. Author manuscript; available in PMC: 2023 Mar 1.

Published in final edited form as: Dev Psychol. 2022 Jan 10;58(3):470–484. doi: 10.1037/dev0001301

Table 4.

Intent-to-Treat (ITT) and Treatment-on-Treated (TOT) Effect Estimates for Grade Level and Special Education Status at the End of Sixth Grade (RCT Analytic Sample)

	ITT						TOT

	Treatment Group Mean^a	Control Group Mean^a	Pooled SD^b	Coefficient for T-C Difference^c	Effect Size^d	p-value^e	Coefficient for T-C Difference^c	Effect Size^d
Observed Values
On grade	.872	.881	.329	−.008	−.025	.531	−.016	−.047
IEP	.117	.084	.304	.033^*	−.107	.010	.062^*	−.203

Weighted Observed Values
On grade	.851	.860	.354	−.009	−.026	.528	−.017	−.049
IEP	.126	.081	.310	.045^*	−.144	.001	.085^*	−.272
	N = 1678–1679	N = 1021		N = 2699–2700

p < .05

Note. On grade is a binary variable: 1=at or above expected grade level, 0 = below expected grade level. IEP = Individualized Educational Program as the formal special education designation coded 1 as yes and 0 as no.

Covariate-adjusted means generated by the multilevel analysis models.

Pooled treatment and control group standard deviations. There are minor variations between the pooled SDs for the ITT and TOT; the mean is presented here but effect sizes are computed on the exact values.

Coefficients for the treatment-control differences from multilevel multiple models with children nested in R-Lists and R-Lists nested in districts and the standard set of covariates (see text). The multipliers for ITT coefficients that estimate TOT coefficients are 1.8907 for expected grade level and 1.8904 for IEP.

Effect size: coefficient for the treatment-control difference divided by the pooled standard deviation.

The p-values for statistical significance are the same for the ITT and TOT coefficients.