Yıl: 2020 Cilt: 36 Sayı: 1 Sayfa Aralığı: 58 - 65 Metin Dili: İngilizce DOI: 10.15312/EurasianJVetSci.2020.260 İndeks Tarihi: 26-11-2020

Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity

Öz:
Aim: As in all parametric methods, the ANCOVA method assumes that normaldistributions of errors, homogeneity of variances, and error terms are independentof each other. However, unusual distributions in practice are morecommon than normal distribution. In this study, it is aimed to examine ANCOVAmethod or type 1 error rates under different distribution conditions andhomogeneity of variances.Materials and Methods: For this purpose, a simulation studies under differentscenarios was conducted. Random numbers were generated from Gamma,Beta and Normal distributions considering different groups and differentsample sizes. In the simulation studies, 10000 replications were run under thenull hypothesis of no group differences and type-I error rates were calculatedfor each scenario.Results: According to the results, in the case of the normal distribution withhomogeneous variance, the proportion of Type I error is high in the groupswith the sample size of n=20 and n=40. In the case of normal distribution withthe heterogeneous variance, the deviation has been observed in the groupswith the sample size of n = 10 and n = 30, and n = 40. These results are thesame as the results of Gamma distribution. In the Beta distribution, , there is adeviation in the groups with n=10 and n=20 where the sample sizes are small.Conclusion: The results showed that type-I error rate is affected by skewnessof the distribution, sample size and homogeneity of variance. Further workcan be extended by simulation studies under different distributions and parametervalues.
Anahtar Kelime:

Farklı dağılım ve varyansların homojenliği koşulları altında ANCOVA'nın sağlamlığı

Öz:
Amaç: Tüm parametrik yöntemlerde olduğu gibi, ANCOVA yönteminde de hataların normal dağıldığı, varyansların homojenliği ve hata terimlerinin bağımsız olduğu varsayılmaktadır. Ancak, pratikte, değişkenlere ilişkin dağılımların sıklıkla normal dağılıma uymadığı bilinmektedir. Bu çalışmada, varyansların homojenliği ve farklı dağılım koşulları altında ANCOVA yönteminin tip I hata oranlarının incelenmesi amaçlanmıştır. Gereç ve Yöntem: Bu amaçla farklı senaryolarda simülasyon çalışmaları yapılmıştır. üç bağımsız grup için birbirine eşit olacak şekilde farklı örneklem büyüklüklerinde Gamma, Beta ve Normal dağılımlardan veri türetimi yapılmıştır. . Simülasyon çalışmalarında, gruplar arasındaki farkın anlamlı olmadığı hipotezi altında, 10000 tekrar ile her bir senaryo için tip I hata oranları hesaplanmıştır. Bulgular: Simülasyon çalışması sonuçlarına göre, homojen varyanslı normal dağılım durumunda, örneklem büyüklüğü n = 20 ve n = 40 olan gruplarda Tip I hatanın yüksek olduğu bulunmuştur. Heterojen varyans ile normal dağılım durumunda, n = 10 ve n = 30 ve n = 40 örneklem büyüklüğündeki gruplarda sapma gözlenmiştir. Bu sonuçlar Gamma dağılımının sonuçları ile aynıdır. Beta dağılımında iki farklı senaryo incelenmiştir. Bunlar dağılım grafiklerinin "U" ve "ters U" biçimlerinde gözlendiği durumlardır ve n = 10 ve n = 20 gibi küçük örneklem büyüklüğünde sapmalar gözlemlenmiştir. Öneri: Sonuçlar, tip I hata oranının, dağılımın çarpıklığı, örneklem büyüklüğü ve varyansın homojenliği gibi faktörlerden etkilendiğini göstermiştir. Farklı dağılımlar ve parametre değerleri için gerçekleştirilecek simülasyon çalışmaları ile sonuçlar genişletilebilir.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Acıtas, S , Senoglu, B . Robust factorial ANCOVA with LTS error distributions. Hacettepe Journal of Mathematics and Statistics, (2018);47 (2), 347-363. Patterson, R.F. &
  • Box, GEP, Muller, ME. A note on the generation of random normal deviates. Annals of Mathematical Statistics, (1958);28, 610-611.
  • Colliver, JA., Markwell SJ. ANCOVA, Selection Bias, Statistical Equating, and Effect Size:Recommendations for Publication. Teaching and Learning in Medicine, (2006);18(4), 284–286.
  • D’Alonzo, KT. The Johnson-Neyman Procedure as an Alternative to ANCOVA. West J Nurs Res. (2004);26(7): 804–812.
  • Elashoff, JA. Analysis of covariance: A delicate instrument. American Educational Research Journal, (1969);6(3), 383- 401.
  • Johnson, CC, Rakow, EA. (1994). Effects of violations of data set assumptions when using the analysis of variance and covariance with unequal group sizes. Paper presented at the annual meeting of the Mid-South Educational Research.
  • Levy, K. J. A monte carlo study of analysis of covariance under violations the assumptions of normality and equal regression slopes. Educational and Psycho- logical Measurement, (1980); 40, 835-840.
  • Olejnik, S. F., & Algina, J. Parametric ANCOVA and the rank transform ANCOVA when the data are conditionally nonnormal and heteroscedastic. Journal of Educational Statistics, (1984);9(2), 129-149.
  • Potthoff, A. F. Some Scheffe-type tests for some Behrens-Fisher type regression problems. Journal of the American Statistical Association, (1965); 60, 1163-1190.
  • Rheinheimer, DC., Penfield, AD. The Effects of Type I Error Rate and Power of the ANCOVA F Test and SelectedAlternatives under Nonnormality and Variance Heterogeneity. The Journal of Experimental Education, (2001); 69(4), 373-391.
  • Shieh, G. Power and Sample Size Calculations for Contrast Analysis in ANCOVA. Multivariate Behavioral Research, (2017); 52(1), 1-11.
  • Shields, JL. (1978). An empirical investigation of the effect of heteroscedasticity and heterogeneity of variance on the analysis of covariance and the Johnson-Neyman technique (Tech. Rep. No. 292). Alexandria, VA: U.S. Army Research Institute for the Behavioral and Social Sciences.
  • Wilcox, R. Robust ANCOVA: Confidence intervals that have some specified simultaneous probability coverage when there is curvature and two covariates. Journal of Modern Applied Statistical Methods, (2017); 16(1), 3-19.
APA ateş c, Tekindal M, KAYMAZ O, ERDOĞAN b (2020). Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. , 58 - 65. 10.15312/EurasianJVetSci.2020.260
Chicago ateş can,Tekindal Mustafa Agah,KAYMAZ OZLEM,ERDOĞAN beyza Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. (2020): 58 - 65. 10.15312/EurasianJVetSci.2020.260
MLA ateş can,Tekindal Mustafa Agah,KAYMAZ OZLEM,ERDOĞAN beyza Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. , 2020, ss.58 - 65. 10.15312/EurasianJVetSci.2020.260
AMA ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. . 2020; 58 - 65. 10.15312/EurasianJVetSci.2020.260
Vancouver ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. . 2020; 58 - 65. 10.15312/EurasianJVetSci.2020.260
IEEE ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b "Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity." , ss.58 - 65, 2020. 10.15312/EurasianJVetSci.2020.260
ISNAD ateş, can vd. "Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity". (2020), 58-65. https://doi.org/10.15312/EurasianJVetSci.2020.260
APA ateş c, Tekindal M, KAYMAZ O, ERDOĞAN b (2020). Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. Eurasian Journal of Veterinary Sciences, 36(1), 58 - 65. 10.15312/EurasianJVetSci.2020.260
Chicago ateş can,Tekindal Mustafa Agah,KAYMAZ OZLEM,ERDOĞAN beyza Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. Eurasian Journal of Veterinary Sciences 36, no.1 (2020): 58 - 65. 10.15312/EurasianJVetSci.2020.260
MLA ateş can,Tekindal Mustafa Agah,KAYMAZ OZLEM,ERDOĞAN beyza Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. Eurasian Journal of Veterinary Sciences, vol.36, no.1, 2020, ss.58 - 65. 10.15312/EurasianJVetSci.2020.260
AMA ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. Eurasian Journal of Veterinary Sciences. 2020; 36(1): 58 - 65. 10.15312/EurasianJVetSci.2020.260
Vancouver ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity. Eurasian Journal of Veterinary Sciences. 2020; 36(1): 58 - 65. 10.15312/EurasianJVetSci.2020.260
IEEE ateş c,Tekindal M,KAYMAZ O,ERDOĞAN b "Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity." Eurasian Journal of Veterinary Sciences, 36, ss.58 - 65, 2020. 10.15312/EurasianJVetSci.2020.260
ISNAD ateş, can vd. "Robustness of analysis of covariance (ANCOVA) under the distributions assumptions and variance homogeneity". Eurasian Journal of Veterinary Sciences 36/1 (2020), 58-65. https://doi.org/10.15312/EurasianJVetSci.2020.260