Treatment SMCV and 95% CI c+-probability SES and 95%CI and 95% CI p-value for αi Age 11 -0.42 (-1.05, 0.21) 0.34 -0.38 (-0.94, 0.19) -15 (-37.6, 7.6) 0.188 Age 12 -0.28 (-0.90, 0.34) 0.39 -0.25 (-0.81, 0.31) -10 (-32.6, 12.6) 0.378 Age 13 0 (-0.62, 0.62) 0.5 0.00 (-0.56, 0.56) 0 (-22.6, 22.6) 1 Age 14 0.28 (-0.34, 0.90) 0.61 0.25 (-0.31, 0.81) 10 (-12.6, 32.6) 0.378 Age 15 0.42 (-0.21, 1.05) 0.66 0.38 (-0.19, 0.94) 15 ( -7.6, 37.6) 0.188

Table 2: The estimates and 95% confidence intervals (CI) of standardized mean of contrast variable (SMCV), standardized effect size (SES) and effect (i.e., ai ) at each age level in the Rosenthal, Rosnow and Rubin’s example about psychomotor skills.