Table 5.
Statistical tests for research question 2: two-step versus one-step word problems.
| Fixed effects | LL | #p | LR | χ2 | df | p | |
|---|---|---|---|---|---|---|---|
| Hypothesis 2a | |||||||
| M0 | - | −3465.9 | 3 | ||||
| M1 | Grade | −3309.0 | 6 | M1-M0 | 313.778 | 3 | <0.001 |
| M2 | Grade+Steps | −3307.5 | 7 | M2-M1 | 3.044 | 1 | 0.081 |
| M3 | Grade*Steps | −3305.5 | 10 | M3-M2 | 4.014 | 3 | 0.26 |
| Hypothesis 2b: reading comprehension process (MOCCA) | |||||||
| M4a | Grade+Steps | −3295.1 | 7 | ||||
| M5a | Grade+Steps+MOCCA | −3261.6 | 8 | M5a-M4a | 63.328 | 1 | <0.001 |
| M6a | Grade+Steps*MOCCA | −3255.8 | 9 | M6a-M5a | 6.480 | 1 | 0.011 |
| M7a | Grade*Steps*MOCCA | −3254.8 | 15 | M7a-M6a | 0.892 | 6 | 0.99 |
| Hypothesis 2b: reading comprehension product (CITO) | |||||||
| M4b | Grade+Steps | −2746.9 | 7 | ||||
| M5b | Grade+Steps+CITO | −2715.2 | 8 | M5b-M4b | 88.702 | 1 | <0.001 |
| M6b | Grade+Steps*CITO | −2712.0 | 9 | M6b-M5b | 0.156 | 1 | 0.69 |
| M7b | Grade*Steps*CITO | −2711.5 | 15 | M7b-M6b | 6.686 | 6 | 0.35 |
| Hypothesis 2b: non-verbal reasoning (RAVEN) | |||||||
| M4c | Grade+Steps | −3307.5 | 7 | ||||
| M5c | Grade+Steps+RAVEN | −3263.1 | 8 | M5c-M4c | 58.582 | 1 | <0.001 |
| M6c | Grade+Steps*RAVEN | −3263.0 | 9 | M6c-M5c | 1.856 | 1 | 0.17 |
| M7c | Grade*Steps*RAVEN | −3259.7 | 15 | M7c-M6c | 2.810 | 6 | 0.83 |
| Hypothesis 2b: working memory (WM) | |||||||
| M4d | Grade+Steps | −3227.5 | 7 | ||||
| M5d | Grade+Steps+WM | −3198.2 | 8 | M5d-M4d | 66.958 | 1 | <0.001 |
| M6d | Grade+Steps*WM | −3197.3 | 9 | M6d-M5d | 11.604 | 1 | 0.001 |
| M7d | Grade*Steps*WM | −3195.9 | 15 | M7d-M6d | 2.032 | 6 | 0.92 |
LL, log-likelihood; #p, number of parameters; LR, likelihood ratio test; χ2, test statistic LR-test; Steps, number of arithmetic steps (one or two).