Gender differences in confidence during number-line estimation

Abstract

Prior research has found gender differences in spatial tasks in which men perform better, and are more confident, than women. Do gender differences also occur in people’s confidence as they perform number-line estimation, a common spatial-numeric task predictive of math achievement? To investigate this question, we analyzed outcomes from six studies (N = 758 girls/women and boys/men with over 20,000 observations; grades 1–5 and adults) that involved a similar method: Participants estimated where a provided number (e.g., ¾, 37) was located on a bounded number line (e.g., 0–1; 0–100), then judged their confidence in that estimate. Boys/men were more precise (g = .52) and more confident (g = .30) in their estimates than were girls/women. Linear mixed model analyses of the trial-level data revealed that girls’/women’s estimates had about 31% more error than did boys’/men’s estimates, and even when controlling for precision, girls/women were about 7% less confident in their estimates than were boys/men. These outcomes should encourage researchers to consider gender differences for studies on math cognition and provide pathways for future research to address potential mechanisms underlying the present gender gaps.

Appendices

Appendix 1: Further Details on Hedges’ g Meta-Analyses

To conduct our Hedges’ g meta-analyses, we followed these four steps: Once an effect size (g) was calculated for all of the samples, we (1) estimated heterogeneity among the effect sizes, (2) estimated the population variability in effect sizes, (3) used this estimate of population variability to provide random-effects weights of sample effect sizes, and (4) used these random-effects weights to estimate a random-effects mean effect size and standard error of this estimate. In particular, heterogeneity was estimated using the Q-statistic (Cochran 1954), computed with the following equation:

$$ Q=\Sigma \left({w}_{\mathrm{i}}\ {\left({g}_{\mathrm{i}}-g\right)}^2\right) $$

(A1)

In Eq. A1, w_i = the weight of study i (w_i = 1/SE²_i, where SE_i = the standard error of the effect size estimate for study i), g_i = the effect size estimate from study i, and g_i = the mean effect size across the samples, such that Q is distributed as chi-square with k-1 degrees of freedom, where k = the number of samples. To estimate population variability in effect sizes (τ²), the following equation was used:

$$ {\uptau}^2=Q-\left(k-1\right)/\left\{\left(\Sigma {w}_{\mathrm{i}}\right)-\left[\left(\Sigma {w^2}_{\mathrm{i}}\right)/\left(\Sigma {w}_{\mathrm{i}}\right)\right]\right\} $$

(A2)

Random-effects weights (w*_i) were computed as: w*_i = 1/(τ² + SE²_i), where SE_i = the standard error of the effect size of study i. Finally, the random-effects mean effect size (g) was calculated with the following equation:

$$ g=\Sigma \left(w\ast g\right)/\Sigma \left(w\ast \right) $$

(A3)

The standard error of this mean effect size was computed as SE_g = [Σ(w*)]^½ .

Appendix 2: Analyses of Gender Differences in Performance

Hedges’ g Meta-Analysis

A medium gender difference in precision occurred favoring boys/men, presented in Fig. 3. Averaged across the 18 effect sizes, boys/men were more precise in their number-line estimates than were girls/women, g = .52, 95% CI [.31, .74], p < .001. No significant heterogeneity was observed among the effect sizes, Q(17) = 24.46, p = .11; I² = 30.50%. Conducting this same meta-analysis on performance using a fixed-effects model resulted in a similar overall mean effect size, g = .48, 95% CI [.32, .63], p < .001.

Linear Mixed Effects Model

Table 4 presents a nested linear mixed effect model predicting trial-level PAE from the participant’s gender. The model replicated the findings from the Hedges’ g meta-analysis on the effect of gender on estimation precision. Using the fixed-effects estimates, women’s PAE is estimated to be .039 points higher than men’s PAE (p < .001). Given the intercept of .126 (p < .001), the fixed-effects estimate of the average man’s PAE was .126 versus .165 (.126 + .039) for women. Thus, it appears that the average girl’s/woman’s estimate had 31% more error than the average boy’s/man’s estimate (.039 /.126 = .3095).

Appendix 3: Gender Differences in Relative Metacognitive Accuracy

No reliable gender difference was observed for relative accuracy, as calculated by computing an intra-individual gamma correlation between confidence judgments and performance (Fig. 4); g = .11, 95% CI [−.13, .35], p = .27. No significant heterogeneity was observed among the effect sizes, Q(17) = 27.47, p = .05, I² = 38.11%. The fixed-effects model resulted in a similar overall mean effect size, g = .07, 95% CI [−.09, .23], p = .28.

Appendix 4: Gender Differences in Confidence (Controlling for Performance) by Grade and Number-Line Scale

Note. Each point represents the effect of gender while controlling for PAE, averaged across experiments involving participants who are in the same grade and estimated within the same number-line scale. Negative values indicate boys/men are more confident than girls/women. The horizontal line represents the grand mean effect of gender (b = −0.38). The size of each dot is mapped to the number of observations (participants x items), with larger sizes representing more observations.

Fig. 3

Forest Plot of Effect Sizes for the 18 Samples Included in the Hedges’ g Meta-Analysis of Performance

Fig. 4

Forest Plot of Effect Sizes for the 18 Samples Included in the Hedges’ g Meta-Analysis of Relative Metacognitive Accuracy

Fig. 5

Gender Differences in Confidence (Controlling for Performance) by Grade and Number-Line Scale

Table 4 Linear Mixed Models Predicting Trial-Level Precision (Measured as PAE)