Fixed and Random Effects for Group Comparisons on Articulation Measures (HLM Full Models)

	Articulation-word rate					Articulation-number rate
Fixed Effects	Coefficient	SE	T-ratio	p	Fixed Effects	Coefficient	SE	T-ratio	p
Model 5a					Model 6a
Intercept	5.69	0.23	24.67	0.00	Intercept	7.50	0.25	30.49	0.00
Strategy vs. Control	0.21	0.29	0.72	0.47	Strategy vs. Control	0.63	0.33	1.91	0.06
No-strategy vs. Control	0.13	0.29	0.46	0.65	No-strategy vs. Control	0.03	0.33	0.08	0.94
Pre-Articulation-word rate	0.50	0.11	4.51	0.00	Pre-Articulation-number rate	0.56	0.10	5.62	0.00
Model 5b					Model 6b
Intercept	5.82	0.23	24.82	0.00	Intercept	7.52	0.25	30.17	0.00
Strategy vs. No-strategy	0.07	0.29	0.25	0.80	Strategy vs. No-strategy	0.60	0.33	1.82	0.08
Control vs. No-strategy	−0.13	0.29	−0.46	0.65	Control vs. No-strategy	−0.03	0.33	−0.08	0.94
Pre-Articulation-word rate	0.50	0.11	4.51	0.00	Pre-Articulation-number rate	0.56	0.10	5.62	0.00
Random Effects	School level variance	Student level residual variance	χ2	BIC	Random Effects	School level variance	Student level residual variance	χ2	BIC
	0.14	0.79	22.18*	167.74		0.09	1.02	15.57	179.91

Note. Coefficient = Unstandardized coefficient in HLM models, the mean difference between study groups adjusted for level-1 covariates; SE = Standard Errors of the coefficient, BIC = Bayesian Information Criterion. Because of Dummy coding, the Random Effects are the same for Model 5a and 5b, and Model 6a and 6b. Models 5a~6b represent the comparison of “Strategy vs. Control” and “No-strategy-instruction vs. Control”.

All coefficients in HLM models became non-significant after application of the Benjamini–Hochberg correction of p values for multiple comparisons (i.e., p < .01).

^*p < .05,

⁺p < .08.