COMPARISON OF TWO INDEPENDENT GROUPS BY USING THE LOWER AND UPPER QUANTILES AND PERCENTILE BOOTSTRAP

Yıl 2016, Cilt: 17 Sayı: 3, 506 - 511, 03.10.2016

Gözde Navruz Abdullah Fırat Özdemir

https://doi.org/10.18038/btda.20571

Öz

The frequently used way of comparing two independent groups is to compare in terms of some measure of location such as mean. For non-normal and heteroscedastic cases, trimmed mean, median or some other robust measures of location can be used instead. However, determination of the differences in the tails of the groups might be of interest. For this reason, comparing the lower and upper quantiles becomes an important issue. In this study, Harrell-Davis estimator and the default quantile estimator of R are compared in terms of actual Type I error rates. When quantiles close to zero or one are compared with small sample sizes Gumbel's estimator, and when quantiles close to median are compared with large sample sizes Harrell Davis estimator saved actual Type I error rate better.

Anahtar Kelimeler

Two independent groups, Gumbel estimator, Harrell Davis estimator, Percentile bootstrap

Kaynakça

• Wilcox RR. Comparing two independent groups via multiple quantiles The Statistician, 1995; 44(1): 99.
• Wilcox RR. Introduction to robust estimation and hypothesis testing. Amsterdam: Elsevier/ Academic Press; 2012.
• Harrell FE, Davis CE. A new distribution-free quantile estimator Biometrika, 1982; 69 : 635-640,
• Gumbel EJ. La Probabilité des Hypothèses Comptes Rendus de l’Académie des Sciences (Paris), ; 209: 645-647. Hyndman RJ, Fan Y. Sample quantiles in statistical packages The American Statistician, 1996; (4): 361-365,
• Hoaglin DC. Summarizing shape numerically: The g-and-h distribution.In: Haoglin D, Mostseller F, Tukey J editors. Exploring data tables trends and shapes, New York: Wiley, 1985; p.461-515.
• Bradley JV. Robustness British Journal of Mathematical and Statistical Psychology, 1978; 31: 144