Research Article
BibTex RIS Cite

ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması

Year 2019, , 193 - 198, 30.06.2019
https://doi.org/10.19159/tutad.524099

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.

References

  • Anonymous, 1999. SAS Institute Inc., SAS OnlineDoc®, Version 8, Cary, NC.
  • Anonymous, 2016. JMP®, Version 12., SAS Institute Inc., Cary, NC
  • Anonymous, 2017. MINITAB 18, Statistical Software, State College, PA: Minitab, Inc.
  • Anonymous, 2018. R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Bakir, S.T., 1989. Analysis of means using ranks. Communications in Statistics-Simulation and Computation, 18(2): 757-776.
  • 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.
  • Bradley, J.V., 1978. Robustness?. British Journal of Mathematical and Statistical Psychology, 31(2): 144-152.
  • Dudewicz, E.J., Nelson, P.R., 2003. Heteroscedastic analysis of means (Hanom). American Journal of Mathematical and Management Sciences, 23(1-2): 143-181.
  • 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.
  • 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.
  • 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.
  • Nelson, P.R., 1983. The analysis of means for balanced experimental designs. Journal of Quality Technology, 15(1): 45-54.
  • Nelson, P.R., Dudewicz, E.J., 2002. Exact analysis of means with unequal variances. Technometrics, 44(2): 152-160.
  • 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.
  • 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.
  • 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.
  • 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.

Comparison of ANOM and ANOMTR Tests with Regard to Performances

Year 2019, , 193 - 198, 30.06.2019
https://doi.org/10.19159/tutad.524099

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.

References

  • Anonymous, 1999. SAS Institute Inc., SAS OnlineDoc®, Version 8, Cary, NC.
  • Anonymous, 2016. JMP®, Version 12., SAS Institute Inc., Cary, NC
  • Anonymous, 2017. MINITAB 18, Statistical Software, State College, PA: Minitab, Inc.
  • Anonymous, 2018. R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Bakir, S.T., 1989. Analysis of means using ranks. Communications in Statistics-Simulation and Computation, 18(2): 757-776.
  • 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.
  • Bradley, J.V., 1978. Robustness?. British Journal of Mathematical and Statistical Psychology, 31(2): 144-152.
  • Dudewicz, E.J., Nelson, P.R., 2003. Heteroscedastic analysis of means (Hanom). American Journal of Mathematical and Management Sciences, 23(1-2): 143-181.
  • 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.
  • 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.
  • 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.
  • Nelson, P.R., 1983. The analysis of means for balanced experimental designs. Journal of Quality Technology, 15(1): 45-54.
  • Nelson, P.R., Dudewicz, E.J., 2002. Exact analysis of means with unequal variances. Technometrics, 44(2): 152-160.
  • 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.
  • 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.
  • 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.
  • 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.
There are 17 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Soner Yiğit 0000-0002-2899-2246

Publication Date June 30, 2019
Published in Issue Year 2019

Cite

APA Yiğit, S. (2019). ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması. Türkiye Tarımsal Araştırmalar Dergisi, 6(2), 193-198. https://doi.org/10.19159/tutad.524099
AMA Yiğit S. ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması. TÜTAD. June 2019;6(2):193-198. doi:10.19159/tutad.524099
Chicago Yiğit, Soner. “ANOM Ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması”. Türkiye Tarımsal Araştırmalar Dergisi 6, no. 2 (June 2019): 193-98. https://doi.org/10.19159/tutad.524099.
EndNote Yiğit S (June 1, 2019) ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması. Türkiye Tarımsal Araştırmalar Dergisi 6 2 193–198.
IEEE S. Yiğit, “ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması”, TÜTAD, vol. 6, no. 2, pp. 193–198, 2019, doi: 10.19159/tutad.524099.
ISNAD Yiğit, Soner. “ANOM Ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması”. Türkiye Tarımsal Araştırmalar Dergisi 6/2 (June 2019), 193-198. https://doi.org/10.19159/tutad.524099.
JAMA Yiğit S. ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması. TÜTAD. 2019;6:193–198.
MLA Yiğit, Soner. “ANOM Ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması”. Türkiye Tarımsal Araştırmalar Dergisi, vol. 6, no. 2, 2019, pp. 193-8, doi:10.19159/tutad.524099.
Vancouver Yiğit S. ANOM ve ANOMTR Testlerinin Performansları Bakımından Karşılaştırılması. TÜTAD. 2019;6(2):193-8.

TARANILAN DİZİNLER

14658    14659     14660   14661  14662  14663  14664        

14665      14667