Remedial Programming and Skill-Targeted SEL in Low-Income and Crisis-Affected Contexts: Experimental Evidence From Niger

Figures & data

Table 1. Control and treatment schools characteristics.

	Condition
	HCT (n = 15)	HCT + Act (n = 15)
Number of Tutoring Classrooms	45	45
Number of Tutoring Students	900	900
Number of Tutoring Teachers	45	45
Total Number of Teachers in Participating Schools	307	289
Number of French Arabic Schools	5	5
Schools in Diffa	9	9
% Female	53%	55%
% Local (vs. Refugee and Internally Displaced Students)	65%	66%
% Kanuri	33%	35%
% Hausa	20%	20%
% Fulfulde	40%	39%
Age Mean	9.31	9.30
Age SD	1.41	1.42
% Remedial ASER Literacy = 0	67%	66
% Remedial ASER Math = 0	54%	55%
% Total ASER Literacy = 2	90%	90%
% Total ASER Math = 2	82%	83%

Table 2. Baseline and endline descriptive statistics by treatment condition, and adjusted differences at baseline between groups.

			HCT schools				HCT + SEL schools				Baseline mean difference Col(1)−Col(2)		Baseline mean difference Col(3)−Col(4)		Baseline mean difference Col(3)−Col(1)
	Full sample (N = 4994)		HCT (n = 900)		Control (n = 1,961)		HCT + SEL (n = 900)		Control (n = 1,233)
			(1)		(2)		(3)		(4)
	M	SD	M	SD	M	SD	M	SD	M	SD	Mean Diff.	SE	Mean Diff.	SE	Mean Diff.	SE
Female	0.525	–	0.526	–	0.518	–	0.536	–	0.529	–	0.004	(0.016)	0.009	(0.020)	0.007	(0.018)
Grade level	2.819	0.798	2.986	0.818	2.716	0.780	2.968	0.812	2.751	0.765	0.252***	(0.052)	0.233**	(0.057)	−0.020	(0.010)
Age	9.062	1.411	9.276	1.423	9.055	1.400	9.094	1.440	8.895	1.376	0.221**	(0.063)	0.231*	(0.085)	−0.164	(0.084)
Refugee status	0.225	–	0.238	–	0.274	–	0.144	–	0.198	–	−0.016	(0.019)	−0.049***	(0.010)	−0.086**	(0.026)
Mother tongue
Kanuri	0.320	–	0.312	–	0.335	–	0.292	–	0.320	–	0.003	(0.020)	0.002	(0.020)	−0.017	(0.040)
Hausa	0.244	−	0.220	−	0.237	−	0.259	−	0.262	−	−0.016	(0.018)	0.002	(0.016)	0.032	(0.036)
Fulfulde	0.360	–	0.396	–	0.354	–	0.362	–	0.341	–	0.015	(0.025)	−0.014	(0.017)	−0.028	(0.054)
Other	0.077	–	0.072	–	0.074	–	0.087	–	0.077	–	−0.003	(0.009)	0.009	(0.007)	0.013	(0.009)
Baseline ASER scores
ASER French	0.348	0.559	0.362	0.544	0.300	0.523	0.406	0.598	0.372	0.589	0.043	(0.020)	0.027	(0.018)	0.041	(0.033)
ASER Math	0.596	0.747	0.622	0.756	0.565	0.733	0.611	0.758	0.614	0.753	0.022	(0.038)	−0.015	(0.027)	0.013	(0.042)
Endline ASER scores (unimputed)
ASER French (n = 4,366)	1.019	0.932	1.148	0.913	0.910	0.891	1.167	0.987	0.984	0.944
ASER Math (n = 4,366)	1.674	1.289	1.820	1.288	1.529	1.247	1.902	1.338	1.621	1.287
School Grades (n = 4,081)	5.300	1.904	5.121	1.945	5.222	1.914	5.512	1.823	5.383	1.902

*p < .05; **p < .01; ***p < .001.

Figure 1. Research design and sample flowchart. All participants initially randomized were retained in the analysis, including those who had missing data at the endline. All missing information were accounted for using the multiply-imputed dataset.

Table 3. HCT and HCT + Act program impacts on ASER French, Math, and average school marks.

	Control^a	Unadjusted effects (${\alpha }_2)$			Covariate-adjusted effects (${\alpha }_2)$
Outcomes	M(SE)	b	dwt		b	dwt
Effects of HCT (vs. Control in the same schools)
French literacy	0.942 (0.042)	0.222** (.050)	0.224		0.190** (.048)	0.261
Math	1.539 (0.040)	0.301** (0.139)	0.246		0.265** (0.066)	0.217
Grades	5.186 (0.054)	−0.103 (0.099)	−0.056		0.083 (0.095)	0.046
Effects of HCT + Act (vs. Control in the same schools)
French literacy	1.039 (0.047)	0.237** (0.060)	0.264		0.210** (0.061)	0.233
Math	1.642 (0.044)	0.347*** (0.056)	0.283		0.301** (0.060)	0.245
Grades	5.32 (0.060)	0.121 (0.101)	0.067		0.286** (0.079)	0.157
Baseline scores^b		X		X	X	X
School fixed-effects		X		X	X	X
Child covariates					X	X

*q < .05; **q < .01; ***q < .001.

Note. Models presented in Table 3 were estimated using the Equation (1)(1) $$Y_{ij}={\delta }_j+{{\alpha }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\alpha }_2{\left(T\right)}_{ij}+\sum {\alpha }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(1) described in the Analysis section. Unadjusted model excludes student covariates from the Equation (1)(1) $$Y_{ij}={\delta }_j+{{\alpha }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\alpha }_2{\left(T\right)}_{ij}+\sum {\alpha }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(1) . The p values were adjusted for Type I error common in multiple hypothesis testing, by controlling the sharpened false discovery rate (FDR: Benjamini et al., 2006). The FDR-adjusted q values are reported here. Impact estimates (b) are comparable to the original scale of each outcome. b represents unstandardized coefficient estimate of the impact indicators. Effect sizes (d_wt) are standardized accounting for nested data structure, adjusting for school and child level variance (Hedges, 2009).

^aControl group M and SE are pooled estimates across 10 imputed datasets.

^bWe do not have baseline data for school grades, which are therefore not adjusted for the baseline.

Table 4. SEL activities impacts on ASER French, Math, and average school marks.

	HCT school^a	Unadjusted effects(${\alpha }_2)$		Covariate-adjusted effects(${\alpha }_2)$
Outcomes	M (SD)	b	dwt	b	dwt
Effects of SEL Activities (HCT + Act vs. HCT schools)
French literacy	1.171 (0.042)	0.015 (0.119)	0.02	0.034 (0.121)	0.036
Math	1.826 (0.046)	0.124 (0.145)	0.097	0.135 (0.147)	0.106
Grades	5.093 (0.078)	0.416* (0.176)	0.252	0.383* (0.174)	0.208
Baseline scores^b		X	X	X	X
School fixed-effects		X	X	X	X
Child covariates			X	X

*q < .05; **q < .01; ***q < .001.

Note. Models presented in Table 4 were estimated using the Equation (2)(2) $$Y_{ij}={\delta }_j+{{\beta }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\beta }_2{\left(\mathit{SEL}\right)}_{ij}+\sum {\beta }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(2) described in the Analysis section. Unadjusted model excludes student covariates from the Equation (2)(2) $$Y_{ij}={\delta }_j+{{\beta }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\beta }_2{\left(\mathit{SEL}\right)}_{ij}+\sum {\beta }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(2) . The p values were adjusted for Type I error common in multiple hypothesis testing, by controlling the sharpened false discovery rate (FDR: Benjamini et al., 2006). The FDR-adjusted q values are reported here. Impact estimates (b) are comparable to the original scale of each outcome. b represents unstandardized coefficient estimate of the impact indicators. Effect sizes (d_wt) are standardized accounting for nested data structure, adjusting for school and child level variance (Hedges, 2009).

^aHCT group M and SE are pooled estimates across 10 imputed datasets.

^bWe do not have baseline for the school grades and therefore were not adjusted for the baseline.

Table 5. Local average treatment effects of HCT and HCT + Act.

	Control^a	Unadjusted effects (${\gamma }_2)$		Covariate-adjusted effects (${\gamma }_2)$
Outcomes	M(SE)	b	dwt	b	dwt
Effects of HCT (vs. Business-as-usual control in the same schools)
French literacy	0.942 (0.042)	0.388*** (0.096)	0.451	0.331*** (0.080)	0.388
Math	1.539 (0.040)	0.566*** (0.086)	0.425	0.459*** (0.103)	0.376
Grades	5.186 (0.054)	−0.177 (0.168)	−0.098	0.145∼ (0.160)	0.080
Effects of HCT + Act (vs. Business-as-usual control in the same schools)
French literacy	1.039 (0.047)	0.384*** (0.081)	0.431	0.346*** (0.096)	0.384
Math	1.642 (0.044)	0.520*** (0.103)	0.462	0.495*** (0.095)	0.404
Grades	5.32 (0.060)	0.198 (0.160)	0.161	0.471*** (0.127)	0.384
Baseline scores		X	X	X	X
School-pair fixed-effects		X	X	X	X
Child covariates				X	X

∼q < .10; *q < .05; **q < .01; ***q < .001.

Note. Models presented in Table 5 were estimated using the Equation (3)(3) $$Y_{ij}={\delta }_j+{{\gamma }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\gamma }_2{\left(\mathit{Att}\right)}_{ij}+\sum {\gamma }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(3) described in the Analysis section. Unadjusted model excludes student covariates from the Equation (3)(3) $$Y_{ij}={\delta }_j+{{\gamma }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\gamma }_2{\left(\mathit{Att}\right)}_{ij}+\sum {\gamma }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(3) . The p values for the impact estimates were adjusted for Type I error common in multiple hypothesis testing, by controlling the sharpened false discovery rate (FDR: Benjamini et al., 2006). Impact estimates (b) are comparable to the original scale of each outcome. The FDR-adjusted q values are reported here. b represents unstandardized coefficient estimate of the impact indicators. Effect sizes (d_wt) are standardized accounting for nested data structure, adjusting for school and child level variance (Hedges, 2009).

^aControl group M and SE are pooled estimates across 10 imputed datasets.

^bWe do not have baseline data for school grades, which are therefore were not adjusted for the baseline.

Appendix A. HCT impact variation

	ASER French						ASER Math						School grades
	Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted
Impact variation by gender
HCT Program	0.183	**	0.045	0.161	**	0.048	0.235	*	0.088	0.196	*	0.088	−0.123		0.129	0.083		0.125
Female	−0.071		0.043	−0.043		0.041	−0.055		0.059	−0.049		0.059	0.092		0.116	0.118		0.113
HCT × Female	0.075		0.070	0.056		0.071	0.127		0.101	0.131		0.104	0.038		0.158	0.001		0.130
Baseline ASER French	0.567	***	0.076	0.380	***	0.073				0.336	***	0.070				0.648	***	0.104
Baseline ASER Math				0.183	***	0.037	0.590	***	0.066	0.424	***	0.052				0.510	***	0.073
Impact variation by grade level
HCT Program	0.200	**	0.062	0.205	**	0.063	0.322	**	0.091	0.329	**	0.097	0.119		0.126	0.178		0.131
Grade level	0.178	***	0.030	0.101	*	0.043	0.172	**	0.042	0.014		0.049	−0.690	***	0.109	−0.947	***	0.128
HCT × Grade level	−0.020		0.057	−0.016		0.059	−0.065		0.085	−0.071		0.089	−0.049		0.117	−0.106		0.103
Baseline ASER French	0.515	***	0.074	0.380	***	0.073				0.338	***	0.070				0.651	***	0.102
Baseline ASER Math				0.183	***	0.036	0.564	***	0.067	0.426	***	0.052				0.511	***	0.072
Impact variation by Refugee Status
HCT Program	0.255	**	0.058	0.223	**	0.056	0.329	**	0.080	0.291	**	0.077	−0.103		0.127	0.080		0.115
Refugee Status	0.033		0.079	0.049		0.078	0.078		0.097	0.067		0.090	0.315	**	0.100	0.051		0.097
HCT × Refugee	−0.135		0.096	−0.133		0.094	−0.111		0.127	−0.106		0.123	0.021		0.217	0.012		0.178
Baseline ASER French	0.568	***	0.075	0.380	***	0.073				0.336	***	0.070				0.648	***	0.103
Baseline ASER Math				0.183	***	0.036	0.592	***	0.066	0.426	***	0.052				0.510	***	0.073
Impact variation by baseline ASER scores
HCT	0.190	*	0.073	0.162	*	0.069	0.311	*	0.107	0.291	*	0.102	−0.091		0.135	0.068		0.127
Baseline ASER French	0.377	***	0.081	0.354	***	0.078	0.368	***	0.075	0.354	***	0.069	0.514	***	0.090	0.693	***	0.107
Baseline ASER Math	0.209	***	0.044	0.183	**	0.043	0.458	***	0.067	0.429	***	0.063	0.408	***	0.076	0.477	***	0.080
HCT × ASER French	0.111		0.089	0.077		0.083	−0.018		0.109	−0.056		0.111	−0.224		0.187	−0.125		0.157
HCT × ASER Math	−0.007		0.066	0.004		0.065	−0.029		0.087	−0.013		0.083	0.059		0.123	0.095		0.123

Note. Models presented in Appendix A were estimated using the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) described in the Analysis section, estimating the impact of HCT as treatment (T) compared to control in HCT schools. Unadjusted model excludes student covariates from the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) .

Appendix B. HCT + Act impact variation

	ASER French						ASER Math						School grades
	Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted
Impact variation by gender		b	SE
HCT + Act Program	0.238	**	0.074	0.214	*	0.079	0.310	**	0.079	0.256	*	0.086	0.169		0.132	0.344	*	0.119
Female	−0.028		0.059	−0.010		0.058	−0.184	*	0.064	−0.186	*	0.068	0.126		0.127	0.210	∼	0.097
HCT + Act × Female	−0.001		0.066	−0.008		0.071	0.071		0.099	0.084		0.101	−0.091		0.170	−0.109		0.145
Baseline ASER French	0.587	***	0.060	0.416	***	0.064				0.361	***	0.081				0.649	***	0.116
Baseline ASER Math				0.183	**	0.049	0.554	***	0.069	0.355	***	0.080				0.479	***	0.090
Impact variation by grade level
HCT + Act Program	0.135	∼	0.063	0.156	*	0.057	0.244	*	0.081	0.249	*	0.081	0.121		0.090	0.149		0.094
Grade level	0.146	∼	0.075	0.097		0.075	0.161	*	0.062	0.055		0.071	−0.648	***	0.064	−0.936	***	0.103
HCT + Act × Grade level	0.071		0.068	0.063		0.063	0.067		0.097	0.060		0.098	0.156		0.093	0.159		0.089
Baseline ASER French	0.542	***	0.073	0.417	***	0.063				0.361	**	0.083				0.652	***	0.116
Baseline ASER Math				0.183	**	0.049	0.522	***	0.073	0.355	***	0.080				0.477	***	0.090
Impact variation by Refugee Status
HCT + Act Program	0.218	**	0.054	0.180	**	0.054	0.324	***	0.064	0.264	**	0.066	0.131		0.101	0.283	**	0.078
Refugee Status	0.033		0.059	0.046		0.051	0.068		0.100	0.073		0.076	0.255	∼	0.128	0.095		0.128
HCT + Act × Refugee	0.143		0.131	0.184		0.124	0.179		0.137	0.219	∼	0.120	0.018		0.180	0.022		0.195
Baseline ASER French	0.588	***	0.060	0.416	***	0.064				0.359	***	0.082				0.650	***	0.116
Baseline ASER Math				0.185	**	0.049	0.562	***	0.069	0.357	***	0.080				0.478	***	0.090
Impact variation by baseline ASER scores
HCT + Act Program	0.228	**	0.060	0.201	**	0.057	0.360	***	0.069	0.335	**	0.071	0.132		0.084	0.279	**	0.081
Baseline ASER French	0.438	***	0.076	0.408	***	0.082	0.402	***	0.085	0.373	**	0.087	0.540	**	0.151	0.666	***	0.125
Baseline ASER Math	0.205	**	0.050	0.182	**	0.055	0.405	***	0.074	0.372	***	0.075	0.405	**	0.110	0.463	***	0.104
HCT + Act × ASER French	0.022		0.078	0.019		0.075	−0.019		0.104	−0.028		0.114	−0.032		0.117	−0.038		0.123
HCT + Act × ASER Math	0.012		0.063	0.002		0.063	−0.031		0.079	−0.038		0.076	−0.010		0.162	0.037		0.139

Note. Models presented in Appendix B were estimated using the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) described in the Analysis section, estimating the impact of HCT + Act as treatment (T) compared to control in HCT + Act schools. Unadjusted model excludes student covariates from the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) .

Appendix C. SEL activities impact variation

	ASER French						ASER Math						School grades
	Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted			Unadjusted			Covariate adjusted
Impact variation by gender
SEL Program	0.030		0.123	0.044		0.125	0.208		0.163	0.215		0.165	0.462	*	0.209	0.400	∼	0.213
Female	0.019		0.053	0.020		0.059	0.072		0.084	0.074		0.085	0.131		0.128	0.126		0.123
SEL × Female	−0.028		0.071	−0.019		0.080	−0.159		0.097	−0.151		0.096	−0.089		0.182	−0.033		0.166
Baseline ASER French	0.600	***	0.054	0.413	***	0.054				0.311	***	0.080				0.598	***	0.102
Baseline ASER Math				0.189	***	0.044	0.536	***	0.054	0.375	***	0.062				0.569	***	0.087
Impact variation by grade level
SEL Program	0.135	∼	0.063	0.156	*	0.057	0.244	*	0.081	0.249	*	0.081	0.121		0.090	0.149		0.094
Grade level	0.146	∼	0.075	0.097		0.075	0.161	*	0.062	0.055		0.071	−0.648	***	0.064	−0.936	***	0.103
SEL × Grade level	0.071		0.068	0.063		0.063	0.067		0.097	0.060		0.098	0.156		0.093	0.159		0.089
Baseline ASER French	0.542	***	0.073	0.417	***	0.063				0.361	**	0.083				0.652	***	0.116
Baseline ASER Math				0.183	**	0.049	0.522	***	0.073	0.355	***	0.080				0.477	***	0.090
Impact variation by Refugee Status
SEL Program	−0.020		0.123	−0.004		0.121	0.085		0.157	0.094		0.158	0.436	*	0.194	0.371	*	0.177
Refugee Status	−0.061		0.090	−0.012		0.087	−0.028		0.122	0.008		0.129	0.256		0.223	0.077		0.196
SEL × Refugee	0.203		0.164	0.206		0.156	0.249		0.187	0.227		0.185	0.014		0.267	0.061		0.252
Baseline ASER French	0.600	***	0.054	0.412	***	0.053				0.311	***	0.079				0.598	***	0.103
Baseline ASER Math				0.190	***	0.043	0.539	***	0.054	0.377	***	0.063				0.569	***	0.087
Impact variation by baseline ASER scores
SEL Program	0.228	**	0.060	0.201	**	0.057	0.360	***	0.069	0.335	**	0.071	0.132		0.084	0.279	**	0.081
Baseline ASER French	0.438	***	0.076	0.408	***	0.082	0.402	***	0.085	0.373	**	0.087	0.540	**	0.151	0.666	***	0.125
Baseline ASER Math	0.205	**	0.050	0.182	**	0.055	0.405	***	0.074	0.372	***	0.075	0.405	**	0.110	0.463	***	0.104
SEL × ASER French	0.022		0.078	0.019		0.075	−0.019		0.104	−0.028		0.114	−0.032		0.117	−0.038		0.123
SEL × ASER Math	0.012		0.063	0.002		0.063	−0.031		0.079	−0.038		0.076	−0.010		0.162	0.037		0.139

Note. Models presented in Appendix C were estimated using the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) described in the Analysis section, estimating the impact of HCT + Act as treatment (T) compared to HCT. Unadjusted model excludes student covariates from the Equation (4)(4) $$o_{ij}={\delta }_j+{{\omega }_1{Y}_{(t-1)ij}}_{\mathrm{ }}+{\omega }_2{\left(T\right)}_{ij}+{\omega }_3{\left(\mathit{Female}\right)}_{ij}+{\omega }_4{\left(T\mathrm{\hspace{0.17em}*\hspace{0.17em}}\mathit{Female}\right)}_{ij}+\sum {\omega }_m{\left(\mathit{Student}\mathrm{ }\mathit{Covariates}\right)}_{\mathit{mij}}+{\epsilon }_{ij}$$(4) .

Benjamini, Y., Krieger, A. M., & Yekutieli, D. (2006). Adaptive linear step-up procedures that control the false discovery rate. Biometrika, 93(3), 491–507. https://doi.org/10.1093/biomet/93.3.491

 Web of Science ®Google Scholar

Hedges, L. V. (2009). Effect sizes in nested designs. In The Handbook of Research Synthesis and Meta-Analysis, 2, 399–416.

 Google Scholar