Table 12 ANOVA of student learning data with Benjamini–Hochberg p-value correction and minimum effect size (Cohen’s D) that can be detected with the sample
Independent variable | Sum of squares | Degrees of freedom | F | Number of groups | Residual degrees of freedom | p | Min Cohen’s D | Significant difference (effect size and Dunn’s post hoc test for interaction effects) |
|---|---|---|---|---|---|---|---|---|
Time | 3357 | 1 | 137.9 | 2 | 2636 | 0.0000 | 0.109 | Post-test > Pre-test \(\Delta =+2.256pts\), \(p<0.0001\), Cohen’s \(D=0.457\) |
Grade | 4007 | 1 | 166.3 | 2 | 2636 | 0.0000 | 0.109 | Grade 4>3 \(\Delta =2.468pts\), Cohen’s \(D=0.502\) |
Gender | 199 | 1 | 7.8 | 2 | 2636 | 0.0052 | 0.109 | Boys > Girls \(\Delta =0.551pts\), \(p=0.0015\), Cohen’s \(D=0.109\) |
Time:grade | 7396 | 3 | 108.0 | 4 | 2634 | 0.0000 | 0.129 | See Fig. 3 |
Time:gender | 3565 | 3 | 48.9 | 4 | 2634 | 0.0000 | 0.129 | Pre-test Boys > Girls \(\Delta =0.664pts\), \(p=0.0079\), Cohen’s \(D=0.131\) Post-test Boys \(\sim\) Girls \(\Delta =0.438pts\), \(p=0.0744\), Cohen’s \(D=0.091\) |
Grade:gender | 4248 | 3 | 58.9 | 4 | 2634 | 0.0000 | 0.129 | Grade 3 Boys > Girls \(\Delta =0.725pts\), \(p=0.004\), Cohen’s \(D=0.145\) Grade 4 Boys \(\sim\) Girls \(\Delta =0.469pts\), \(p=0.0604\), Cohen’s \(D=0.098\) |
Time:grade:gender | 7660 | 7 | 48.1 | 8 | 2630 | 0.0000 | 0.148 | See Fig. 3 |