Levene, Bartlett, Neyman-Pearson ve Bartlett 2 Testlerinin 1.Tip Hata Olasılıkları Bakımından Karşılaştırılması

Abstract

Bu çal ışmada, Levene, Bartlett, Neyman-Pearson ve Bartlett 2 testlerinin de ğ iş ik deneme koş ulları nda gerçekleşen 1.Tip hata olas ı l ı kları bak ı mı ndan karşı laştı nlmalan yap ı lm ışt ı r. Yap ı lan 50000 simülasyon denemesi sonunda ele al ı nan bütün testlerin dağı l ı m şekli ve örnek hacminden oldukça etkilendikleri görülmü ştür.

Keywords

• varyanslar ı n homojenliğ i
• varyans analizi
• 1.Tip hata olas ı l ığı varyansları n homojenlik testleri

The Comparisons of Levene, Bartlett, Neyman-Pearson and Bartlett 2 Tests in Terms of Actual Type I Error Rates

Abstract

In this study, Levene, Bartlett, Neyman-Pearson and Bartlett 2 tests were compared in terms of actual Type I error rates under various experimental conditions. At the end of 50000 simülation experiment it was seen that all of these tests were effected distribution shapes and sample size.

Keywords

• homogeneity of variance
• variance analysis
• Type I error rates
• homogeneity of variance tests

References

1. Anonymous, 1994. FORTRAN Subroutines for Mathematical Applications. IMSL MATH/LIBRARY. Voll -2. Visual Numerics, Inc., Houston, USA.
2. Bradley, J. C. 1978. Robustness. British Journal of Mathematical and Statistical Psychology, 31, 144-152.
3. Brown, M. B. and A. B. Forsythe, 1974. The small sample behaviour of some statistics which test the equality of several means. Technometrics, 16, 129-132.
4. Canover, W. J., M. E. Johnson and M. M. Johnson, 1981. A comparative study of tests for homogneity of variances, with applications to outer continental shelf bidding data. Technometrics, 23, 351-361.
5. Cochran, W. G. 1954. Some methods for strengthening the common x2 -tests.Biometrics, 10, 417-451.
6. Ghost, M. and Y. H. Kim, 2001.The Behrens-Fisher problem revisited: A Bayes-frequentist synthesis. The Canadian Journal of Statistics, 29, No:1
7. Krutchkoff, R. G 1988. One-way fixed effects analysis of variance when the error variances may be unequal. J. Statist. Comput. Simul., 30, 259-71
8. Ott, L. 1998. An Introduction to Statistical Methods and Data Analysis. Third Edition. PWS-Kent Publishing Company. USA, 835 s.

9. Piepho., H. P. 1996. A Monte Carlo test for variance homogeneity in linear models. Biometrical Journal, 38,461-473.
10. Sokal, R. R. and F. J. Rohlf, 1995. Biometry.The Prenciples and Practice of Statistics in Biological Research.Third Ed.W.H.Freeman and Co. New York, 887 s.
11. Tomarken, A. J. and R. C. Serlin, 1986. Comparison of ANOVA alternatives under variance heterogeneity and specific noncentrality structures. Psychological Bulletin, 99, 90-99
12. Winer, B. J., D. R. Brown and K. M. Michels, 1991.Statistical Princeples in Experimental Design.Third Ed., McGraw-Hill, Inc. USA, 1057 s.
13. Wludyka, P. S. and P. R. Nelson, 1997. An analysis of means type test for variances from normal populations. Technometrics, 39, 274-286.
14. Zar, J. H. 1999. Biostatistical Analysis.Fourth Ed.,Prentice-Hall, inc. USA, 683 s.
15. Zimmerman, D. W. 1998. Invalidation of parametric and nonparametric statistical tests by concurrent violation of two assumptions. J. of Experimental Education, 67, 55-69.