Mathematics, gender, spatial performance, and cerebral organization: A suppression effect in talented students.

Two experiments were conducted to investigate the generalizability of the suppression effect of mathematical achievement on gender differences in spatial abilities observed by Voyer (1996a). Specifically, the generalizability of this finding to mathematically talented samples and to a computerized task was examined. Mathematical talent was determined indirectly on the basis of the program of study in which participants were enrolled. By use of grades comparison, it was shown in both experiments that science students were mathematically talented, whereas arts students were mathematically less endowed. The first study was a re-analysis of data presented by Voyer. The pattern of correlations and the suppression effect observed by this author was shown to generalize to mathematically talented and less endowed students. The second study extended these findings to a computerized task designed to assess cerebral asymmetries. The results of the present experiments demonstrate the robust qualities of the suppression effect reported in previous research. Implications of these findings for future research and admission decisions are discussed.

Past research on the relation between gender differences on spatial tasks and mathematical achievement focused exclusively on the use of paper-and-pencil tests of mathematics performed in a laboratory setting (see Friedman, 1995, for a review). The implicit rationale underlying this emphasis is that performance on tests of mathematics completed in a laboratory reflects reliably the level of mathematical achievement one is likely to reach. This rationale is supported by studies demonstrating the value of such tests in predicting academic performance (Benbow, 1992; Bridgeman & Wendler, 1991; Shepperd, 1992).

The interest in studying the relation between gender differences in spatial performance and mathematical performance lies in the reasoning that gender differences in mathematical abilities mediate those found on spatial tasks. For instance, in a classic study, Hyde, Geiringer, and Yen (1975) demonstrated that gender differences on the rod-and-frame test were eliminated (made nonsignificant) when mathematical test performance was controlled statistically.

Voyer (1996a) presented data which put a different light on this area of research. This author demonstrated that a clear distinction had to be made between results obtained with tests of mathematical abilities performed in a laboratory and measures of mathematical skills derived from classroom performance. Specifically, Voyer (1996a) hypothesized that mathematics performance was a suppressor variable in the relation between gender and spatial performance. He claimed that this hypothesis would be supported if the correlation between gender and the score on a spatial task was greater when performance in high school mathematics was controlled (partialed out) than when it was not. This prediction was confirmed in three separate studies. This finding indicated that, contrary to the common finding, controlling for mathematical performance in the classroom increased the magnitude of gender differences in spatial tasks. Furthermore, it was found that gender differences favor women when classroom performance in mathematics is considered, whereas they favor men when laboratory-administered tests are used.

These findings have several theoretical and applied implications. At the theoretical level, they suggest that classroom performance in mathematics acts as a suppressor variable in its relation with gender differences in spatial abilities. This is a particularly important finding given the rarity of suppressor variables in most settings (Darlington, 1968; Pedhazur, 1982).

At another level, Voyer' s (1996a) findings also have an important implication for applied settings. Laboratory-based measures of mathematical abilities, such as the Mathematical subtest of the Scholastic Aptitude Test (SAT-M), are often used as a basis for admission decisions in colleges and universities. The finding of gender differences in favor of women in high-school mathematics grades, as opposed to the gender differences in favor of men on the SATM (Hyde, Fenneman, & Lamon, 1990), suggests that laboratory-based measures of mathematical abilities might underestimate the achievement potential of women. This also suggests that there are important differences between the assessment situations encountered in the laboratory and in the classroom measures of mathematical abilities (see Voyer, 1996a, for a discussion of some of these differences). The question one might ask based on this statement is: How do we define mathematical talent -- based on grades or based on performance in laboratory-administered measures?

Gender, spatial skills, mathematical achievement, and talent

In view of the fact that one purpose of the present report is to demonstrate that the findings obtained by Voyer (1996a) are also obtained in a mathematically talented sample, the definition of talent is important. However, in considering such a definition, one must ask the following question: at the individual level, what is the most important measure that will determine career choices? In answering this question, one must consider that grades in high school tend to be the primary criterion for admission decisions in college, whereas scores on tests such as the SAT are likely to be used as a secondary criterion (even though the actual weight given these measures varies from college to college). Furthermore, grades are of great importance when a student applies for scholarships and awards. Therefore, in the present report, high school grades in mathematics will be used as an indicator of the ability level for specific individuals.

However, it is not practical to analyze separately the performance of individuals with high and low grades in mathematics (or even in other subjects), while attempting to partial out mathematical performance. This is because classifying individuals on the basis of academic performance would, in fact, partial out the influence of this factor. In order to get around this problem, a reasoning similar to that made by Voyer (1996a) in his first study was used. Specifically, it is likely that mathematically talented students will seek admission in a study program where mathematics are prominent, whereas students who are less endowed will seek admission in a program where mathematics courses are not a basic requirement.

This reasoning is easily applied at the university where the present studies were conducted (St. Francis Xavier University, in Antigonish, Nova Scotia, Canada). There are two basic study programs at this undergraduate university: science and arts. Admission requirements are the same in the arts and science programs (high school diploma with an overall average of at least 65% and no marks below 50%). However, upon admission, science students are expected to take a number of required mathematics courses as part of their study program, whereas arts students have no mathematics requirement. Note that the absence of a mathematics requirement for arts students is somewhat at variance with practice at other small Canadian universities. Nevertheless, this difference between the arts and science programs provides a useful means for the classification of students in the present study. Specifically, this distinction suggests a crude but easily applicable criterion for mathematical talent: science students should be more mathematically talented than arts students. This can be readily verified by comparing high school grades in mathematics obtained by students enrolled in the science and arts program. If the above reasoning is correct, high school grades in mathematics should be significantly greater in science students than in arts students. Once this has been demonstrated, it will be legitimate to determine whether or not the findings obtained by Voyer (1996a) are found in talented (science students) and less endowed (arts students) samples.

Gender, spatial skills, mathematical achievement and cerebral organization

Gender differences in cognitive abilities are well documented, especially in spatial (Voyer, Voyer, & Bryden, 1995), verbal (Hedges & Nowell, 1995) and mathematical skills (Hyde et al., 1990). The apparent pervasiveness of these gender differences has prompted a number of researchers to hypothesize that they were due to sex differences in cerebral organization. For instance, Levy (1972) stated that men use the right cerebral hemisphere for non-verbal tasks and the left hemisphere for verbal tasks, whereas women tend to use both hemispheres regardless of the nature of the task. This means that men are more lateralized than women since their cerebral organization is more asymmetrical. Based on this hypothesis, it is expected that men will show a laterality effect on specific tasks (meaning that there will be a difference between the processing ability of the two cerebral hemispheres), whereas such an effect should not be significant in women. Harris (1978) found convincing support for this prediction in a careful literature review, and Voyer (1996b) corroborated this interpretation in a meta-analysis.

It is thus likely that sex differences in cerebral organization mediate, at least in part, gender differences in spatial and mathematical skills. However, if this is the case, what would become of the relation between gender, spatial skills, and mathematical achievement reported by Voyer (1996a) when a spatial task is used in the context of a laterality study? It is a second purpose of the present report to provide an answer to this question. Tentatively, it is hypothesized that if the suppression effect reported by Voyer (1996a) is robust, the correlation between gender and overall accuracy in a spatial task measuring laterality should be greater when high school grades in mathematics are partialed out than when they are not. Furthermore, the importance of this suppression effect should be emphasized by an increase in the magnitude of sex differences in laterality when high school grades in mathematics are partialed out compared to when they are not.

Experiment 1

Experiment 1 addresses directly the first question of interest in the present report, that is, it aims at demonstrating that the findings obtained by Voyer (1996a) are also obtained in a mathematically talented sample. Therefore, it investigates whether or not the suppression effect of grades in mathematics will be obtained when talented students (enrolled in a science program) and less endowed students (enrolled in an arts program) are compared. This study is a re-analysis of the data presented by Voyer (1996a), Experiment 3(1).

Method

Participants. The 53 men (39 enrolled in arts, 14 in science) and 70 women (48 enrolled in arts, 22 in science) who participated in the study were undergraduate students enrolled in introductory psychology. Based on recent enrollment data, 60% of the participants were from Nova Scotia, 32% from other provinces, and 8% from other countries. In addition, all the participants had at least a 12th-grade education, and their mean age was 19.4 years, with a range from 17 to 26 years. Their socio-economic status was not available. Participants were tested in a classroom in two groups of about 65 students. Because testing was conducted during the regularly scheduled introductory psychology class, participants were told that they could withdraw from the experiment at any time, without prejudicing their grade in the course, in agreement with the American Psychological Association ethical guidelines (APA, 1993). None chose to withdraw.

Materials. The Vandenberg and Kuse Mental Rotations Test (MRT: Vandenberg & Kuse, 1978) was used as one measure of spatial abilities. This test is a paper-and-pencil version of the Shepard and Metzler (1971) mental rotation task. The MRT consists of 20 multiple-choice items composed of a target figure, two correct alternatives, and two distractors. Correct alternatives are always identical to the target but are shown in various rotations. Participants are required to indicate which two of the four test figures are identical to the target. Even though there are different ways to score this test (Voyer et al., 1995), the total score on the MRT was determined by giving two credits for an item with both choices correct, and one point was given if only one choice was selected and it was correct. As a way to compensate for guessing, no credit was given if one choice was correct but the other incorrect, or if both were incorrect. This is the scoring procedure recommended by Vandenberg (1985), and it results in a maximum score of 40.

In addition to the MRT, the Water Level Task (WLT; Robert & Morin, 1993) was also used. The WLT consists of 16 drawings of tilted containers. Participants are instructed to draw a line representing the orientation of the liquid in each container, given that it is presumed to be half full with water. Performance on this test was scored on a 5 degrees criterion, following the procedure suggested by Robert and Morin (1993). This means that lines that deviated from the horizontal by more than 5 degrees were counted as wrong answers, whereas lines within this range were counted as correct answers. The maximum score that can be obtained on this test is 16.

The mean grade in high school mathematics (averaged across grades) was used as a measure of performance in mathematics courses. Participants were required to indicate the average of all their high school mathematics courses (in percentage) on a single piece of paper after completion of the spatial tests. In an attempt to minimize the influence of social desirability, instructions emphasized the confidentiality of the data collected in the experiment and encouraged the participants to be honest in their answers.

Procedure. The order of the two spatial measures was counterbalanced across the two groups of students. For both tests, the experimenter read aloud the instructions on the cover page of the test. Students then performed sample problems to make sure that they understood the tasks. They were allowed 10 minutes to complete the MRT and unlimited time to complete the WLT (this test is usually completed in approximately 10 minutes as well), following the procedure recommended by Robert and Morin (1993). The question concerning the mean high school mathematics grade was always completed last.

Results

Preliminary analysis

In view of the fact that the present study is based on the assumption that students in arts and science represent different levels of talent in mathematics, it is necessary to ensure that this assumption is correct. This was done by means of a t-test comparing arts and science students on the mean grade in high school mathematics measure. Results of this analysis showed that science students obtained significantly higher high school grades in mathematics (mean = 78.9%) than students in arts (mean = 69.5%), t(121) = 4.10, p [is less than] .001. This finding supports the basic assumption required in the present study for a comparison of talented students with less endowed students. Even though science students in the present sample are not clearly outstanding in absolute terms, with a mean below 80%, they definitely have better mathematical skills than their arts counterpart. This finding, therefore, makes further analyses comparing arts and science students legitimate.

Correlational analysis 

Overall sample: As a starting point, the correlational analysis for the whole sample will be considered. The analysis procedure used with these data was exactly the same as in Voyer's (1996a) study. An effect coding scheme was applied to the categorical variable gender: men were attributed a value of + 1 and women a value of -1. The significance level ([Alpha]) was set at .05 in all the correlational analyses.

Results revealed a significant correlation between gender and the score on both tests, r(121) = .31 for the WLT, and r(121) = .35 for the MRT. The correlations reflected significant gender differences in favor of men on both tests. The means relevant to these findings are shown in Table 1. A positive but non-significant correlation was obtained between the score on the MRT and high school grades in mathematics, r(121) =. 14, whereas the score on the WLT and grades in mathematics were significantly correlated, r(121) = .24. Finally, a significant negative correlation was obtained between gender and high school grades in mathematics, r(121) = -.26, reflecting a gender difference in favor of women. Means relevant to this finding are presented in Table 1 as well.

Mean score on the Water Level Test, Mental Rotations
Test, and High School Grades in Experiment 1

Measure                     Overall                   Arts
                       Men         Women         Men         Women

WLT                    8.85         5.66         9.28         5.63
MRT                   28.13        20.40        27.49        20.35
Grades                68.59        75.00        66.03        72.29

Measure                     Science
                       Men         Women

WLT                   7.64          5.23
MRT                   29.93        20.50
Grades                75.71        72.24

Note: MRT = Mental Rotations Test; WLT = Water Level Test; Grades = Average Grades in High School Mathematics

Table 1

The correlation between gender and the score on each of the two spatial tasks, while partialing out the mean high school grades in mathematics (partial correlation), was calculated to determine whether or not a suppression effect was present. At this point, it is important to remember that Pedhazur (1982) stated that a suppressor variable is present when a partial correlation is larger than its associated zero-order correlation. The partial correlation for the MRT, r(120) = .41, was greater than its associated zero-order correlation (r = .35). For the WLT, the partial correlation, r(120) = .40, was also greater than the associated zero-order correlation (r = .31). These findings clearly support the notion that high school grades in mathematics act as a suppressor variable in gender differences on spatial tasks. This was to be expected given that the present report is based on a re-analysis of data where this effect was observed. However, it had to be clearly established before we can legitimately turn to the question of whether or not talent makes a difference in the suppression effect.

Separate analyses: Zero-order correlations for arts and science students are presented in Table 2. The data presented in this table indicate that gender differences are significant on all three dependent measures (MRT, WLT, and grades in mathematics) in arts students, as reflected by the significant correlations between the score on these measures and gender. As can be seen in the means presented in Table 1, in arts students, gender differences favor men on the WLT and MRT, whereas they favor women on the high school grades in mathematics.

Correlations for Arts and Science Students on the Measures Used in Experiment 1 (Arts Students Above the Diagonal, n = 87; Science Students Below the Diagonal, n = 36)

                      WLT          MRT         Grades       Gender

WLT                  -            0.56(*)      0.26(*)      0.35(*)
MRT                  0.41(*)      -            0.16         0.36(*)
Grades               0.34(*)      0.06         -           -0.26(*)
Gender                 0.19       0.45(*)      0.26         -

Note: MRT = Mental Rotations Test; WLT = Water Level Test; Grades = Average Grades in High School Mathematics

(*) p < .05

Table 2

In science students, only the MRT shows a significant correlation, demonstrating a significant gender difference favoring men (see Table 1). The WLT and grades in mathematics reveal non-significant differences favoring men.

The partial correlations between gender and score on the WLT and MRT, with mathematics grades partialed out, were calculated separately for arts and science students. For arts students, the partial correlation was 0.45 (p [is less than] .05) on the WLT and 0.43 (p [is less than] .05) on the MRT. Science students obtained a partial correlation of 0.31 (ns) on the WLT and 0.48 (p [is less than] .05) on the MRT. These data indicate that, in both arts and science students, the partial correlation between gender and spatial performance, with mathematics grades partialed out, is greater than the corresponding zero-order correlation on both spatial measures. This reflects the definition of a suppressor variable proposed by Pedhazur (1982). It thus appears that high school grades in mathematics act as a suppressor variable in the relation between gender and spatial task performance in both arts and science students.

Discussion

The results of the present study support the notion that the mean grade in high school mathematics is a suppressor variable in the relation between gender and performance in two spatial tasks, regardless of the talent of the sample. This statement is supported by the finding that the suppression effect is present in both arts and science students.

There are, however, a number of issues that compromise the value of the present study in a rigorous investigation of the research question. First of all, the suppression effect had to be expected in the overall sample. The present data were previously published because they showed that effect in the first place. These data, therefore, do not provide an independent investigation of the research question. Second, the data were collected in groups of students. According to Voyer et al. (1995), group testing is likely to reduce the magnitude of gender differences in some spatial tasks. This might account in part for the lack of significant gender differences on the WLT in science students, in addition to the small sample size. Finally, only two introductory psychology classes were tested. It is unlikely that students were enrolled in these classes in a random fashion. Their enrollment in two specific sections of introductory psychology was dependent on their overall course selection. It is thus likely that students enrolled in these specific sections are a more or less homogeneous group of participants, thus reducing within-sample variability, which, in turn, affects the likelihood of detecting individual differences (Howell, 1992).

Experiment 2 was conducted in part to address these problems but also to extend the suppressor effect investigation to a spatial task performed on a computer, which allows an assessment of cerebral specialization for this type of task. The first problem mentioned above was addressed in the second experiment with the use of a new sample of participants. The second concern was overcome by the use of individual testing. Finally, the last issue was addressed by sampling left- and right-handed students from eight different sections of introductory psychology. Recruiting from several different classes was expected to increase heterogeneity in terms of course enrollment. Furthermore, because left-handers tend to be more variable in terms of cerebral organization (Bryden, 1982), this factor should also contribute to a greater heterogeneity of the sample in Experiment 2. Even though it is likely that left-handers were included in the sample of Experiment 1, they were not selected systematically. In fact, handedness was not formally measured in Experiment 1. Left-handers were selected systematically to form a large proportion of the sample in Experiment 2. In addition, hand preference was measured with a standardized instrument.

Experiment 2

Method

Participants. Ninety-eight introductory psychology students (52 women, 34 in arts, 18 in science; 46 men, 32 in arts, 14 in science) participated in the experiment. All participants had normal or corrected to normal vision. They had the same demographic characteristics as the participants in Experiment 1, except that their mean age was 21.2 with a range from 17 to 40. Participation was voluntary following the policies of the subject pool in the department of psychology at St. Francis Xavier University.

Materials. As in Experiment 1, individual differences in spatial ability were assessed with the WLT (Robert and Morin, 1993) and the MRT (Vandenberg and Kuse, 1978). The administration procedure used for these tests was exactly the same as in Experiment 1.

The Waterloo Handedness Questionnaire (WHQ: Steenhuis & Bryden, 1989) was used to assess hand preference. This is a 32-item questionnaire in which participants are required to indicate which hand they always or usually use for specific activities. Left always answers are scored as -2, and right-always answers are scored as +2. Intermediate answers are scored as -1 (usually left), 0 (no preference), and + 1 (usually right). This results in a total score with a range from -64 (completely left-handed) to +64 (completely righthanded). Classification of the participants based on answers to this questionnaire indicated that 22 men and 23 women were left-handed, whereas 24 men and 29 women were right-handed.

The lateralized embedded figures task was designed using the Micro-Experimental Laboratory software (Schneider, 1990) on a Gateway 2000 386/25 micro-computer. Sixteen complex figures drawn from the Hidden Pattern Test of the Kit of Factor-Referenced Cognitive Tests (Ekstrom, French, & Harman, 1976) were used in this task. Four models were constructed with the constraint that they had to be present in at least four of the complex figures, and they also had to be absent in four of the complex figures. This allowed for a sufficient number of trials without the risk of practice effects arising from the constant repetition of the same model-complex figure associations. The models and the complex figures subtended 2.0 [degrees] of visual angle at a viewing distance of 85 cm. On each trial, a mask was presented after the complex stimulus until a response was given. The mask, similar to the one used by Voyer and Bryden (1993), was composed of a radial pattern of lines intersecting in their center and subtending 3 [degrees] of visual angle. The mask thus covered the complex figure completely.

Stimuli were presented on a Gateway Crystal Scan 1024 NI color monitor. A timing unit integrated into the computer controlled presentation time of the stimuli and stored the subject's accuracy for each trial.

Procedure. Participants were tested individually, and the order of the paper-and-pencil tests and the lateralized task was counterbalanced across subjects. In the lateralized task, participants first read the instructions presented on the computer screen. The instructions stated that they were to decide whether or not the model shown to them was present in the pattern presented on the screen. The instructions emphasized the importance of fixating at the center of the screen and discouraged trying to anticipate on which side the stimuli would appear. Participants then pressed the spacebar on the computer keyboard to start the experiment. After the subject had pressed the spacebar, the model was first presented for one second. This was followed by a warning signal (`GET READY') presented in the center of the screen for 750 ms. The complex figure was then presented 4.0 [degrees] to the left or right of fixation for 33 ms, and was followed by the mask presented at the same location as the complex figure, until response. Participants performed 24 practice trials to familiarize themselves with the task. They then performed 192 experimental trials (2 visual fields x 2 response types (yes, no) x 16 complex figures x 3 blocks of trials). Participants were required to indicate whether or not the model was embedded in the complex figure by pressing the appropriate key on the keyboard (0,1). For half the participants, the fight hand was used for "Yes" (0) responses and the left hand was used for "No" (1) responses. The remaining participants had the opposite arrangement. Accuracy was the only dependent variable measured in this task.

For the two pencil-and-paper tests and the measure of grades in high school mathematics, the procedure was exactly the same as in Experiment 1. Participants always answered the question about their grades in mathematics last.

Results

Preliminary analysis

As in Experiment 1, a preliminary analysis was performed by means of a t-test comparing arts and science students on high school grades in mathematics. This ensured that the assumption that students in arts and science represent different levels of talent in mathematics was correct. Once again, results of this analysis showed that science students obtained significantly greater high school grades in mathematics (mean = 81.3%) than students in arts (mean = 73.4%), t(96) = 3.15, p [is less than] .01. The basic assumption required in the present study for a comparison of talented students with less endowed students is therefore supported, thus making it legitimate to use program of study as an indirect measure of talent in mathematics.

Correlational analysis

Overall sample: As before, the correlational analysis for the whole sample will be considered first. As in Experiment 1, an effect coding scheme was applied to the categorical variable gender, and the significance level ([Alpha]) was set at .05 in all the correlational analyses. In addition to gender, the variables considered were: overall accuracy on the lateralized task, a laterality index (left visual field accuracy minus right visual field accuracy on the lateralized task), score on the WLT, score on the MRT, and mean high school grade in mathematics.

Correlations relevant to this analysis are presented in Table 3. The results presented in this table indicate significant correlations between gender and the score on both spatial tests. These correlations reflect significant gender differences in favor of men on both tests, as illustrated by the means presented in Table 4. The non-significant correlations between gender and overall accuracy in the lateralized task, as well as between gender and the laterality index, indicate that gender differences are not significant on these measures, as seen in Table 4. A non-significant correlation was obtained between the score on the MRT and high school grades in mathematics, as well as between the score on the WLT and grades in mathematics. Finally, a significant negative correlation was obtained between gender and high school grades in mathematics, reflecting a gender difference favoring women. Means relevant to this finding are presented in Table 4 as well.

Zero-Order Correlations Among the Measures and Partial Correlations Between Gender and the Dependent Meansures in Experiment 2 (Zero-Order Correlations Above the Diagonal, Partial Correlations Below the Diagonal)

                     Accuracy    Laterality    MRT        WLT

Accuracy             -           -0.19         0.36(*)    0.35(*)
Laterality           -            -            0.16       0.04
MRT                  -            -            -          0.44(*)
WLT                  -            -            -          -
Grades               -            -            -          -
Gender               0.21(*)      0.05         0.57(*)    0.36(*)

                     Grades       Gender
Accuracy             0.20         0.15
Laterality           0.14         0.01
MRT                  0.10         0.52(*)
WLT                 -0.03         0.35(*)
Grades               -           -0.25(*)
Gender               -            -

Note: Accuracy = Overall Accuracy in the Lateralized Task: Laterally = Laterality Index; MRT = Mental Rotations Test; WLT = Water Level Test; Grades = Average Grades in High School Mathematics

(*) P <.05

Table 3

Mean Score on Overall Accuracy, the Laterality Index, the Water Level Test, the Mental Rotations Test, and High School Grades in Mathematics in Experiment 2

Measure              Overall                    Arts
                 Men         Women         Men         Women
Accuracy         71.38        67.88        68.95       68.28
Laterality       -1.16        -1.25        -1.48       -1.24
WLT              10.76         7.29        10.13        7.56
MRT              31.24        21.06        30.88       20.88
Grades           72.83        79.04        70.00       76.77

Measure               Science
                  Men         Women
Accuracy         76.95        67.11
Laterality       -0.32        -1.28
WLT              12.21         6.78
MRT              32.07        21.39
Grades           79.29        83.33

Note: Accuracy = Overall Accuracy in the Lateralized Task; Laterality Index; MRT = Mental Rotations Test; WLT = Water Level Tests; Grades = Average Grades in High School Mathematics

Table 4

The correlation between gender and the score on each of the measures, while partialing out the mean high school grades in mathematics (partial correlation), was calculated to determine whether or not a suppression effect was present. The results of this analysis are also presented in Table 3 to allow comparison with their corresponding zero-order correlations. The data presented in Table 3 indicate that all the measures fit the definition of a suppression effect. Specifically, they demonstrate a partial correlation (with high school grades in mathematics partialed out) that is greater than the corresponding zero-order correlation. In fact, gender differences in overall accuracy achieve significance when grades in mathematics are partialed out. These findings clearly support the notion that high school grades in mathematics act as a suppressor variable in gender differences on spatial tasks.

Separate analyses: Zero-order correlations for arts and science students are presented in Table 5. The data presented in this table indicate that in arts students, gender differences are significant on the MRT, WLT, and grades in mathematics but not on the overall accuracy in the lateralized task and on the laterality index. In science students, gender differences are significant on the MRT, WLT, and overall accuracy in the lateralized task but not on high school grades in mathematics and on the laterality index. Gender differences favor men on the WLT and MRT, as well as on overall accuracy in the lateralized task for science students, whereas they favor women on the high school grades in mathematics (see Table 4).

Correlations Among the Measures for Arts and Science Students in Experiement 2 (Arts Students Above the Diagonal, n = 66; Science Students Below the Diagonal, n = 32)

                 Accuracy    Laterality      MRT       WLT

Accuracy          -           -0.23        0.31(*)     0.28(*)
Laterality       -0.05         -           0.20        0.04
MRT               0.45(*)      0.04        -           0.34(*)
WLT               0.46(*)      0.06        0.59(*)     -
Grades            0.25        -0.09        0.16        0.05
Gender            0.38(*)      0.11        0.52(*)     0.50(*)

                  Grades       Gender

Accuracy          0.14         0.03
Laterality        0.20        -0.02
MRT               0.08         0.52(*)
WLT              -0.09         0.28(*)
Grades            -           -0.27(*)
Gender           -0.20         -

Note: Accuracy= Overall Accuracy in the Lateralized Task; Laterality = Laterality Index; MRT = Mental Rotations Test; WLT = Water Level Test; Grades = Average Grades in High School Mathematics

(*) p < .05

Table 5

The corresponding partial correlations between gender and the score on each of the measures for arts and science students are presented in Table 6. For arts students, the partial correlation between gender and spatial performance with mathematics grades partialed out is greater than the corresponding zero-order correlation for the MRT, the laterality index, and overall accuracy in the lateralized task but not the WLT. For science students, the partial correlation between gender and spatial performance with mathematics grades partialed out is greater than the corresponding zero-order correlation for the MRT, the WLT, and overall accuracy but not for the laterality index. In general, findings correspond to the definition of a suppressor variable proposed by Pedhazur (1982). It thus appears that high school grades in mathematics act as a suppressor variable in the relation between gender and spatial task performance in arts and science students. However, this conclusion does not hold on the WLT for arts students and on the laterality index for science students.

Partial Correlation Between Gender and the Dependent Measures (with Grades in High School Mathematics Partialed Out) for Arts and Science Students in Experiment 2

Measure                        Arts                 Science

Overall Accuracy               0.07                 0.45(*)
Laterality Index              -0.06                 0.07
Mental Rotations Test          0.57(*)              0.58(*)
Water Level Test               0.27(*)              0.52(*)

(*) p < .05

Table 6

General Discussion

The overall analysis of both studies confirms the suppression role of high school grades in mathematics in the relation between gender and spatial performance. This finding is especially important in the second experiment because it presents previously unpublished data. The present results thus clearly indicate that the suppression effect reported by Voyer (1996a) is robust and generalizable. Specifically, Experiment 2 extends the suppression findings to a computerized task assessing the lateralization of spatial functions. Not only does it show that the suppression affects gender differences in overall accuracy in the computer task, it also demonstrates a suppression effect on gender differences in laterality (albeit only for arts students). That is, for arts students the correlation between gender and laterality is greater when high school grades in mathematics are partialed out than when they are not. Even though gender differences do not achieve significance, the fact that the partial correlation is larger than its corresponding zero-order correlation satisfies the requirement for a suppressor variable (Pedhazur, 1982). Note that the trend observed in the present data is towards a greater lateralization in females than in males, in contradiction with what is typically reported in the literature (Voyer, 1996b). Nevertheless, the lack of statistical significance for this finding confirms the conclusion reached by Voyer (1996b) that gender differences in laterality are small.

The main aspect of the present studies concerned a comparison of mathematically talented and less endowed individuals. In both experiments, this was accomplished by comparing students enrolled in a science program of study with students enrolled in an arts program. It was shown in both studies that this comparison reflected a dimension of mathematical talent because science students outperformed arts students when high school grades in mathematics were considered.

In Experiment 1, results showed that the suppression effect was present for both arts and science students in the two spatial measures considered. This finding suggests that talent does not affect the suppression effect. However, slight differences were found between arts and science students in Experiment 2. Specifically, the suppression effect was not obtained on the WLT for arts students, whereas it was not found on the laterality index for science students. Even though it is possible that the small sample size for science students affected the results, this interpretation is not tenable for arts students. It appears that the present data do not allow a satisfactory explanation for these findings. Nevertheless, it should be noted that, in Experiment 2, the magnitude of gender differences on the WLT is smaller in arts students than in science students, as illustrated by the correlations presented in Table 6. This is surprising given that science students are more likely than arts students to be taught about the gravity principles underlying the WLT (Robert & Harel, 1996) and this would lead one to expect smaller sex differences in science students, due to training effects (Goldstein & Chance, 1965). The findings of Experiment 1 indirectly support this notion by showing significant gender differences on the WLT in arts students but not in science students (see Table 2). However, it is possible that these findings are only specific to the present samples. Further research with a variety of samples is needed to replicate the present results. In view of the fact that the majority of the students sampled here were in their first year of study, it would also be interesting to investigate whether or not the magnitude of gender differences varies as a function of year of study in a science program, especially for physics students. White and Ferstenberg (1978) compared the performance of senior and first year students in science and nonscience programs on a deductive reasoning task. They found that seniors performed better than first year students when they were science majors but not when they were nonscience majors. This type of experiment has yet to be conducted when spatial tasks are used.

Considering the magnitude of the difference between zero-order correlation and the partial correlation in the different analyses, one might argue that the suppression effect is negligible. However, it is not really possible to quantify the suppression effect. Furthermore, such a situation is so rare that whenever the partial correlation is greater than its corresponding zero-order correlation, suppression is the unavoidable conclusion (Pedhazur, 1982). Nevertheless, to confirm the validity of the present results, an independent assessment of the suppression effect was computed by means of the definition provided by Velicer (1978). According to this author, a suppressor variable is present when the squared multiple correlation with all the relevant predictors entered in the regression equation ([R.sup.2]t.gm) is greater than the sum of the squared correlation between each predictor and the dependent variable ([r.sup.2]tg + [r.sup.2]tm). Results relevant to this analysis are presented in Table 7. From this Table, it appears that conclusions reached with the Pedhazur (1982) criterion are confirmed in all cases, except for arts students when the laterality index and the WLT are considered.

Results of the Present Experiments Based on Velicer's
(1978) Definition of a Suppressor Variable

                                    Overall
Measure                 [R.sup.2]t.gm   [r.sup.2]tg+[r.sup.2]tm

Experiment 1

MRT                      0.21              0.12
WLT                      0.20              0.18

Experiment 2

Accuracy                 0.08              0.06
Laterality               0.02              0.01
MRT                      0.33              0.28
WLT                      0.13              0.12

                                  Arts Students
Measure                 [R.sup.2]t.gm  [r.sup.2]tg+[r.sup.2]tm

Experiment 1

MRT                      0.20              0.16
WLT                      0.26              0.19

Experiment 2

Accuracy                 0.03              0.02
Laterality               0.04              0.04
MRT                      0.33              0.28
WLT                      0.08              0.09

                               Science Students
Measure                  [R.sup.2].gm    [r.sup.2]tg+[r.sup.2]tm

Experiment 1

MRT                      0.23              0.21
WLT                      0.20              0.16

Experiment 2

Accuracy                 0.26              0.21
Laterality               0.02              0.02
MRT                      0.35              0.30
WLT                      0.27              0.25

Note: MRT = Mental Rotations Test; WLT = Water Level Test; [R.sup.2]t.gm = squared multiple correlation when all the predictors are entered in the regression equation with task performance as dependent variable, and gender and grades in mathematics as predictors; [r.sup.2]tg = squared correlation between task performance and gender; [r.sup.2]tm = squared correlation between task performance and grades in mathematics.

Table 7

In spite of these slight variations in the pattern of results, it is legitimate to state that high school grades in mathematics act as a suppressor variable on the relation between gender and spatial performance, regardless of the mathematical talent of the sample. This finding can be interpreted in the same terms used by Voyer (1996a). Specifically, a statistical interpretation of suppression implies that:

...performance in mathematics courses

and gender share common variance 

that is irrelevant to the prediction

of spatial tests scores on the basis of

gender. This means that gender and

performance in mathematics courses

have something in common and that

this common factor is irrelevant to

spatial performance. Therefore, the

suppression effect suggests that the

factors responsible for gender differences

in performance in mathematics

courses are not relevant to gender differences

on spatial test scores. For

this reason, partialing out these factors

controls for irrelevant variance

(Voyer, 1996a, p. 567).

Voyer (1996a) suggested that reading ability is a plausible candidate to account for the suppression effect. This speculation applies to the present findings as well. However, the present studies do not provide data to support or reject this interpretation.

It is obvious that the present results replicate the typical finding of gender differences favoring men on spatial tasks. However, the finding that underlies the suppression effect is that gender differences in high school grades in mathematics favor women. This finding is present in both experiments, either as a trend or as a statistically significant result (even though the trend favors men for science students in Experiment 1; see Table 3). In view of the reports that gender differences favor men when laboratory-administered tasks of mathematical ability are considered, it appears that such tasks underestimate women's potential for achievement. Admission decisions based on the administration of this type of tasks are therefore biased against women.

It is important at this point to consider that the use of self-reported grades in the present study hinders the formulation of strong conclusions. Memory and social desirability problems might affect the validity of the self report. However, given the robust quality and replicability of the present findings, it is unlikely these problems had a strong influence on the results. Nevertheless, readers concerned with this issue are referred to Voyer's (1996a, p. 568) discussion of the social desirability and memory problems.

In conclusion, the present studies demonstrate that performance in high school mathematics acts as a suppressor variable on the relation between gender and spatial performance in a variety of spatial tasks. In general, this finding is not affected by mathematical talent. The present findings also bring into question the use of laboratory-based measures of mathematical achievement, as opposed to classroom-based measures (grades), in college and university admission decisions. Even though the present studies demonstrate the robustness of the suppression effect, more research is needed to identify the factors underlying this effect.

(1) Experiment 3 in the Voyer (1996a) article included 125 participants. Two participants did not report the program of study in which they were enrolled. For this reason, results based on 123 participants are reported here.

(*) The research reported here was supported by grants from the St. Francis Xavier University Council for Research and from Human Resources Development - Canada. The author wishes to thank Brenda J. Baird, Wendy Digout, and Thomas J. Pennington for their assistance in the collection and scoring of the data.

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Daniel Voyer is associate professor of psychology at St. Francis Xavier University, Nova Scotia, Canada. He specializes in the study of individual differences in cognitive abilities and cerebral asymmetries.

Manuscript submitted January, 1997. Revision accepted November, 1997.