Table 1.
Standard errors (SE) for each of b 0 (44.076), b 1 (11.089), b 2 (− 4.036), and b 3 (2.867), as well as random intercept variance at the learning group level (k), random intercept variance and random slope variance and their covariance at the student level (j), and the lowest-level residual (e) and associated SEs (between parentheses)
| Model | OLS regression (single level) |
Split-plot ANOVA (two levels) |
Three-level mixed-effects |
|---|---|---|---|
| SE(b 0) | 1.481a | 1.481a | 5.344 |
| SE(b 1) | 2.095a | 2.095a | 7.557 |
| SE(b 2) | 2.095b | 0.267 | 0.267 |
| SE(b 3) | 2.962b | 0.378 | 0.378 |
| s 2(v 0 k) | – | – | 422.301 (110.551) |
| s 2(u 0jk) (SE) | – | 485.599 (32.498)c | 90.020 (6.212) |
| s 2(u 2jk) (SE) | – | – | 16.048 (1.070) |
| cov(u 0jk, u 2jk) (SE) | – | – | 0.980 (1.854) |
| e (SE) | 493.624 (23.167) | 8.025 (0.533)d | 0.000 (0.000) |
aunderestimation of SE due to overestimation of degrees of freedom
boverestimation of SE, since within-subject variance is not separated from between-subject variance
c u 0j for this model, since k is ignored here
dthis is the difference between 493.624 and 485.599; it is the variance assumed for both treatment conditions