Researchers’ choice of the number and range of levels in experiments affects the resultant variance-accounted-for effect size

In psychology, the reporting of variance-accounted-for effect size indices has been recommended and widely accepted through the movement away from null hypothesis significance testing. However, most researchers have paid insufficient attention to the fact that effect sizes depend on the choice of the number of levels and their ranges in experiments. Moreover, the functional form of how and how much this choice affects the resultant effect size has not thus far been studied. We show that the relationship between the population effect size and number and range of levels is given as an explicit function under reasonable assumptions. Counterintuitively, it is found that researchers may affect the resultant effect size to be either double or half simply by suitably choosing the number of levels and their ranges. Through a simulation study, we confirm that this relation also applies to sample effect size indices in much the same way. Therefore, the variance-accounted-for effect size would be substantially affected by the basic research design such as the number of levels. Simple cross-study comparisons and a meta-analysis of variance-accounted-for effect sizes would generally be irrational unless differences in research designs are explicitly considered.