Executive Summary
Key findings on student achievement gaps across demographic groups
Analysis of 1000 students reveals achievement gaps across all three subjects. The race/ethnicity group gap in math scores is 12.2 points (d = 0.8 maximum effect size). Socioeconomic status (lunch program) shows a Cohen's d of 0.782 for math. The strongest single intervention signal is parental education.
Score Distributions by Subject
Mean math, reading, and writing scores broken down by student gender
Mean scores by gender show that females score higher in reading (72.61) and writing (72.47), while males score higher in math (68.73). Overall averages are: math 66.1, reading 69.2, writing 68.1.
Gender Achievement Gap
Mean scores and Cohen's d effect sizes comparing male and female students per subject
Gender gaps: math d = 0.34 (small), reading d = -0.5 (medium-to-large), writing d = -0.63 (medium-to-large). Positive d values indicate males scoring higher; negative indicate females scoring higher. Females outperform males in reading and writing, while males show a slight advantage in math.
Race/Ethnicity Achievement Gap
Mean scores by race/ethnicity group across math, reading, and writing
Across race/ethnicity groups, group E students achieve the highest mean math score (73.8) while group A students score lowest (61.6), a gap of 12.2 points. Kruskal-Wallis test: p = 1.19e-11 (statistically significant). Reading and writing follow similar patterns with group gaps of 8.4 and 8.7 points respectively.
Parental Education Impact
Mean scores by parental education level, ordered from lowest to highest attainment
Students whose parents hold a master's degree average 69.8 in math, versus 62.1 for those with high school — a 7.6-point gap. Scores increase broadly with parental education level across all three subjects. The pattern is consistent: higher parental education correlates with higher student achievement.
Test Preparation Effect
Mean scores comparing students who completed vs. did not complete test preparation
Students who completed test preparation score higher across all subjects. Math gain: +5.6 points. Reading gain: +7.4 points. Writing gain: +9.9 points. Test preparation shows a consistent positive association with performance across all three subjects.
Effect Size Heatmap
Cohen's d effect sizes by race/ethnicity group and subject (relative to top-performing group)
Cohen's d effect sizes relative to the top-performing group reveal that group A shows the largest composite gap. Maximum observed effect size: d = 0.8. 5 out of 15 group-subject combinations exceed the medium effect size threshold (0.5). The heatmap highlights where achievement gaps are most severe and where targeted interventions would have the greatest impact.
Pairwise Statistical Comparisons
Adjusted p-values from pairwise Dunn/Wilcox tests comparing race/ethnicity groups per subject
| race_ethnicity | math_score | reading_score | writing_score |
|---|---|---|---|
| group A - group B | 0.9698 | 0.5668 | 0.4118 |
| group A - group C | 0.337 | 0.0395 | 0.02 |
| group B - group C | 1 | 1 | 0.9175 |
| group A - group D | 0.0026 | 0.0161 | 0.0003 |
| group B - group D | 0.0325 | 0.4868 | 0.0236 |
| group C - group D | 0.0654 | 1 | 0.3862 |
| group A - group E | 0 | 0.0001 | 0.0001 |
| group B - group E | 0 | 0.004 | 0.0065 |
| group C - group E | 0 | 0.0541 | 0.0986 |
| group D - group E | 0.0004 | 0.1983 | 1 |
Pairwise comparisons (bonferroni-adjusted) across 10 group pairs. Significant pairs (p < 0.05): math = 6, reading = 4, writing = 5. Values represent adjusted p-values; lower values indicate stronger evidence of group differences. Pairs with p < 0.05 represent statistically meaningful achievement gaps between those groups.
Socioeconomic Status Impact
Mean scores by lunch program type (standard vs. free/reduced) as a proxy for socioeconomic status
Students on the standard lunch program score 11.1 points higher in math (7 in reading, 7.8 in writing) than peers on free/reduced lunch. SES Cohen's d for math = 0.78, which exceeds the gender gap (d = 0.34). Socioeconomic status is among the strongest predictors of student achievement in this dataset.