Implications of Inflexibility in the Size of One Sample for the Statistical Power of Tests of Mean Contrasts

Abstract

Factors beyond the control of researchers often limit the sizes of samples included in their studies. When these factors limit the total sample size, the statistical power of tests of contrasts of means may be unacceptably low. Sometimes these factors limit the size of only one sample (called the Fixed N Sample), whose mean is to be contrasted with the mean of one other sample or with the average of the means of (g-1) other samples. In such situations, the upper bound for the statistical power of the contrast test may be much below the minimum power values conventionally considered acceptable, even though the total sample size could, in theory, be indefinitely large. Such unacceptably low powers occur not only for Cohen's (1988) small effect sizes but also for medium and large effect sizes when the fixed Ns are of magnitudes no smaller than the sample sizes often reported in psychological research.