SQ-C and EQ-C are Uncorrelated

In line with the TD sample in the study conducted by Auyeung and colleagues13, there was no relation between EQ-C and SQ-C scores. This suggests the constructs of empathizing and systemizing are independent of one another (r(110) = 0.086, p = 0.37).

SQ-C and EQ-C Differ by Gender

Boys and girls did not differ in age, the Wechsler Abbreviated Scale of Intelligence31 full-scale IQ (FSIQ), reading achievement as measured by the Woodcock Johnson III (WJ-III)32 Basic Reading composite, or math achievement as measured by WJ-III mathematics subscales (Table 1). There was a marginally significant gender difference on SQ-C, with boys scoring higher than girls. In contrast, boys and girls differed significantly on EQ-C with girls scoring higher than boys (Table 1).

Table 1 Social and cognitive measures in boys and girls. Full size table

Relation between SQ-C and Mathematical Achievement

Pearson correlations were used to examine the relationship between systemizing and two distinct components of math achievement – symbolic arithmetic ability as measured by the WJ-III Calculation Skills composite, and mathematical reasoning skills, as measured by the WJ-III Applied Problems subtest. Table 2 summarizes the relation between SQ-C, and the cognitive measures. SQ-C was not correlated with the Calculation Skills composite (r(110) = 0.07, p = 0.44), however, it was marginally positively correlated with the Applied Problems subtest (r(110) = 0.16, p = 0.08). Given the marginally significant gender differences in SQ-C scores, we then examined these relations in each gender. The relationships between SQ-C and the math measures were not significant in separate groups of boys or girls (Table 2).

Table 2 Relation between SQ-C and cognitive measures. Full size table

Since Applied Problems was strongly correlated with FSIQ and the Basic Reading composite (Supplementary Table S1; r(110) = 0.64, p < 0.001 and r(110) = 0.57, p < 0.001 respectively), we further examined the relationship between SQ-C and Applied Problems after accounting for FSIQ and reading achievement using a hierarchical regression analysis. The domain general cognitive capacities of FSIQ and the Basic Reading composite scores accounted for 50.1% (Adjusted R2 = 0.49) of the variance in Applied Problems scores (F(2, 109) = 54.69, p < 0.001). Adding SQ-C to the model did not account for significant additional variance (F change(1, 108) = 1.45, p = 0.23; Supplementary Table S2). Taken together, these results suggest that SQ-C is not an independent predictor of math achievement in children.

Relation between EQ-C and Mathematical Achievement

Table 3 summarizes the relation between EQ-C and cognitive measures. There was a negative correlation between EQ-C and the Calculation Skills composite score with greater empathizing predicting lower math achievement (r(110) = −0.22, p = 0.02). EQ-C was not significantly correlated with Applied Problems (r(110) = −0.01, p = 0.91). To further examine the relationship between EQ-C and the Calculation Skills composite we conducted a hierarchical regression analysis after accounting for FSIQ and the Basic Reading composite. The domain general predictors accounted for 23.4% (Adjusted R2 = 0.22) of the variance (F(2, 109) = 16.61, p < 0.001). Including EQ-C in the model accounted for an additional 3.8% of the variance in math achievement (F change(1, 108) = 5.71, p = 0.02) (Table 4). These results demonstrate that empathizing is a previously unknown predictor of math skills in TD children.

Table 3 Relation between EQ-C and cognitive measures. Full size table

Table 4 Hierarchical regression analysis of Math Calculation Skills. Full size table

The Relationship between EQ-C and Mathematical Achievement in Boys vs. Girls

Given the significant gender differences in EQ-C scores, the relation between EQ-C and the Calculation Skills composite was then examined separately in boys and girls. The relationship was significant in girls (r(55) = −0.29, p = 0.03), but not in boys (r(53) = −0.14, p = 0.32; Fig. 1); however, these effects were not statistically different from each other (z = −0.81, p = 0.42). Regression analyses, conducted separately in each group, revealed that the variance accounted for in the Calculation Skills composite by EQ-C, after accounting for FSIQ and the Basic Reading composite was significant in girls (R2 change = 0.07, p = 0.02), but not in boys (R2 change = 0.02, p = 0.25). Finally, when gender was entered into the model as a fixed factor in the full group model, EQ-C did not significantly interact with gender (F(1, 106) = 0.55, p = 0.46). These results demonstrate that gender is not a significant predictor of the relation between empathizing and math achievement.

Figure 1 Relation between EQ-C and Math Calculation Skills (r = −0.22, p < 0.05). Full size image

EQ-C/SQ-C Discrepancy and Mathematical Achievement

We also examined the discrepancy, or difference, between systemizing and empathizing as it relates to math achievement. In line with Auyeung and colleagues13, the genders differed on the discrepancy between SQ-C and EQ-C scores (t(110) = −4.11, p < 0.001), with boys having on average positive scores (M = 0.04, SD = 0.09) and girls having on average negative scores (M = −.03, SD = .09).

We next examined the relationship between the math measures and the Difference score. The Difference score was positively correlated with the Calculation Skills composite (r(110) = .22, p = .02), but was not correlated with Applied Problems (r(110) = .13, p = .18). In order to test whether the Difference score, per se, rather than just the known empathizing effect was driving the relationship between the Difference score and the Calculation Skills composite, we ran a stepwise regression analysis. The stepwise regression tested for the unique contributions of EQ-C and the Difference score to the explained variance in the Calculation Skills composite, after accounting for FSIQ and the Basic Reading composite. The step-wise regression analysis selected EQ-C as the stronger predictor of the Calculation Skills composite, after accounting for FSIQ and the Basic Reading composite (F change(1, 108) = 5.71, p = 0.02). After adding EQ-C to the model, the Difference score was not a significant predictor and was not included in the model (p = 0.51).

Finally, we examined whether there were any differences in math achievement between the ‘brain type’ groups. The brain types did not significantly differ from one another on the Calculation Skills composite (F(2, 109) = 1.59, p = 0.21, h2 = 0.02) or Applied Problems (F(2, 109) = 1.89, p = 0.16, h2 = 0.03). The brain types also did not differ from one another on the Calculation Skills composite (F(2, 107) = 1.06, p = 0.35, partial h2 = 0.03) or Applied Problems (F(2, 107) = 0.41, p = 0.67, partial h2 = 0.008) after accounting for FSIQ and reading achievement.

The Effect of Math Anxiety on the Relationship between EQ-C and Mathematical Achievement

We next sought to determine whether the negative relationship between math calculation skills and empathizing could be explained by children’s math anxiety, a known negative contributor to math achievement2,4. We used partial correlations to examine the relation between the Scale for Early Mathematics Anxiety (SEMA)4 and both EQ-C and the Calculation Skills composite, after accounting for FSIQ and the Basic Reading composite. SEMA scores significantly, negatively correlated with the Calculation Skills composite (r(110) = −0.37, p < 0.001); however, EQ-C was not significantly related to SEMA (r(110) = −0.12, p = 0.23). There were no differences between the genders in SEMA scores (t(109) = 4.50, p = 0.65). Thus, children’s self-ratings of math anxiety did not explain the relationship between empathizing and math achievement.

Relationship between Social Skills and Mathematical Achievement

We then investigated whether the relationship between math achievement and empathizing could be explained by broader social abilities assessed with the Social Responsiveness Scale (SRS). The SRS has four social subscales including Social Awareness, Social Cognition, Social Communication, and Social Motivation. We also included the Autistic Mannerisms SRS subscale to assess whether the relationship between empathizing and math achievement is related to social ability, rather than an indirect connection between low empathizing and autistic behavioral tendencies. Higher scores on the SRS subscales indicate a lack of social abilities and more severe autistic mannerisms.

The Social Awareness, Social Cognition, and Social Communication subscales were negatively correlated with EQ-C (Table 5), indicating that those children with higher empathizing scores also had lower scores on the social subscales (i.e. fewer difficulties with social abilities). With the exception of the Social Motivation subscale, all the social SRS subscales were positively related to the Calculation Skills composite score, indicating that children with higher social abilities tended to have lower math skills. The Autistic Mannerisms subscale was negatively related to EQ-C; however, it was not significantly related to math achievement after accounting for FSIQ and reading achievement. These results indicate that multiple measures of social skills are related to math achievement.

Table 5 Relation between Math Calculation Skills and each of the SRS social subscales. Full size table

Relationship between Social Skills and Mathematical Achievement in Boys vs. Girls

We examined whether the relation between the SRS subscales, EQ-C, and math achievement differed by gender. All of the SRS social subscales were correlated with EQ-C in both boys and girls, with the exception of Social Motivation in girls; however, only in girls did SRS measures – specifically Social Awareness, Social Cognition, Social Communication, and Autistic Mannerisms – also correlate with the Calculation Skills composite (Table 5). Direct statistical comparison between the genders revealed that differences in correlation coefficients were significant only for Social Awareness (z = 2.18, p = 0.03). Thus, the relationship between social abilities and math achievement is, to a limited extent, stronger in girls than in boys.

Social Ability as a Potential Mediator between Empathizing and Mathematical Achievement

To further characterize the role of social abilities in the relationship between empathizing and math achievement we conducted a series of mediation analyses. Since the Social Awareness, Social Cognition, Social Communication, and Autistic Mannerisms subscales were significantly related to both EQ-C and the Calculation Skills composite, either in the whole group or in girls, they were each examined in mediation analyses. First, we assessed the strength of the relationship between EQ-C and the Calculation Skills composite after accounting for FSIQ and reading achievement (c). Then, in separate analyses, we added each of the SRS social subscales (Awareness, Cognition, and Communication) and the Autistic Mannerisms subscale to the model and measured the remaining relationship (c’) and the change in strength (ab).

The Social Cognition subscale significantly mediated the relationship between EQ-C and the Calculation Skills composite score. Social Awareness was a marginal mediator (Table 6). The relationship between EQ-C and the Calculation Skills composite score was not mediated by the Social Communication or the Autistic Mannerisms subscales. These results suggest that the link between empathizing and math achievement may be related to social awareness and cognition rather than autistic behaviors.

Table 6 Mediation analysis with SRS measures as mediators between EQ-C and Math Calculation Skills in the whole group, and in boys and girls separately. Full size table

Social Ability as a Potential Mediator between Empathizing and Mathematical Achievement in Boys vs. Girls

We next evaluated mediation models in each gender in order to assess whether the mediation effects differed by gender. When considering girls alone, there was a significant indirect effect of Social Cognition, Social Awareness and Social Communication in mediating the relationship between EQ-C and the Calculation Skills composite (Fig. 2; Table 6). None of the mediation models were significant in boys (Table 6). There was a significant difference between boys and girls only for the Social Awareness subscale (t = −2.36, p = 0.02). The relationship between EQ-C and the Calculation Skills composite was not mediated by the Autistic Mannerisms subscale in either boys or girls. These results demonstrate that Social Awareness plays a differential role in mediating the relationship between EQ-C and math achievement in girls.