Distribution Theory for Glass's Estimator of Effect size and Related Estimators

Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. The minimum variance unbiased estimator is obtained and shown to have uniformly smaller variance than Glass's (biased) estimator. Measurement error is shown to attenuate estimates of effect size and a correction is given. The effects of measurement invalidity are discussed. Expressions for weights that yield the most precise weighted estimate of effect size are also derived.