Comparison of Variance Homogenity Tests for Different Distributions
Yıl: 2017 Cilt: 9 Sayı: 3 Sayfa Aralığı: 197 - 212 Metin Dili: İngilizce DOI: 10.5336/biostatic.2017-56316 İndeks Tarihi: 16-03-2019
Comparison of Variance Homogenity Tests for Different Distributions
Öz: Objective:The reliability of the hypothesis tests to be performed using variance analysis depends on the holding of the assumptions. In the analysis of variance, the sensitivity of the results obtained for the test statistic is most influenced by the heterogeneity of the variances. In this study, it is aimed to compare the variance homogeneity tests widely used in different literature for different distributions in terms of type-I error level and power.Material and Methods:1000 repetitive simulations were performed for the Levene median, Levene mean, Levene trimmed mean, bootstrap Levene median, Bartlett and Cochran tests. Four cases where the sample sizes are equal were taken as n1=n2=n3=15; n1=n2=n3=30; n1=n2=n3=45; n1=n2=n3=100 and the two cases where the sample sizes are not equal were taken as n1=15, n2=30, n3=45; n1=15, n2=30, n3=100. For different distributions, the data were generated by taking into account the skewness and kurtosis coefficients. For power, the variance ratios of 1:1:2, 1:2:4, 1:2:2 and 1:4:4 were taken and different variances were corresponded to different sample sizes.Results:In terms of type-I error rates, the bootstrap Levene median test gave the best result for all distributions. For power; if the sample sizes were equal, for medium and large sample sizes bootstrap Levene median and Levene median tests gave the best results. For large sample sizes Bartlett test gave similar results to these two tests. Conclusion:It was seen that, while the performances of the tests were affected from the distribution, the best result against the deviations from normality was obtained for the bootstrap Levene median test and the performance of the tests was affected from the variance-sample size combination.
Anahtar Kelime: Konular:
Farklı Dağılımlar İçin Varyans Homojenlik Testlerinin Karşılaştırılması
Öz: Amaç:Varyans analizi kullanılarak yapılacak olan hipotez testlerinin güvenilirliği, varsayımlarının sağlanmış olmasına bağlıdır. Varyans analizinde test istatistiği için elde edilen sonuçların duyarlılığı en çok varyansların heterojenliğinden etkilenmektedir. Bu çalışmada, farklı örneklem büyüklüklerinde, farklı dağılımlar için literatürde yaygın olarak kullanılan varyans homojenite testlerinin tip-I hata düzeyi ve güç bakımından karşılaştırılması amaçlanmıştır.Gereç ve Yöntemler:Levene medyan, Levene ortalama, Levene budanmış ortalama, bootstrap Levene medyan, Bartlett ve Cochran testleri için 1000 tekrarlı simülasyon çalışması gerçekleştirilmiştir. Örneklem büyüklüklerinin eşit olduğu dört durum n1=n2=n3=15; n1=n2=n3=30; n1=n2=n3=45; n1=n2=n3=100 ve örneklem büyüklüklerinin eşit olmadığı iki durum n1=15, n2=30, n3=45, n1=15, n2=30, n3=100 olarak alınmıştır. Farklı dağılımlar için çarpıklık ve basıklık katsayıları dikkate alınarak veriler türetilmiştir. Güç için, 1:1:2, 1:2:4, 1:2:2 ve 1:4:4 varyans oranları, farklı örneklem büyüklüklerine farklı varyans oranları denk gelecek şekilde alınmıştır.Bulgular:Tip-I hata oranları açısından, bootstrap Levene medyan testi tüm dağılımlar için en iyi sonucu vermiştir. Güç için; örneklem büyüklüklerinin eşit olması durumunda, orta ve yüksek örneklem büyüklüklerinde bootstrap Levene medyan ve Levene medyan testleri en iyi sonuçları vermiştir. Yüksek örneklem büyüklüklerinde Bartlett testi de bu iki teste benzer sonuçlar vermiştir.Sonuç:Test performanlarının dağılım yapısından etkilendiği görülmekle birlikte normallikten sapmalara karşı en iyi sonucun bootstrap Levene medyan testi için elde edildiği ve testlerin performansının varyans-örneklem büyüklüğü kombinasyonundan etkilendiği görülmüştür.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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| APA | BAYDILI K, Sigirli D (2017). Comparison of Variance Homogenity Tests for Different Distributions. , 197 - 212. 10.5336/biostatic.2017-56316 |
| Chicago | BAYDILI Kürşad Nuri,Sigirli Deniz Comparison of Variance Homogenity Tests for Different Distributions. (2017): 197 - 212. 10.5336/biostatic.2017-56316 |
| MLA | BAYDILI Kürşad Nuri,Sigirli Deniz Comparison of Variance Homogenity Tests for Different Distributions. , 2017, ss.197 - 212. 10.5336/biostatic.2017-56316 |
| AMA | BAYDILI K,Sigirli D Comparison of Variance Homogenity Tests for Different Distributions. . 2017; 197 - 212. 10.5336/biostatic.2017-56316 |
| Vancouver | BAYDILI K,Sigirli D Comparison of Variance Homogenity Tests for Different Distributions. . 2017; 197 - 212. 10.5336/biostatic.2017-56316 |
| IEEE | BAYDILI K,Sigirli D "Comparison of Variance Homogenity Tests for Different Distributions." , ss.197 - 212, 2017. 10.5336/biostatic.2017-56316 |
| ISNAD | BAYDILI, Kürşad Nuri - Sigirli, Deniz. "Comparison of Variance Homogenity Tests for Different Distributions". (2017), 197-212. https://doi.org/10.5336/biostatic.2017-56316 |
| APA | BAYDILI K, Sigirli D (2017). Comparison of Variance Homogenity Tests for Different Distributions. Türkiye Klinikleri Biyoistatistik Dergisi, 9(3), 197 - 212. 10.5336/biostatic.2017-56316 |
| Chicago | BAYDILI Kürşad Nuri,Sigirli Deniz Comparison of Variance Homogenity Tests for Different Distributions. Türkiye Klinikleri Biyoistatistik Dergisi 9, no.3 (2017): 197 - 212. 10.5336/biostatic.2017-56316 |
| MLA | BAYDILI Kürşad Nuri,Sigirli Deniz Comparison of Variance Homogenity Tests for Different Distributions. Türkiye Klinikleri Biyoistatistik Dergisi, vol.9, no.3, 2017, ss.197 - 212. 10.5336/biostatic.2017-56316 |
| AMA | BAYDILI K,Sigirli D Comparison of Variance Homogenity Tests for Different Distributions. Türkiye Klinikleri Biyoistatistik Dergisi. 2017; 9(3): 197 - 212. 10.5336/biostatic.2017-56316 |
| Vancouver | BAYDILI K,Sigirli D Comparison of Variance Homogenity Tests for Different Distributions. Türkiye Klinikleri Biyoistatistik Dergisi. 2017; 9(3): 197 - 212. 10.5336/biostatic.2017-56316 |
| IEEE | BAYDILI K,Sigirli D "Comparison of Variance Homogenity Tests for Different Distributions." Türkiye Klinikleri Biyoistatistik Dergisi, 9, ss.197 - 212, 2017. 10.5336/biostatic.2017-56316 |
| ISNAD | BAYDILI, Kürşad Nuri - Sigirli, Deniz. "Comparison of Variance Homogenity Tests for Different Distributions". Türkiye Klinikleri Biyoistatistik Dergisi 9/3 (2017), 197-212. https://doi.org/10.5336/biostatic.2017-56316 |
