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

摘要

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