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

References

• Algina , J. , Keselman , H. J. and Penfield , R. D. 2005 . An alternative to Cohen's standardized mean difference effect size: A robust parameter and confidence interval in the two independent groups case . Psychol. Methods , 10 : 317 – 328 . (doi:10.1037/1082-989X.10.3.317)
   PubMed Web of Science ®Google Scholar
• Anderson , C. L. and Berry , J. C. 2009 . On a simple measure of dominance . J. Statist. Plann. Inference , 139 : 1098 – 1108 . (doi:10.1016/j.jspi.2008.07.001)
   Web of Science ®Google Scholar
• J. Andersen, R.S. Larsen, A. Giversen, T.B. Pedersen, A.H. Jensen, and J. Skyt, Analyzing clickstreams using subsessions, Tech. Rep. tr-00-5001, Department of Computer Science, Aalborg University, 2000.
   Google Scholar
• Barlow , R. E. and Proschan , F. 1975 . Statistical Theory of Reliability and Life Testing: Probability Models , New York : Holt, Reinhart and Winston .
   Google Scholar
• Cahan , S. and Gamliel , E. 2011 . First among others? Cohen's d vs. alternative standardized mean group difference measures . Pract. Assess. Res. Eval. , 16 ( 10 ) : 1 – 6 .
   Google Scholar
• Cleveland , W. S. 1994 . The Elements of Graphing Data , Murray Hill, NJ : AT&T Bell Laboratories .
   Google Scholar
• Cliff , N. 1993 . Dominance statistics: Ordinal analyses to answer ordinal questions . Psychol. Bull. , 114 : 494 – 509 . (doi:10.1037/0033-2909.114.3.494)
   Web of Science ®Google Scholar
• R. Coe, It's the Effect Size, Stupid. What Effect Size is and Why it is Important, Proceedings of the Annual Conference of the British Educational Research Association, University of Exeter, England, September, 2002.
   Google Scholar
• Cohen , J. 1977 . Statistical Power Analysis for the Behavioral Sciences , New York : Academic Press .
   Google Scholar
• Cohen , J. 1992 . A power primer . Psychol. Bull. , 112 : 112 – 159 .
   Web of Science ®Google Scholar
• Darlington , R. B. 1973 . Comparing two groups by simple graphs . Psychol. Bull. , 79 ( 2 ) : 110 – 116 . (doi:10.1037/h0033854)
   Web of Science ®Google Scholar
• Davison , A. C. and Hinkley , D. 2006 . Bootstrap Methods and their Application , 8 , Cambridge : Cambridge University Press .
   Google Scholar
• Descôteaux , J. 2007 . Statistical power: An historical introduction . Tutor. Quant. Methods Psychol. , 3 ( 2 ) : 28 – 34 .
   Google Scholar
• Doksum , K. A. 1977 . Some graphical methods in statistics: A review and some extensions . Statist. Neerlandica , 31 : 53 – 68 . (doi:10.1111/j.1467-9574.1977.tb00752.x)
   Google Scholar
• Doksum , K. A. and Samarov , A. 1995 . Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression . Ann. Statist. , 23 : 1443 – 1473 . (doi:10.1214/aos/1176324307)
   Web of Science ®Google Scholar
• Doksum , K. A. and Sievers , G. L. 1976 . Plotting with confidence – Graphical comparisons of 2 populations . Biometrika , 63 : 421 – 434 . (doi:10.1093/biomet/63.3.421)
   Web of Science ®Google Scholar
• Fleming , T. R. , O'Fallon , J. R. , O’ Brien , P. C. and Harrington , D. P. 1980 . Modified Kolmogorov–Smirnov test procedures with applications to arbitrarily right-censored data . Biometrics , 36 : 607 – 625 . (doi:10.2307/2556114)
   Web of Science ®Google Scholar
• Gigerenzer , G. 1993 . “ The superego, the ego, and the id in statistical reasoning ” . In A Handbook for Data Analysis in the Behavioral Sciences: Methodological Issues , Edited by: Keren , G. and Lewis , C. 311 – 339 . Hillsdale, NJ : LEA .
   Google Scholar
• Gilchrist , W. G. 2000 . Statistical Modelling with Quantile Functions , Boca Raton : Chapman and Hall .
   Google Scholar
• Glass , G. V. , McGaw , B. and Smith , M. L. 1981 . Meta-analysis in Social Research , Beverly Hills, CA : Sage .
   Google Scholar
• Grissom , R. J. 1994 . Probability of the superior outcome of one treatment over another . J. Appl. Psychol. , 79 ( 2 ) : 314 – 316 . (doi:10.1037/0021-9010.79.2.314)
   Web of Science ®Google Scholar
• Grissom , R. J. and Kim , J. J. 2005 . Effect Size for Research , London : Psychology Press, Taylor and Francis Group .
   Google Scholar
• Hedges , L. V. and Friedman , L. 1993 . Gender differences in variability in intellectual abilities: A reanalysis of Feingold's results . Rev. Educ. Res. , 63 ( 1 ) : 94 – 105 . (doi:10.3102/00346543063001094)
   Web of Science ®Google Scholar
• M.R. Hess and J.D. Kromrey, Robust Confidence Intervals for Effect Sizes: A Comparative Study of Cohens d and Cliffs Delta Under Non-normality and Heterogeneous Variances, Proceedings of Annual Meeting of the American Educational Research Association, San Diego, April 12–16, 2004.
   Google Scholar
• Hesterberg , T. , Monaghan , S. , Moore , D. S. , Clipson , A. and Epstein , R. 2003 . The Practice of Business Statistics , London : W.H. Freeman and Company .
   Google Scholar
• Hinkley , D. V. 1969 . On the ratio of two correlated normal random variables . Biometrika , 56 ( 3 ) : 635 – 639 . (doi:10.1093/biomet/56.3.635)
   Web of Science ®Google Scholar
• Hedges , L. V. and Olkin , I. 1985 . Statistical Methods for Meta-analysis , San Diego : Academic Press .
   Google Scholar
• Holmgren , E. C. 1995 . The p-p plot as a method of comparing treatment effects . J. Am. Statist. Assoc. , 90 ( 429 ) : 360 – 365 . (doi:10.1080/01621459.1995.10476520)
   Web of Science ®Google Scholar
• A. Jamalzadeh, Statistical analysis of web usage data, Ph.D. thesis, Mathematical Science Department, Durham University, 2010.
   Google Scholar
• Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1994 . Continuous Univariate Distributions , 2 , Vol. 1 , New York : John Wiley and Sons .
   Google Scholar
• Keselman , H. J. , Huberty , C. J. , Lix , L. M. , Olejnik , S. , Cribbie , R. A. , Donahue , B. , Kowalchuk , R. K. , Lowman , L. L. , Petoskey , M. D. , Keselman , J. C. and Levin , J. R. 1998 . Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA, and ANCOVA analyses . Rev. Educ. Res. , 68 ( 3 ) : 350 – 386 . (doi:10.3102/00346543068003350)
   Web of Science ®Google Scholar
• Krueger , J. 2001 . Null hypothesis significance testing on the survival of a flawed method . Am. Psychol. , 56 ( 1 ) : 16 – 26 . (doi:10.1037/0003-066X.56.1.16)
   PubMed Web of Science ®Google Scholar
• Kulinskaya , E. and Staudte , R. G. 2006 . Interval estimates of weighted effect sizes in the one-way heteroscedastic ANOVA . Br. J. Math. Statist. Psychol. , 59 : 97 – 111 . (doi:10.1348/000711005X68174)
   PubMed Web of Science ®Google Scholar
• Kullback , S. 1968 . Information Theory and Statistics , Mineola, New York : Publications .
   Google Scholar
• Ledesma , R. D. , Macbeth , G. and Cortada de Kohan , N. 2009 . Computing effect size measures with vista . Tutor. Quant. Methods Psychol. , 5 ( 1 ) : 25 – 34 .
   Google Scholar
• Lenth , R. V. 2001 . Some practical guidelines for effective sample-size determination . Am. Stat. , 55 ( 3 ) : 187 – 193 . (doi:10.1198/000313001317098149)
   Web of Science ®Google Scholar
• Li , G. , Tiwari , R. C. and Wells , M. T. 1996 . Quantile comparison functions in two-sample problems, with application to comparisons of diagnostic markers . J. Am. Statist. Assoc. , 91 ( 434 ) : 689 – 698 . (doi:10.1080/01621459.1996.10476937)
   Web of Science ®Google Scholar
• Mann , H. B. and Whitney , D. R. 1947 . On a test of whether one of two random variables is stochastically larger than the other . Ann. Statist. , 18 : 50 – 60 . (doi:10.1214/aoms/1177730491)
   Web of Science ®Google Scholar
• Markov , Z. and Larose , D. T. 2007 . Data Mining the Web: Uncovering Pattern in Web Content, Structure, and Usage , Hoboken, NJ : Jonh Wiley & Sons .
   Google Scholar
• Thompson , B. 1998 . Statistical significance and effect size reporting: Portrait of a possible future . Res. Schools , 5 ( 2 ) : 33 – 38 .
   Google Scholar
• Tukey , J. W. 1960 . A survey of sampling from contaminated distributions. in Contributions to Probability and Statistics , Edited by: Olkin , I. , Ghurye , S. , Hoeffding , W. , Madow , W. and Mann , H. 448 – 485 . Stanford, CA : Stanford University Press .
   Google Scholar
• Weibull , W. 1951 . A statistical distribution function of wide applicability . ASME J. Appl. Mech., Trans. Am. Soc. Mech. Eng. , 18 ( 3 ) : 293 – 297 .
   Web of Science ®Google Scholar
• Wilcox , R. R. 2005 . Introduction to Robust Estimation and Hypothesis Testing , New York : Academic Press .
   Google Scholar
• Wilcox , R. R. and Tian , T. S. 2011 . Measuring effect size: A robust heteroscedastic approach for two or more groups . J. Appl. Stat. , 38 ( 7 ) : 1359 – 1368 . (doi:10.1080/02664763.2010.498507)
   Web of Science ®Google Scholar
• Wilk , M. B. and Gnanadesikan , R. 1968 . Probability plotting methods for the analysis of data . Biometrika , 55 : 1 – 17 .
   PubMed Web of Science ®Google Scholar
• Wilson Van Voorhis , C. R. and Morgan , B. L. 2007 . Understanding power and rules of thumb for determining sample sizes . Tutor. Quant. Methods Psychol. , 3 ( 2 ) : 43 – 50 .
   Google Scholar