Table 8.

Sensitivity analysis of effect size measurement, outliers, clustered assignment of treatment and risk of bias items using multiple meta‐regressions

	ES measurement		Outliers		Clustered		Risk of bias
Moderator	Coef.	95% CI	Coef.	95% CI	Coef.	95% CI	Coef.	95% CI
CAI	0.09	[−0.07, 0.25]	0.07	[−0.06, 0.20]	0.07	[−0.08, 0.22]	0.07	[−0.11, 0.25]
Coaching	−0.02	[−0.14, 0.10]	−0.02	[−0.14, 0.09]	−0.03	[−0.15, 0.08]	−0.02	[−0.15, 0.10]
Incentives	0.09	[−0.06, 0.25]	0.08	[−0.06, 0.22]	0.09	[−0.06, 0.23]	0.08	[−0.09, 0.26]
Medium‐group	0.18	[−0.11, 0.47]	0.15	[−0.07, 0.38]	0.17	[−0.09, 0.43]	0.21	[−0.20, 0.62]
Peer‐assisted	0.40	[0.12, 0.69]	0.36	[0.14, 0.59]	0.39	[0.13, 0.64]	0.39	[0.04, 0.73]
Progress mon.	−0.09	[−0.20, 0.03]	−0.08	[−0.19, 0.02]	−0.08	[−0.19, 0.02]	−0.09	−[0.22, 0.03]
Small‐group	0.34	[0.11, 0.57]	0.31	[0.14, 0.48]	0.32	[0.11, 0.53]	0.33	[0.06, 0.59]
Comprehension	0.03	[−0.12, 0.17]	0.04	[−0.09, 0.17]	0.04	[−0.09, 0.18]	0.01	[−0.15, 0.16]
Decoding	0.00	[−0.12, 0.13]	0.01	[−0.10, 0.13]	0.00	[−0.12, 0.12]	0.05	[−0.09, 0.20]
Fluency	−0.05	[−0.19, 0.08]	−0.06	[−0.19, 0.06]	−0.06	[−0.19, 0.06]	−0.06	[−0.21, 0.10]
Spelling/writing	0.11	[−0.01, 0.22]	0.11	[0.00, 0.22]	0.12	[0.01, 0.24]	0.09	[−0.03, 0.22]
Vocabulary	−0.07	[−0.19, 0.05]	−0.07	[−0.18, 0.04]	−0.06	[−0.17, 0.05]	−0.08	[−0.20, 0.05]
Algebra	−0.16	[−0.31, −0.01]	−0.16	[−0.31, −0.01]	−0.15	[−0.30, −0.01]	−0.17	[−0.35, 0.02]
Fractions	0.37	[0.06, 0.67]	0.36	[0.05, 0.67]	0.37	[0.09, 0.65]	0.33	[0.05, 0.62]
Geometry	0.03	[−0.17, 0.22]	0.02	[−0.15, 0.18]	0.03	[−0.15, 0.22]	0.04	[−0.20, 0.28]
Number sense	−0.01	[−0.19, 0.18]	−0.02	[−0.19, 0.16]	−0.01	[−0.18, 0.16]	−0.09	[−0.27, 0.10]
Operations	−0.11	[−0.28, 0.06]	−0.10	[−0.26, 0.06]	−0.10	[−0.26, 0.06]	−0.09	[−0.27, 0.09]
Prob. solving	0.07	[−0.04, 0.19]	0.08	[−0.04, 0.19]	0.07	[−0.04, 0.19]	0.10	[−0.04, 0.24]
Gen. academic	−0.08	[−0.32, 0.16]	−0.09	[−0.28, 0.11]	−0.06	[−0.28, 0.16]	−0.12	[−0.36, 0.12]
Meta‐cognitive	−0.02	[−0.17, 0.13]	0.01	[−0.11, 0.13]	0.00	[−0.14, 0.14]	0.01	[−0.13, 0.16]
Social‐emotional	−0.08	[−0.41, 0.25]	−0.10	[−0.36, 0.16]	−0.09	[−0.40, 0.23]	−0.09	[−0.43, 0.24]
QES	−0.04	[−0.22, 0.15]	−0.02	[−0.19, 0.15]	−0.05	[−0.24, 0.15]
General test	0.06	[−0.11, 0.24]	0.06	[−0.09, 0.20]	0.07	[−0.10, 0.24]	0.08	[−0.12, 0.27]
Mean Grade	−0.03	[−0.06, ‐0.00]	−0.03	[−0.06, −0.01]	−0.03	[−0.06, −0.01]	−0.03	[−0.05, 0.00]
Math	0.07	[−0.12, 0.26]	0.08	[−0.08, 0.24]	0.07	[−0.12, 0.26]	0.11	[−0.10, 0.33]
Raw mean	0.03	[−0.06, 0.13]
Glass's δ	0.24	[−0.01, 0.48]
Unclear ES type	−0.16	[−1.11, 0.80]
Super‐pop.	0.01	[−0.20, 0.22]
Blinding							0.01	[−0.08, 0.10]
Incomplete out.							−0.04	[−0.17, 0.09]
Reporting							−0.05	[−0.16, 0.07]
Other bias							0.02	[−0.09, 0.13]
Constant	−0.02	[−0.24, 0.21]	0.01	[−0.16, 0.18]	0.01	[−0.19, 0.20]	0.00	[−0.26, 0.26]
Effect sizes	1030		1030		1030		981
Study clusters	189		189		189		172
N	206,186		206,186		206,186		152,581
Q	412.1		382.3		488.0		385.3
I 2	61.4		57.4		66.6		62.9
$\tau$ 2	0.056		0.043		0.048		0.058

Abbreviations: CAI, computer‐assisted instruction; CI, confidence interval; ES, effect sizes; QES, quasi‐experimental studies.