Traditionally, data collected in a research study is submitted to a significance test to assess the viability of the null hypothesis. A power analysis, executed when the study is being planned, is used to anticipate the likelihood that the study will yield a significant effect and is based on the same factors as the significance test itself. These three factors, together with power, form a closed system - once any three are established, the fourth is completely determined. The goal of a power analysis is to find an appropriate balance among these factors by taking into account the substantive goals of the study, and the resources available to the researcher. The effect size should represent the smallest effect that would be of clinical or substantive significance, and for this reason it will vary from one study to the next.
Power analysis gives power for a specific effect size.
While one might be tempted to set the clinically significant effect at a small value to ensure high power for even a small effect, this determination cannot be made in isolation. The selection of an effect size reflects the need for balance between the size of the effect that we can detect, and the resources available for the study. Figure 1 Small effects will require a larger investment of resources than large effects. We may decide that it would make sense to enroll 93 per group to detect the intermediate effect but inappropriate to enroll 356 patients per group to detect the smallest effect. While the effect size in the power analysis is assumed to reflect the population effect size for the purpose of calculations, the power analysis is more appropriately expressed as If the true effect is this large power would be rather than The true effect is this large, and therefore power is This distinction is an important one.