19 of 45 pairwise comparisons (42%) remain statistically significant after Holm-Bonferroni correction at alpha = 0.05. The analysis compared 6 parental education levels across three student outcomes (math, reading, and writing scores), testing 15 unique group pairs per outcome. 5 group pair(s) show significance consistently across all outcomes, indicating robust education-level gaps that survive rigorous family-wise error control.

Across 6 parental education groups, the highest-scoring group on the first outcome is 'master's degree' and the lowest is 'high school', a raw gap of 7.6 points before significance testing. Sample sizes are roughly balanced across groups, supporting reliable t-test inference. Groups higher in educational attainment (e.g., master's or bachelor's degree) tend to have the largest mean scores, while 'some high school' or 'high school' groups typically score lowest.

'master's degree' students score highest and 'high school' students score lowest on average across outcomes. The education-level ranking is highly consistent across all three outcomes. These raw differences motivate the pairwise testing: we need Holm-Bonferroni correction to determine which gaps are statistically reliable rather than sampling noise.

Each education group shows substantial within-group variability: the median interquartile range on the first outcome is approximately 19.6 points. This overlap in distributions means many pairwise differences are not detectable at the individual level, which is why formal significance testing — and then Holm-Bonferroni correction — is needed to avoid over-claiming. Groups with wider distributions require larger true mean differences to achieve significance.

19 of 45 pairwise comparisons survive Holm-Bonferroni correction at alpha = 0.05. The smallest adjusted p-value is 0, indicating the most robustly significant group difference. The largest raw p-value is 0.883. Comparing raw vs adjusted p-values reveals how much the correction inflates thresholds for lower-ranked tests — pairs near the boundary are most affected.

19 pairwise comparisons remain significant after Holm-Bonferroni correction. The largest gap is between 'high school vs master's degree' at 13.23 points — a practically meaningful education-level effect. Bars are ordered by absolute mean difference so the most impactful gaps appear first, distinguishing statistical significance from effect magnitude.

5 of 15 unique group pairs show an average adjusted p-value below the 0.05 threshold across all outcomes. Darker cells (lower p-values) indicate pairs where education-level differences are most consistently detectable. Pairs involving the highest and lowest education levels tend to produce the strongest signal, while adjacent levels often do not differ significantly after correction.