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Tests of Location Equality under Non-Identical Distributions

Year 2017, Volume: 32 Issue: 2, 1 - 13, 04.12.2017

İrem Yılmaz A. Fırat Özdemir Gözde Navruz

https://doi.org/10.24988/deuiibf.2017322531

Abstract

The ANOVA-F test is the most known procedure for comparing at least three population means. However, this conventional test might give misleading results when it’s underlying assumptions are violated. In this study, Welch’s test with trimmed mean, Welch’s test with trimmed mean and a bootstrap-t, newly proposed Btk2 test and ANOVA-F test were compared in terms of actual Type I error rates under not only non-normality and heteroscedasticity, but also with non-identical distribution shapes. The newly proposed method outperformed ANOVA-F and other alternatives under various situations.

Keywords

ANOVA-F test Welch test Non-Identical Distribution Shapes Type I error Btk2 test

References

  • BAILEY, B. J. R. (1980), “Accurate normalizing transformations of student's t variate”, Applied Statistics, 29, 304-306.
  • BEHRENS, W. V. (1929), “Ein beitrag zur fehlerberechnung bei wenigen beobachtungen“, LandwirischaftlicheJahrburcher, 68, 807-837.
  • BRADLEY, J. V. (1978), “Robustness?”, British Journal of Mathematical and Statistical Psychology, 31, 144-152.
  • CRIBBIE, R. A., FIKSENBAUM, L., KESELMAN, H.J., WILCOX, R. R. (2012), “Effects of non-normality on test statistics for one-way independent group designs”, British Journal of Mathematical and Statistical Psychology, 65, 56-73.
  • FISHER, R. A. (1935), “The fiducial argument in statistical inference”, Annals of Eugenics, 6, 198-391.
  • HOAGLIN, D. C. (1985), Summarizing shape numerically: The g-and-h distribution, In: Haoglin D., Mostseller F., Tukey J. editors. Exploring data tables trends and shapes. Wiley New York, 461-515.
  • MICCERI, T. (1989), “The Unicorn, the normal curve, and other improbable creatures”, Psychological Bulletin 105: 156-166.
  • ÖZDEMİR, A. F., YILDIZTEPE, E. (2013), “Bir konum ölçüsü ile k bağımsız grubun karşılaştırılması için bir test”, Anadolu University Journal of Science and Technology A-Applied Science and Engineering, 14, 241-249.
  • WELCH, B. L. (1947), “The generalization of 'student's' problem when several population variances are involved”, Biometrika, 34, 28-35.
  • WELCH, B. L. (1951), “On the comparison of several mean values: An alternative approach”, Biometrika, 38, 330–336.
  • WESTFALL, P. H., YOUNG, S. S. (1993), Resampling based multiple testing, Wiley, New York.
  • WILCOX, R. R. (2012), Introduction to robust estimation and hypothesis testing (third edition), Elsevier Academics Press San Diago, California.

Aynı Olmayan Dağılımlar Altında Konum Eşitlik Testleri

Year 2017, Volume: 32 Issue: 2, 1 - 13, 04.12.2017

İrem Yılmaz A. Fırat Özdemir Gözde Navruz

https://doi.org/10.24988/deuiibf.2017322531

Abstract

ANOVA-F testi, en az üç kitle ortalamasının karşılaştırılması için en çok bilinen yöntemdir. Ancak, bu geleneksel yöntem varsayımları ihlal edildiğinde yanıltıcı sonuçlar verebilir. Bu çalışmada budanmış ortalama ile Welch testi, budanmış ortalama ve bootstrap-t ile Welch testi, yeni önerilen Btk2 testi ve ANOVA-F testi gerçekleşen 1. Tip hata oranlarına göre, sadece normalliğin ve homojen varyanslılığın sağlanmadığı durumlarda değil, aynı zamanda aynı olmayan dağılım şekilleri altında da karşılaştırılmıştır. Yeni önerilen yöntem, ANOVA-F ve diğer alternatiflere göre farklı durumlar altında daha iyi sonuçlar vermiştir.

Keywords

ANOVA-F Test Welch Test Aynı Olmayan Dağılım Şekilleri 1. Tip Hata Btk2 test

References

  • BAILEY, B. J. R. (1980), “Accurate normalizing transformations of student's t variate”, Applied Statistics, 29, 304-306.
  • BEHRENS, W. V. (1929), “Ein beitrag zur fehlerberechnung bei wenigen beobachtungen“, LandwirischaftlicheJahrburcher, 68, 807-837.
  • BRADLEY, J. V. (1978), “Robustness?”, British Journal of Mathematical and Statistical Psychology, 31, 144-152.
  • CRIBBIE, R. A., FIKSENBAUM, L., KESELMAN, H.J., WILCOX, R. R. (2012), “Effects of non-normality on test statistics for one-way independent group designs”, British Journal of Mathematical and Statistical Psychology, 65, 56-73.
  • FISHER, R. A. (1935), “The fiducial argument in statistical inference”, Annals of Eugenics, 6, 198-391.
  • HOAGLIN, D. C. (1985), Summarizing shape numerically: The g-and-h distribution, In: Haoglin D., Mostseller F., Tukey J. editors. Exploring data tables trends and shapes. Wiley New York, 461-515.
  • MICCERI, T. (1989), “The Unicorn, the normal curve, and other improbable creatures”, Psychological Bulletin 105: 156-166.
  • ÖZDEMİR, A. F., YILDIZTEPE, E. (2013), “Bir konum ölçüsü ile k bağımsız grubun karşılaştırılması için bir test”, Anadolu University Journal of Science and Technology A-Applied Science and Engineering, 14, 241-249.
  • WELCH, B. L. (1947), “The generalization of 'student's' problem when several population variances are involved”, Biometrika, 34, 28-35.
  • WELCH, B. L. (1951), “On the comparison of several mean values: An alternative approach”, Biometrika, 38, 330–336.
  • WESTFALL, P. H., YOUNG, S. S. (1993), Resampling based multiple testing, Wiley, New York.
  • WILCOX, R. R. (2012), Introduction to robust estimation and hypothesis testing (third edition), Elsevier Academics Press San Diago, California.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İrem Yılmaz This is me

A. Fırat Özdemir

Gözde Navruz

Publication Date December 4, 2017
Acceptance Date June 2, 2017
Published in Issue Year 2017 Volume: 32 Issue: 2

Cite

APA Yılmaz, İ., Özdemir, A. F., & Navruz, G. (2017). Tests of Location Equality under Non-Identical Distributions. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi, 32(2), 1-13. https://doi.org/10.24988/deuiibf.2017322531
AMA Yılmaz İ, Özdemir AF, Navruz G. Tests of Location Equality under Non-Identical Distributions. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi. December 2017;32(2):1-13. doi:10.24988/deuiibf.2017322531
Chicago Yılmaz, İrem, A. Fırat Özdemir, and Gözde Navruz. “Tests of Location Equality under Non-Identical Distributions”. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi 32, no. 2 (December 2017): 1-13. https://doi.org/10.24988/deuiibf.2017322531.
EndNote Yılmaz İ, Özdemir AF, Navruz G (December 1, 2017) Tests of Location Equality under Non-Identical Distributions. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi 32 2 1–13.
IEEE İ. Yılmaz, A. F. Özdemir, and G. Navruz, “Tests of Location Equality under Non-Identical Distributions”, Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi, vol. 32, no. 2, pp. 1–13, 2017, doi: 10.24988/deuiibf.2017322531.
ISNAD Yılmaz, İrem et al. “Tests of Location Equality under Non-Identical Distributions”. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi 32/2 (December 2017), 1-13. https://doi.org/10.24988/deuiibf.2017322531.
JAMA Yılmaz İ, Özdemir AF, Navruz G. Tests of Location Equality under Non-Identical Distributions. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi. 2017;32:1–13.
MLA Yılmaz, İrem et al. “Tests of Location Equality under Non-Identical Distributions”. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi, vol. 32, no. 2, 2017, pp. 1-13, doi:10.24988/deuiibf.2017322531.
Vancouver Yılmaz İ, Özdemir AF, Navruz G. Tests of Location Equality under Non-Identical Distributions. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi. 2017;32(2):1-13.
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