Purpose

Data Integrity: All 1,000 observations retained with zero rows removed, ensuring complete analysis without data loss
Categorical Variables: 5 demographic/program factors across 17 total categories analyzed (gender, race/ethnicity, parental education, lunch program, test prep)
Performance Metrics: Mean math score of 66.09 (SD=15.16); grade distribution heavily skewed toward lower grades (F=28.5%, A=5.2%)
Statistical Significance: All 15 ANOVA tests significant (p<0.05); zero significant chi-square associations among categorical variables
Strongest Effect: Lunch program status on math scores (\u03b7\u00b2=0.123), with standard lunch students scoring 11.11 points higher than free/reduced lunch students
Score Correlations: Reading-writing correlation exceptionally strong (r=0.955); math moderately correlated with both (r\u22480.81)

This section identifies where categorical variables show the strongest associations in the dataset. The mosaic plot visualizes the relationship between gender and race/ethnicity, with residuals indicating which demographic combinations occur more or less frequently than statistical independence would predict. Understanding these patterns helps identify whether demographic groups are distributed evenly across the population or show meaningful clustering.

Key Findings

Strongest Association: Parental education × test preparation course (Cramér's V = 0.098) - This represents the weakest association among all categorical pairs tested, indicating minimal dependency between these variables
Gender × Race/Ethnicity Residuals: Range from -1.49 to +1.54, all below the ±2 threshold for notable deviation - No cell combinations show statistically meaningful departures from expected frequencies
Pattern Observed: All 10 chi-square tests yielded non-significant results (p > 0.05), suggesting categorical variables operate largely independently of one another

Interpretation

Despite testing 10 categorical variable pairs, none demonstrate meaningful statistical associations. The residuals clustering near zero indicate that observed frequencies closely match expected values under independence. This suggests demographic characteristics (gender, race/ethnicity, parental education, lunch program status, test preparation) are distributed relatively uniformly across the sample without strong interdependencies.

Context

These weak associations contrast sharply with the strong