might be due to a mixture of socio-economic and biological factors. Entering the labor market is much easier for male teenagers, and therefore more males than females abandon school at sixteen, when the period of compulsory education ends. In addition, it is well known that males are over-represented at the low end of the IQ distribution, probably due to the fact that more men than women have severe language dis- abilities, such as dyslexia (Vandenberg, 1987), and it is taken for granted that a normal IQ level is required to reach the last year of high school.

Materials

Participants took two psychometric tests typically used as markers for the factors of Spatial Relations and Visualization-examples of which can be found in Eliot and Smith’s (1983) directory. First, the RFM test (Yela, 1968), the Spanish adaptation of the Rotation of Solid Figures developed by Thurstone and Thurstone in 1949-a three-dimensional mental rotation test loading in the factor of spatial relations. Each of the twenty-one items of the RFM gives a drawing of a three-dimensional figure (the model), and, to its right, five response options, rotated by different amounts, of which only one is identical to the model. Second, a reduced version of the Spanish adaptation of the DAT-SR (TEA, 1990; Bennet, Seashore, & Wesman, 1974), a surface development test, loading in the factor of spatial visualization. Each of the thirty items of this reduced version gives an unfolded two-dimen- sional shape (the model), together with four response options consisting of drawings of three-dimensional objects, of which only one, when folded, is identical to the model. Throughout the text they will be referred to as MR and VZ, respectively. Items in the Span-

410 DELGADO AND PRIETO

ish adaptations are identical to those of their corresponding American versions, and only minor changes were made in the standardization process.

Procedure

Both tests were taken by the students in their usual classroom and during the usual time-table. Natural groups resulted of about 30 participants per class. Following general instructions for timed tests-work quickly and accurately-participants had 5 minutes to complete the MR test, 12 for the VZ test.

Sex of the Experimenter was balanced across conditions by having half of the groups for each condition tested by a male psychologist while the rest were tested by a female psychologist.

Results and Discussion

Figures 1 and 2 show the score distributions of MR and VZ for males and females. Sex differences in means, variances and numbers of extreme scores are shown in Table 1. Vari- ance ratios were similar to those reported by Hedges and Nowell (1995) for spatial ability and mechanical reasoning (Project Talent dataset). Also according to previous research (Feingold, 1992; Maccoby & Jacklin, 1974) variability was, for both tests, higher in the male subsample. This in combination with the male-female average difference, explains the high sex-related difference in the number of extreme scores.

Significant differences were found between males and females in the number of items answered correctly. Male subjects had more correct answers for both MR (Ft,,,, = 123.74; p < .OOl) and VZ (F1,697 = 24.34; p < ,001) tests. That is to say, in correlational terms, that there were two non-zero correlations: between sex and VZ (r = -.1837; p c ,001; the nega- tive sign indicating that female coding was 1, male coding was 0) and between sex and MR (r = -.3883; p c .OOl). The correlation between MR and VZ was also significant (r = -

SO62; p < .OOl). Once we had the three requisite correlations, we carried out preliminary analyses to

prove that the assumptions as to the linearity of the relation between dependent variable and covariate, and the homogeneity of regression were not violated. Then an ANCOVA was performed to determine whether sex differences in VZ would be eliminated when MR was covaried out. Results indicate that sex differences are actually eliminated (F1,696 = .18; p > .05). In other words-the R2 change produced by entering sex as a predictor of VZ

Table 1. Sex Differences in Means, Variance and Numbers of Extreme Scores*

Test d VR <Cl0 <QI 2 Q_j 1 CYO

Mental Rotation .85 C.08) 1.36 .21 .22 2.14 4.00 Visualization .38 (.08) I .46 .56 .65 I .23 2.22

Note: * Differences in means are expressed as I! values (standard errors are in parentheses). Differences in variance are expressed as VRvalues(ratiosofmalescorevariance tofemalescorevariance). Differencesinnumbersofextremescoresareexpressed

as ratios of the number of males to the number of females who scored under the tenth percentile, under the first quartile, on or over the third quartile and on or over the ninetieth percentile of the overall distribution.

SEX DIFFERENCES IN MENTAL ROTATION 411

after entering MR is an insignificant .0002, when the total R2 for the equation is .26 (F2 hg6 = 120.02; p < .OOOl). Correlational research does not permit the inference of causality from correlation, but does permit discarding causality when correlation is not found. Because we are reasoning from an intrinsically correlational design, it should be noted that the opposite relationship between both variables is empirically not true-sex differences in MR are not eliminated when VZ is covaried out, (F1,696 = 96.11; p < .OOl). A logical anal- ysis of the tasks could also be taken into account: while tests loading on the visualization factor are complex, tests loading on the spatial relations factor are simple speeded tasks implying mental rotation or reflection. It seems to be logical to expect the simpler phenom-

25-

3 : 0 20- iz

%5-

i? :

lo-

( q females 1

Figure 1. Distributions of Visualization Scores for Males and Females

412 DELGADO AND PRIETO

,Y

60-

50-

2 ij 40- 5

g 30- 2

20

10

0 L4llJ

( n Males 1

70

60-

50

3 B 5

40

g 2 30

20

10

0 10 m m VI rg WI’” ‘c! u-j ‘” ‘? d t-4 i rd 06 6 2 * \o 00 g

_ 3 -

Figure 2. Distributions of Mental Rotation Scores for Males and Females

ena to explain the more complex ones (and although this approach might not be the most parsimonious, it is well known that biology does not select systems by reason of their par- simony). An alternative explanation for the statistical pattern could be that there is a simple spatial factor and MR is a better marker. This explanation cannot be ruled out from our data; however, there is some evidence for a differentiation between VZ and SR factors (Carroll, 1993), and a recent study by Stumpf and Eliot (1995) in the field of sex-related differences shows that, when a general spatial ability factor k is extracted from a battery of psychometric spatial tests, Surface Development tests are among the best markers.

SEX DIFFERENCES IN MENTAL ROTATION 413

Although it can be seen from Figures 1 and 2 that there is substantial overlapping between the score distributions for males and females, the additive effects of differences in central tendency and variability can be seen at the tails (see Table 1). If a cutoff had to be established for selection of the subjects with the best scores-e.g., in order to admit ten per cent of them for a high-level technical course requiring excellent spatial abilities-and we decided to use the VZ test as a selector, we would find that four female subjects would be admitted to the course for each nine male subjects selected. If, instead of VZ, we had decided to apply the MR test (because we know that success in the course will require speeded performance of rotation or reflection simple tasks) then four females would have been selected for each sixteen males! The opposite is true for the lower tail- if we had to select ten per cent of them for a remedial training course directed towards those with poor spatial abilities the ratios would be approximately the reverse. The ratios of the number of males to the number of females for a less extreme cutoff-e.g., in order to select twenty- five per cent of the sample-show a similar pattern.

If MR is a mediator for sex-differences in VZ, it should be so along the whole range of this ability, even for extreme scores. In order to test that corollary of the hypothesis, and given that the samples for the tails defined by the tenth and ninetieth percentile points would be too small and homogeneous, we tried to replicate previous results on the three subsamples defined by the first and third quartiles (X = 8 and X = 16, respectively) of the overall VZ distribution (Low-scorers: subjects scoring under 8. Intermediate-scorers: sub- jects scoring between 8 and 15, both values included. High-scorers: subjects scoring 16 and over). The fact that scores are integers determines that the percentage of subjects at both extremes of the distribution is neither exactly 25% of the entire sample, nor is it iden- tical for the extreme subsamples. Intercorrelations among the variables for the three subsamples are displayed in Table 2.

Unexpectedly, the three non-zero correlations required were only found for the high- scorers subsample. In fact, only for this group was the correlation between sex and VZ sig- nificant, which cannot be explained merely by the range restriction (the correlation coefficient between sex and VZ found for the 145 low-scorers, r = .09, would only reach significance at the alpha level .Ol if sample size had been increased to 822!).

Assumptions as to the linearity of the relation between dependent variable and covari- ate, and the homogeneity of regression were not violated for the high-scorers subsample either. Then, having the three required correlations, we carried out an ANCOVA to see whether sex differences in VZ would be eliminated after covarying out MR. Results show that sex differences are eliminated (F1,2u7 = 3.76; p > .05). The R2 change produced by entering sex as a predictor of VZ, after entering MR, was .015, when the total R2 for the

Table 2. Variable Intercorrelations for the Subsamples

Low-scorers Intermediate-scorers High-scorers

(n=i45) (n=344) (n=210)

MR vz MR vz MR VZ

VZ .06 .20** .42** Sex -.31** -.09 -.43** -.08 -.32** -.25**

Note: ‘p-z.05, **p-c01

414 DELGADO AND PRIETO

equation had been .19 (F2 2u7 = 23.98; p -C .OOl). Therefore, mental rotation skills are plau- sible mediators for sex-differences in visualization scores in the high-scorers subsample.

Although in a different way than expected, it remains true that sex differences in VZ disappear when MR is covaried out whatever the level of ability. Since sex differences only appeared at the higher level of visualization ability and, at this level, the prediction was fullfilled. The properties of the correlation estimate might play a role in this result, but the difference between the high-scorers and the rest of the sample is too large and clear-cut as to be attributed to a statistical artifact. Neither sex nor mental rotation skills would serve as predictors for VZ scores in the VZ low-scorers subsample. MR served as a predictor for VZ for the intermediate-scorers subsample (but, at this level, we cannot qualify it as a mediator for sex-differences in VZ, because no sex-differences in VZ appeared). These results could help to explain why sex-related differences are not consistently found in the meta-analytic literature on visualization, even when the tests used had a mental rotation component. As far as we know, the visualization ability level of the sample has not been employed to par- tition the effect sizes into categories showing homogeneous effects. Additionally, the fact that the correlation between MR and VZ is higher in the upper tail indicates that it should not be attributed to a general factor g, given that psychometric tests correlate more highly at lower ability levels (Detterman & Daniel, 1989).

Finally, if a test has a mental rotation component, what does it entail? Among other things, it implies that, for a complex task judged to be composed of some mental rotation subtasks (as well as of various other subtasks judged to be of a spatial nature), subjects hav- ing good mental rotation skills will have a higher probability of correctly solving more items in the same period of time, but only ifthey solve the task by putting into practice their mental rotation resources (using a MR strategy). We believe that the pattern of correlations between MR and VZ found for the subsamples (see Table 2) can serve as a clue for the interpretation of sex-differences in solving complex visuo-spatial tasks. It could well be: (1) if the subjects resolved these tasks by using a MR strategy, they would obtain higher scores; and (2) women would not have this strategy available. The fact is that a simple instructional intervention-such as placing women and men together for discussion after practice sessions with an extremely complex laboratory spatial task-dramatically reduces sex differences (Regian & Shute, 1993). This is probably related to learning the best strat- egy, and it seems to be that the best strategy is related to mental rotation skills. Other authors have reached a disagree with the concept of trainability of spatial aptitude: Berg, Hertzog, and Hunt (1982) found results supporting the independence of the effects of sex and practice on MR. They did concede that the difficulty of the task might have been a decisive factor, given that it is possible that the rotation task must be relatively difficult before sex-differences can be found. The evidence for both sides of the question is far from conclusive and more research is needed before a clear conclusion about the effects of prac- tice on sex-related differences in visual-spatial aptitude can be reached. It appears that it will be necessary to take into account the aptitude level of the sample as well as the com- plexity of the task in order to reach reliable conclusions.

As Eagly (1995) has put forward, if sex differences arise from socio-cultural factors, psychologists should devise ways to give females access to experiences which train spatial ability. If it is more related to biological factors, women would prefer a different cue sys- tem for negotiating spatial tasks (Kimura, 1992), and so training programs could be specially designed to take these preferred strategies into account. In any case, we believe

SEX DIFFERENCES IN MENTAL ROTATION 415

that the design of efficient training programs might be facilitated by the information that sex differences in spatial aptitude when measured by complex tasks appear only for the higher range of the ability, and that mental rotation skills mediate such differences.

REFERENCES

Bejar, 1.1. (1993). A generative approach to psychological and educational measurement. In N. Frederiksen, RI.

Mislevy, & 1.1. Bejar (Eds.), Test theory for a new generation of rests. Hillsdale, NJ: LEA. Bennet, Cl., Seashore, H., & Wesman, A. (1974). Differential aptitude test manual, 5th ed. New York:

Psychological Corporation. Berg, C., Hertzog, C., & Hunt, E. (1982). Age differences in the speed of mental rotation. Developmental

Psychology, 18, 95-107. Caplan, P.J., MacPherson, G.M., & Tobin, P. (1985). Do sex-related differences in spatial abilities exist?

American Psychologist, 40, 786799.

Carroll, J.B. (1993). Human cognitive abilities. New York Cambridge University Press. Casey, M.B., Nuttall, R., Pezaris, E., & Benbow, C.P. (1995). The influence of spatial ability on gender

differences in math college entrance test scores across diverse samples. Developmental Psychology, 31,

697-705. Delgado, A.R. & Prieto, G. (1996). Sex differences in visuospatial ability: Do performance factors play such an

important role? Memory & Cognition, 24, 504-5 10. Denmark, F., Russo, N.F., Frieze, I.H., & Sechzer, J.A. (1988). Guidelines for avoiding sexism in psychological

research. A report of the Ad Hoc Committee on Nonsexist Research. American Psychologisf, 43, 582-

585.

Detterman, D.K. & Daniel, M.H. (1989). Correlations of mental tests with each other and with cognitive variables

are highest for low IQ groups. Intelligence, 13, 349-359.

Eagly, A.H. (1995). The science and politics of comparing women and men. American Psychologist, 50, 145-

158. Eliot, J. & Smith, I.M. (1983). Internafional directory of spatial tests. Slough, UK NFER-Nelson. Embretson, S. (1993). Psychometric models for learning and cognitive processes. In N. Frederiksen, & R.I.

Mislevy y 1.1. Bejar (Eds.), Test theory for a new generation of tests. Hillsdale, NJ: LEA. Feingold, A. (1988). Cognitive gender differences are disappearing. American Psychologist, 43, 95-103. Feingold, A. (1992). Sex differences in variability in intellectual abilities: A new look at an old controversy.

Review of Educational Research, 62, 61-84. Feingold, A. (1995). The additive effects of differences in central tendency and variability are important in

comparison between groups. American Psychologist, 50, 5-13. Ford, M. (1995). Two modes of mental representation and problem solution in syllogistic reasoning. Cognition,

54, 1-71. Halpem, D.F. (1992). Sex diflerences in cognitive abilities, 2nd ed. London: LEA. Hedges, L.V. & Friedman, L. (1993). Computing gender difference effects in tails of distributions: The

consequences of differences in tail size, effect size, and variance ratio. Review of Educational Research,

63, 110-l 12. Hedges, L.V. & Nowell, A. (1995). Sex differences in mental tests scores, variability, and numbers of high-

scoring individuals. Science, 269,41&45. Hunt, E. (1995). Will we be smart enough? New York: Russell Sage Foundation. Hyde, J.S. (1981). How large are cognitive gender differences? A meta-analysis using w2 and d. American

Psychologist, 36, 892-901. Kimura, D. (1992). Sex differences in the brain. Scientific American, (September), 119-125. Kyllonen, P.C., Lohman, D.F. & Woltz, D.J. (1984). Componential modeling of alternative strategies for

performing spatial tasks. Journal of Educational Psychology, 76, 1325-l 345. Linn, M.C. & Petersen, A.C. (1985). Emergence and characterisation of gender differences in spatial abilities: A

meta-analysis. Child Development, 56, 1479-1498.

Lohman, D.F. (1979). Spatial ability: A review and reanalysis of the correlational literature. (Tech. Rep. 8). Stanford, CA: Stanford University Press.

416 DELGADO AND PRIETO

Maccoby, E.E. & Jacklin, C.N. (1974). The psychology of sex differences. Stanford, CA: Stanford University Press.

MacLeod, C.M., Hunt, E.B., & Mathews, N.N. (1978). Individual differences in the verification of sentence- picture relationships. Journal of Verbal Learning and Verbal Behavior, 17, 493-507.

Masters, MS. & Sanders, B. (1993). Is the gender difference in mental rotation disappearing? Behavior Genetics, 23,337-341.

Pellegrino, J.W. Alderton, D.L., & Shute, V.J. (1984). Understanding spatial ability. Educational Psychologist, 19, 239-253.

Regian, J.W. & Shute, V.J. (1993). Basic research on the pedagogy of automated instruction. In T. de Jong, H. Spada, and D.M. Towne (Eds.). The use of computer models for explication, analysis, and experiential leaning. New York, NY: Springer-Verlag.

Resnick, SM. (1993). Sex differences in mental rotations: An effect of time limits? Brain and Cognition 21, 71- 79.

Rosenthal, R. (1988). Evaluating explanations of sex differences in mathematical reasoning scores. Behavioral and Brain Sciences, 11,207-208.

Snow, R.E. & Lohman, D.F. (1989). Implications of Cognitive Psychology for Educational Measurement. In R.L. Linn (Ed.) Educational Measurement, 3rd ed. New York: Macmillan.

Stumpf, H. & Eliot, J. (1995). Gender-related differences in spatial ability and the k factor of general spatial ability in a population of academically talented students. Personality and Individual Differences, 19, 33- 45.

TEA (1990). DAT. Tests de Aptitudes Diferenciales. Manual. IO”Ed. Madrid: TEA. Thomas, H. & Kail, R. (1991). Sex differences in speed of mental rotation and the X-linked genetic hypothesis.

Intelligence, 15, 17-32. Thurstone, T.G. & Thurstone, L.L. (1949). Mechanical Aptitude II: Description of Group Tests. Chicago, Ill.:

Univ. of Chicago, Psychometric Laboratory, Report 54, March, 1949. Vandenberg, S.G. (1987). Sex differences in mental retardation and their implications for sex-differences in

ability. In J.M. Reinisch, L.M. Rosenblum & S. A. Sanders (Eds.), Masculiniry/feminity: Basic perspectives. New York: Oxford.

Voyer, D., Voyer, S. & Bryden, M.P. (1995). Magnitude of sex-differences in spatial abilities: A meta-analysis and consideration of critical variables. Psychological Bulletin, I1 7, 250-270.

Yela, M. (1968). Rotacidn defiguras macizas. Manual. Madrid: TEA.