Quant #18: Effect Size

To determine sample size in quantitative research, power analysis is often conducted. Two of the factors that influence sample size are the effect size and the significance criterion. Effect size refers to the strength of a relationship between the independent variable and the dependent variable. It is a quantitative measure of the magnitude of a given phenomenon. Thus, the effect size not only helps in detecting an effect but also reflects the magnitude of the effect.

While conducting quantitative research, one way to determine an effect size is to look at the literature of the current research (when possible) and then determine the typical effect size (typically the mean). However, this approach is not always feasible. The alternative approach is to follow the conventional definitions of the small, medium, and large effect size as proposed by Cohen (1988). Cohen’s d provides a measure of effect size; it is the standardized mean difference between two group means. Cohen’s d= .2, .5, and .8 denotes a small, medium, and large effect size, respectively.

In the case of multiple regression, f2 is used as the effect size index, which is equal to .02 for a small effect, .15 for a medium effect, and .35 for a large effect. The recommendation is to base the power analysis on small effect sizes. This recommendation is justified by the notion that a study that has sufficient power to detect small effects will also detect medium and large effects. In contrast, a study that has the power to detect large effects runs the risk of missing small effects. Thus, a study that assumes a small effect size runs little risk of making type I or type II errors.