Varyans analizi tekniğinin ön şartları yerine gelmediğinde varyans unsurları tahmininde I. tip hata
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Dosyalar
Tarih
2010
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Namık Kemal Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışma ile Varyans Analizi Tekniğinin normal dağılım, homojenlik gibi ön şartları yerine gelmediğinde Varyans Unsurları tahmin edilmiş ve I. Tip Hata olasılıkları hesaplanmıştır. Varyans Unsurları tahmininde Varyans Analizi Tekniği (ANOVA), En İyi Olabilirlik (Maximum Likelihood, ML) ve Kısıtlanmış En İyi Olabilirlik (Restricted Maximum Likelihood, REML) yöntemleri kullanılmıştır. Çalışmada simülasyon tekniği ile Z (0,1), t (10), (3), (5,2) dağılımlarından belirli örnek genişliklerinde (n=5, 10, 20, 30, 40, 50), belirli grup sayılarında (k= 3, 4, 10) ve varyans oranları 3 grup; 2=1:1:1, 1:1:5, 1:1:10; 4 grup; 2= 1:1:1:1, 1:1:1:5, 1:1:1:10, 10 grup; 2=1:1:1:1:1:1:1:1:1:1, 1:1:1:1:1:1:1:1:1:5, 1:1:1:1:1:1:1:1:1:10 olacak şekilde tesadüf sayıları üretilmiştir. Her bir deneme kombinasyonu için 100000 simülasyon çalışması yapılmıştır. Simülasyon çalışması ile elde edilen tesadüf sayıları standardize edilmiştir, ANOVA, ML ve REML yöntemlerine göre varyans unsurları tahmin edilmiş ve I. tip hata olasılıkları ( ) karşılaştırılmıştır. Varyans unsurları tahmin edilirken Rasgele Etkili Model (Random Effect Model) kullanılmıştır. ANOVA ve ML ile yapılan varyans unsuru tahminlerinde I. tip hata olasılıkları ( ) örnek genişliğinin küçük (n=4, 10) olduğu durumlarda ön şartlar sağlanmış olsa bile korunamazken REML yönteminde korunmaktadır. Her üç yöntemde de ön şartlardan homojenlik bozulduğunda ( 2= 1:1:5, 1:1:10 gibi) artmaktadır. Ayrıca grup sayısı (k= 5, 10) arttıkça da 'nın arttığı gözlenmiştir.
In this thesis, variance components and probability of Type I Error were estimated when the assumptions of Analysis of Variance (ANOVA) were violated. ANOVA, Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods were used to estimate variance components, Random numbers from Z (0,1), t (10), (3), (5,2) distributions were generated, with the various sample sizes (n=5, 10, 20, 30, 40, 50), group numbers (k=3, 4, 10) and the variance ratios for 3 group 2=1:1:1, 1:1:5, 1:1:10; 4 group; 2= 1:1:1:1, 1:1:1:5, 1:1:1:10, 10 group; 2=1:1:1:1:1:1:1:1:1:1, 1:1:1:1:1:1:1:1:1:5, 1:1:1:1:1:1:1:1:1:10. The simulation program was run 100000 times for each combination. These random numbers were standardized and variance components were estimated by ANOVA, ML and REML methods. Simple Random Effect Model was used for estimating the variance components. Depending on the findings of this study, it is concluded that probability of type I error ( ) estimated by ANOVA and ML was not protected in small sample sizes (n=5, 10) even if assumption of analysis of variance were met. However, REML protected it under the same conditions. The calculated probability of type I error ( ) by using all methods increased when the assumption of variance homogeneity was violated. Moreover, the probability of type I error ( ) increased when the number of group (k= 4, 10) increased.
In this thesis, variance components and probability of Type I Error were estimated when the assumptions of Analysis of Variance (ANOVA) were violated. ANOVA, Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods were used to estimate variance components, Random numbers from Z (0,1), t (10), (3), (5,2) distributions were generated, with the various sample sizes (n=5, 10, 20, 30, 40, 50), group numbers (k=3, 4, 10) and the variance ratios for 3 group 2=1:1:1, 1:1:5, 1:1:10; 4 group; 2= 1:1:1:1, 1:1:1:5, 1:1:1:10, 10 group; 2=1:1:1:1:1:1:1:1:1:1, 1:1:1:1:1:1:1:1:1:5, 1:1:1:1:1:1:1:1:1:10. The simulation program was run 100000 times for each combination. These random numbers were standardized and variance components were estimated by ANOVA, ML and REML methods. Simple Random Effect Model was used for estimating the variance components. Depending on the findings of this study, it is concluded that probability of type I error ( ) estimated by ANOVA and ML was not protected in small sample sizes (n=5, 10) even if assumption of analysis of variance were met. However, REML protected it under the same conditions. The calculated probability of type I error ( ) by using all methods increased when the assumption of variance homogeneity was violated. Moreover, the probability of type I error ( ) increased when the number of group (k= 4, 10) increased.
Açıklama
Anahtar Kelimeler
Varyans Analizi, Varyans Unsurları, I.Tip Hata Olasılığı, Simülasyon, Analysis of Variance, Variance Components, Probability of Type I Error, Simulation
