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

Wooff, D.A.; Jamalzadeh, A.

doi:10.1080/02664763.2013.818625

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

Wooff, D.A.; Jamalzadeh, A.

Authors

D.A. Wooff

A. Jamalzadeh

Abstract

The effect size (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 mo- tivating 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 phe- nomena 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.

Citation

Wooff, D., & Jamalzadeh, A. (2013). Robust and scale-free effect sizes for non-Normal two-sample comparisons, with applications in e-commerce. Journal of Applied Statistics, 40(11), 2495-2515. https://doi.org/10.1080/02664763.2013.818625

Journal Article Type	Article
Publication Date	Jul 1, 2013
Deposit Date	Oct 6, 2010
Publicly Available Date	Jul 4, 2013
Journal	Journal of Applied Statistics
Print ISSN	0266-4763
Electronic ISSN	1360-0532
Publisher	Taylor and Francis Group
Peer Reviewed	Peer Reviewed
Volume	40
Issue	11
Pages	2495-2515
DOI	https://doi.org/10.1080/02664763.2013.818625
Keywords	Effect size, Two-sample comparison, Non-Normal distribution, Weibull, Quantile function, E-commerce, Long-tail distribution.

Files

Accepted Journal Article (744 Kb)
PDF

Copyright Statement
This is an electronic version of an article published in Wooff, D. A. and Jamalzadeh, A. (2013) 'Robust and scale-free effect sizes for non-normal two-sample comparisons, with applications in e-commerce.', Journal of applied statistics., 40 (11). pp. 2495-2515. Journal of applied statistics is available online at: http://dx.doi.org/10.1080/02664763.2013.818625