Robust and scale-free effect sizes for non-Normal two-sample comparisons, with applications in e-commerce

The <italic>effect size</italic> (ES) has been mainly introduced and investigated for changes in location under an assumption of Normality for the underlying population. However, there are many circumstances where populations are non-Normal, or depend on scale and shape and not just a location parameter. Our motivating application from e-commerce requires an ES which is appropriate for long-tailed distributions. We review some common ES measures. We then introduce two novel alternative ES for two-sample comparisons, one scale-free and one on the original scale of measurement, and analyse some theoretical properties. We examine these ES for two-sample comparison studies under an assumption of Normality and investigate what happens when both location and scale parameters differ. We explore ES for phenomena for non-Normal situations, using the Weibull family for illustration. Finally, for an application, we assess differences in customer behaviour when browsing E-commerce websites.