Table 3.
Main Effects Multi-Levels Model Results (n=391)
| Model/Parameter | Estimate | SE | p-value | B-H critical | Hedges g ES |
|---|---|---|---|---|---|
| Arithmetic | |||||
| Fixed Effects | |||||
| Intercept | 8.675 | 1.049 | <.0001 | ||
| Adjusted Mean Difference | |||||
| NK v. control | 7.419 | 1.528 | <.0001 | .0125 | 0.59 |
| WP v. control | 7.985 | 1.475 | <.0001 | .0083 | 0.65 |
| WP[L] v. control | 9.154 | 1.272 | <.0001 | .0042 | 0.79 |
| WP v. NK | 0.566 | 1.882 | .764 | .0167 | 0.03 |
| WP[L] v. NK | 1.735 | 1.496 | .246 | .0208 | 0.14 |
| WP v. WP[L] | 1.169 | 1.345 | .385 | .0250 | 0.10 |
| Pretest effect | 1.332 | 0.110 | .001 | ||
| Variance Components | |||||
| Student-level residual | 99.374 | 6.385 | |||
| Classroom-level intercept | 3.367 | 7.133 | |||
| School-level intercept | 6.426 | 6.071 | |||
| Word Problems | |||||
| Fixed Effects | |||||
| Intercept | 2.383 | 0.360 | <.0001 | ||
| Adjusted Mean Difference | |||||
| NK v. control | 0.260 | 0.401 | .517 | .0250 | 0.09 |
| WP v. control | 4.045 | 0.526 | <.0001 | .0125 | 1.08 |
| WP[L] v. control | 6.416 | 0.550 | <.0001 | .0042 | 1.75 |
| WP v. NK | 3.785 | 0.576 | <.0001 | .0167 | 0.94 |
| WP[L] v. NK | 6.156 | 0.563 | <.0001 | .0083 | 1.55 |
| WP v. WP[L] | 2.371 | 0.684 | .0001 | .0208 | 0.47 |
| Pretest effect | 0.632 | 0.171 | <.0001 | ||
| Variance Components | |||||
| Student-level residual | 14.746 | 1.280 | |||
| Classroom-level intercept | 0.715 | 1.395 | |||
| Word-Problem Language | |||||
| Fixed Effects | |||||
| Intercept | 13.511 | 0.355 | <.0001 | ||
| Mean Difference | |||||
| NK v. control | −0.386 | 0.413 | .349 | .0250 | 0.17 |
| WP v. control | 0.573 | 0.504 | .255 | .0208 | 0.16 |
| WP[L] v. control | 2.164 | 0.559 | <.0001 | .0125 | 0.56 |
| WP v. NK | 0.960 | 0.386 | .013 | .0167 | 0.24 |
| WP[L] v. NK | 2.550 | 0.331 | <.0001 | .0042 | 0.63 |
| WP v. WP[L] | 1.590 | 0.444 | <.0001 | .0083 | 0.41 |
| Variance Components | |||||
| Student-level residual | 13.064 | 1.084 | |||
| Classroom-level intercept | 1.180 | 1.034 | |||
| School-level intercept | 0.283 | 0.315 |
Note. p-values for z-tests of variance components are conservative and thus often not reported (divide est/SE and compare to +1–1.96 to discern significance according to z-test). An adjustment Fitzmaurice et al. (2011, p. 209) suggest is to employ α = .10 rather than α = .05; it performs similarly to other correction methods (Ke & Want, 2015). B-H is the Benjamini-Hochberg procedure critical value. ES is effect size.