Purpose

This density overlay visualization compares the distribution shapes and central tendencies between female and male groups. It provides a visual foundation for understanding whether observed differences are driven by shifts in the entire distribution or concentrated in specific regions, complementing the statistical test results.

Key Findings

Mean Difference: Males score 5.1 points higher (68.73 vs. 63.63), representing a rightward shift in the male distribution
Spread Similarity: Both groups show comparable variability (SD: 15.49 female, 14.36 male), indicating consistent dispersion across groups
Distribution Shape: Both distributions appear approximately symmetric (skew ≈ -0.08), suggesting the difference is primarily a location shift rather than shape distortion
Overlap Pattern: Substantial curve overlap indicates considerable within-group variation relative to between-group differences

Interpretation

The density curves reveal that while males demonstrate a statistically significant higher mean (p < 0.001), the distributions overlap considerably. This aligns with the small effect size (Cohen's d = -0.341), indicating the practical magnitude of difference is modest despite statistical significance. The parallel spread patterns suggest the groups have homogeneous variance, supporting the equal variance assumption used in the Welch's t-test.

Context

The visual representation assumes kernel density estimation accuracy. The range extension (−