Table 2.

Relationship between sample size required for 80% statistical power, effect size of treatment, and correlation between covariate and outcome measure.

	Effect Size
ρ	d = 0.1	d = 0.2	d = 0.3	d = 0.4	d = 0.5
0.0	3142	788	352	200	128
0.1	3111	780	348	198	127
0.3	2859	717	320	182	116
0.5	2357	591	264	150	96
0.7	1602	402	180	102	65

Note. ρ = correlation between covariate and dependent variable; All estimates are based on error rates of α = 0.05 and 1 − β = 0.80; Values in each cell represent the total number of participants to detect the specified effect size in a two-group randomized experiment with equal sample sizes in each group. In cases where the covariate is expected to be strongly related to the dependent variance (ρ = 0.5), including the covariate reduces the required sample size by roughly 25% (compare values in rows 1 and 4 of the table).