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THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY

Year 2010, Volume: 1 Issue: 1, 57 - 71, 29.07.2011

Esra Yiğit Hamza Gamgam

Abstract

Classical F-test to compare several means depends on the assumptions of homogenety of populations variances and normality. When these assumptions-especially the equality of variance-is dropped, classical F-test fails to reject the null hypothesis even the data actually provides strong evidence to do so. This can be considered as a serious problem in some applications especially when the sample size is not large. For this problem, a large number of tests are available in the literature. In this study Brown-Forsythe, generalized F, Scott-Smith, Welch, Xu-Wang are introduced. Also a simulation study is performed to compare these tests in different combination of variance, means, population number and sample size.

Keywords

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References

  • Brown, M.B. ve Forsythe, A.B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics 16, 129-132.
  • Chen, S. ve Chen, J.H. (1998). Single-Stage analysis of variance under heteroscedasticity. Communi- cations in Statistics and Simulations 27(3), 641-666.
  • Gamage, J. ve Weerahandi, S. (1998). Size performance of some tests in one-way ANOVA Communi- cations in Statistics and Simulations 27(3), 625-640.
  • Gerami, A. ve Zahedian, A. (2001). Comparing the means of normal populations with unequal vari- ances. roceedings of the 53rd Session of Intenational Statistical Institute, Seoul, Korea.
  • Scheffe, H. (1959). The analysis of variance, Wiley, New York, 30-80.
  • Scott, A.J. ve Smith, T.M.F. (1971). Interval estimates for linear combinations of means. Applied Sta- tistics 20(3), 276-285.
  • Weerahandi, S. (1995a). ANOVA under unequal error variances. Biometrica 38, 330-336.
  • Weerahandi, S. (1995). Exact statistical method for data analysis. Springer-Verlag, NewYork, 2-50.
  • Weerahandi, S. (2004). Generalized inference in repeated measures: Exact methods in MANOVA and mixed models. Wiley, New York, 1-60.
  • Welch, B.L. (1947). The generalization of student’s problem when several different population vari- ances are involved. Biometrika 34, 28-35.
  • Welch, B.L. (1951). On the comparison of several mean values: An alternative approach. Biometrica 38, 330-336.
  • Xu, L. ve Wang, S. (2007). A new generalized p-value and its upper bound for ANOVA under un- equal erros variances. Communications in Statistics Theory and Methods 37, 1002-1010.

Year 2010, Volume: 1 Issue: 1, 57 - 71, 29.07.2011

Esra Yiğit Hamza Gamgam

Abstract

References

  • Brown, M.B. ve Forsythe, A.B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics 16, 129-132.
  • Chen, S. ve Chen, J.H. (1998). Single-Stage analysis of variance under heteroscedasticity. Communi- cations in Statistics and Simulations 27(3), 641-666.
  • Gamage, J. ve Weerahandi, S. (1998). Size performance of some tests in one-way ANOVA Communi- cations in Statistics and Simulations 27(3), 625-640.
  • Gerami, A. ve Zahedian, A. (2001). Comparing the means of normal populations with unequal vari- ances. roceedings of the 53rd Session of Intenational Statistical Institute, Seoul, Korea.
  • Scheffe, H. (1959). The analysis of variance, Wiley, New York, 30-80.
  • Scott, A.J. ve Smith, T.M.F. (1971). Interval estimates for linear combinations of means. Applied Sta- tistics 20(3), 276-285.
  • Weerahandi, S. (1995a). ANOVA under unequal error variances. Biometrica 38, 330-336.
  • Weerahandi, S. (1995). Exact statistical method for data analysis. Springer-Verlag, NewYork, 2-50.
  • Weerahandi, S. (2004). Generalized inference in repeated measures: Exact methods in MANOVA and mixed models. Wiley, New York, 1-60.
  • Welch, B.L. (1947). The generalization of student’s problem when several different population vari- ances are involved. Biometrika 34, 28-35.
  • Welch, B.L. (1951). On the comparison of several mean values: An alternative approach. Biometrica 38, 330-336.
  • Xu, L. ve Wang, S. (2007). A new generalized p-value and its upper bound for ANOVA under un- equal erros variances. Communications in Statistics Theory and Methods 37, 1002-1010.

HOMOJEN OLMAYAN VARYANS VARSAYIMI ALTINDA ORTALAMALARIN EŞİTLİĞİ İÇİN BAZI TEST İSTATİSTİKLERİ VE KARŞILAŞTIRMALARI

Year 2010, Volume: 1 Issue: 1, 57 - 71, 29.07.2011

Esra Yiğit Hamza Gamgam

Abstract

İkiden fazla yığının ortalamalarının eşitliği hipotezinin testi amacıyla kullanılan klasik F testi, normallik ve yığın varyanslarının homojenlik varsayımına dayanır. Bu varsayımlar özellikle varyansların homojenlik varsayımı, sağlanmadığında klasik F testinin kullanılması uygun olmamaktadır. Bu durum özellikle örneklem hacmi büyük olmadığında, önemli bir sıkıntı doğurmaktadır. Literatürde bu konuyla ilgili bir çok test istatistiği geliştirilmiştir. Bu çalışmada Brown-Forsythe, genelleştirilmiş F, Scott-Smith, Welch, Xu-Wang testleri tanıtılmış ve testlerin farklı yığın parametreleri ve örnek hacimleri altında deneysel I.tip hata oranı ve testin gücü bakımından karşılaştırılması yapılmıştır

Keywords

Brown-Forsythe testi Genelleştirilmiş F testi Scott-Smith testi Welch testi Xu-Wang testi

References

  • Brown, M.B. ve Forsythe, A.B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics 16, 129-132.
  • Chen, S. ve Chen, J.H. (1998). Single-Stage analysis of variance under heteroscedasticity. Communi- cations in Statistics and Simulations 27(3), 641-666.
  • Gamage, J. ve Weerahandi, S. (1998). Size performance of some tests in one-way ANOVA Communi- cations in Statistics and Simulations 27(3), 625-640.
  • Gerami, A. ve Zahedian, A. (2001). Comparing the means of normal populations with unequal vari- ances. roceedings of the 53rd Session of Intenational Statistical Institute, Seoul, Korea.
  • Scheffe, H. (1959). The analysis of variance, Wiley, New York, 30-80.
  • Scott, A.J. ve Smith, T.M.F. (1971). Interval estimates for linear combinations of means. Applied Sta- tistics 20(3), 276-285.
  • Weerahandi, S. (1995a). ANOVA under unequal error variances. Biometrica 38, 330-336.
  • Weerahandi, S. (1995). Exact statistical method for data analysis. Springer-Verlag, NewYork, 2-50.
  • Weerahandi, S. (2004). Generalized inference in repeated measures: Exact methods in MANOVA and mixed models. Wiley, New York, 1-60.
  • Welch, B.L. (1947). The generalization of student’s problem when several different population vari- ances are involved. Biometrika 34, 28-35.
  • Welch, B.L. (1951). On the comparison of several mean values: An alternative approach. Biometrica 38, 330-336.
  • Xu, L. ve Wang, S. (2007). A new generalized p-value and its upper bound for ANOVA under un- equal erros variances. Communications in Statistics Theory and Methods 37, 1002-1010.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Esra Yiğit This is me

Hamza Gamgam

Publication Date July 29, 2011
Published in Issue Year 2010 Volume: 1 Issue: 1

Cite

APA Yiğit, E., & Gamgam, H. (2011). THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 1(1), 57-71.
AMA Yiğit E, Gamgam H. THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY. AUBTD-B. July 2011;1(1):57-71.
Chicago Yiğit, Esra, and Hamza Gamgam. “THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1, no. 1 (July 2011): 57-71.
EndNote Yiğit E, Gamgam H (July 1, 2011) THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1 1 57–71.
IEEE E. Yiğit and H. Gamgam, “THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY”, AUBTD-B, vol. 1, no. 1, pp. 57–71, 2011.
ISNAD Yiğit, Esra - Gamgam, Hamza. “THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1/1 (July 2011), 57-71.
JAMA Yiğit E, Gamgam H. THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY. AUBTD-B. 2011;1:57–71.
MLA Yiğit, Esra and Hamza Gamgam. “THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 1, no. 1, 2011, pp. 57-71.
Vancouver Yiğit E, Gamgam H. THE TESTS PROPOSED FOR THE ONE-WAY ANOVA UNDER UNEQUAL VARIANCES AND SIMULATION STUDY. AUBTD-B. 2011;1(1):57-71.
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