Fig. 1
Study design used as example in this paper
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