ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması

Abstract

Bu çalışmada, tek yönlü Ortalamaların Analizi (ANOM) ve Transforme Edilmiş Ranklara Dayalı Ortalamaların Analizi (ANOMTR) testleri varyansları homojen normal olmayan dağılımlarda 1. tip hata olasılığı ve testin gücü bakımından karşılaştırılmıştır. Yapılan 100000 simülasyon denemesi sonucunda, dikkate alınan deneme koşulları ne olursa olsun ANOMTR testi bakımından gerçekleşen 1. tip hata olasılıkları % 4.50-5.50 içinde kalmıştır. Ancak ANOM testi bakımından gerçekleşen 1. tip hata olasılıklarının genel olarak bu sınırlar içerisinde kalmadığı görülmüştür. ANOM testinin dağılımın eğriliğinden ziyade, dikliğinden oldukça olumsuz etkilendiği tespit edilmiştir.  Varyanslar homojen olduğu sürece, dağılımın şekli ve tekerrür sayısı ne olursa olsun ANOMTR testi oldukça güvenilir sonuçlar vermiştir.

Keywords

• ANOM,ANOMTR,1. tip hata,testin gücü,simülasyon

Comparison of ANOM and ANOMTR Tests with Regard to Performances

Abstract

In this study, one-way ANOM (Analysis of Means) and ANOMTR (Analysis of Means Based on Transformed Ranks) tests were compared in non-normal distributions with homogeneous variances in terms of the Type I error rate and test power. As a result of 100.000 simulation experiments conducted, regardless of the experimental conditions considered, actual Type I error rates occurred in ANOMTR was within the limits of 4.50-5.50%. However, it was observed that actual Type I error rates occurred in ANOM test was generally not within these limits. The ANOM test was found to be affected quite negatively by the kurtosis rather than the skewness of the distribution. As long as the variances were homogeneous, the ANOMTR test has given very reliable results regardless of the shape of the distribution and the number of replications.

Keywords

• ANOM,ANOMTR,type I error rate,test power,simulation

References

1. Anonymous, 1999. SAS Institute Inc., SAS OnlineDoc®, Version 8, Cary, NC.
2. Anonymous, 2016. JMP®, Version 12., SAS Institute Inc., Cary, NC
3. Anonymous, 2017. MINITAB 18, Statistical Software, State College, PA: Minitab, Inc.
4. Anonymous, 2018. R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
5. Bakir, S.T., 1989. Analysis of means using ranks. Communications in Statistics-Simulation and Computation, 18(2): 757-776.
6. Bernard, A.J., Wludyka, P.S., 2001. Robust I-sample analysis of means type randomization tests for variances. Journal of Statistical Computation and Simulation, 69(1): 57-88.
7. Bradley, J.V., 1978. Robustness?. British Journal of Mathematical and Statistical Psychology, 31(2): 144-152.
8. Dudewicz, E.J., Nelson, P.R., 2003. Heteroscedastic analysis of means (Hanom). American Journal of Mathematical and Management Sciences, 23(1-2): 143-181.

9. Hoaglin, D.C. 1985. Summarizing shape numerically: The g-and-h distributions. In D. Hoaglin, F. Mosteller and J. Tukey (Eds.), Exploring data tables, trends, and shapes. New York: Wiley.
10. Mendeş, M., Yiğit, S., 2013. Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power. Journal of Statistical Computation and Simulation, 83(11): 2093-2104.
11. Mendeş, M., Yiğit, S., 2018. An alternative approach for multiple comparison problems when there are a large number of groups: ANOM technique. Journal of Animal & Plant Sciences, 28(4): 1075-1079.
12. Nelson, P.R., 1983. The analysis of means for balanced experimental designs. Journal of Quality Technology, 15(1): 45-54.
13. Nelson, P.R., Dudewicz, E.J., 2002. Exact analysis of means with unequal variances. Technometrics, 44(2): 152-160.
14. Nelson, P.R., Wludyka, P.S., Copeland, K.A.F., 2005. The Analysis of Means: A Graphical Method for Comparing Means, Rates and Proportions. SIAM, Philadelphia.
15. Rao, C.V., Deva Raaj, V.J., 2006. ANOM for testing the equality of several intercepts in a k-sample regression model. Statistical Methods, 8(1): 60- 72.
16. Rao, C.V., Kumar, M.P., 2002. ANOM-type graphical methods for testing the equality of several correlation coefficients. Gujarat Statistical Review, 29: 47-56.
17. Yiğit, S., Mendeş, M., 2017. ANOM technique for evaluating practical significance of observed difference among treatment groups. International Journal of Agricultural Science Research, 6(1): 1-7.