Does Slight Skewness Matter?

Abstract

Researchers feel they have the green light to ignore low levels of skewness because the central limit theorem indicates that such levels do not seriously compromise the validity of significance tests (e.g., Rouaud, 2013). And yet, significance testing is not the only issue, and the present focus is on two other issues where the central limit theorem does not come to the rescue. First, there is the question of how well the sample location statistic estimates the population location parameter. Surprisingly, skewness increases the precision of the estimation, and this increase in precision is impressive even with very low levels of skewness. Thus, by ignoring low levels of skewness, researchers are throwing away an important advantage. Second, experimental manipulations can cause differences in means across conditions, when there is no difference in locations across conditions; so the experiment seems to have worked based on means, when it really has not worked based on locations. Thus, moderate effect sizes can be caused by slight changes in skewness. For both reasons, it is recommended that researchers always attend to skewness, even when it is slight; and consider locations whenever they consider means.