The Investigation of Bartlett and Levene' s Test Statistics in Terms of Type I Error Rates in SmaII Samples

Abstract

In this study, It was aimed that the investigation of Bartlett and Levene' s test statistics in terms of Type I error rates a. = 0.50, 0.25, 0.20, 0.15, 0.10, 0.05 and 0.01 in small samples. For this, samples had 3 and 4 treatment groups were drawn from a normal N 0.1 population and balanced equal sample sizes were increased from 2 to 30. In these samles, Type I error rates were obtained empirically. In order to obtain Type I error rates, 100000 replications were done for each sample sizes. In addition, the critical values of Bartlett and Levene's test statistics at a = O. 05 ve 0.01 Type I error levels were obtained from 1000000 replications for each sample sizes. As a result, It was emphasised that Bartlett's test is better

Keywords

• Bartlett's test
• Levene's test
• Type I error
• homogeneity of variance

Küçük Örneklerde Bartlett ve Levene Test İstatistiklerinin I. Tip Hata Bakımından incelenmesi

Öz

Bu çal ışmada, Bartlett ve Levene test istatistiklerinin I. Tip hata bak ı m ı ndan incelenmesi amaçlanm ışt ı r. Bu amaçla; normal da ğı l ı m N 0,1 gösteren populasyondan 3 ve 4 gruplu örnekler al ı nm ış ve örnek genişliğ i her grupta eş it olacak şekilde 2' den ba ş lat ı larak 30' a kadar art ı rı lm ışt ı r. Bu örneklerde kararlaşt ı rı lan I. Tip hata; a = 0.50, 0.25, 0.20, 0.15, 0.10, 0.05 ve 0.01 oldu ğ unda, Bartett ve Levene test istatistikleri için gerçekle şen I. Tip hatalar ampirik olarak elde edilmiştir. Bunun için her örnek geni şliğinde 100000 deneme yap ı lm ışt ı r. Buna ilaveten a = O. 05 ve 0.01'deki Bartlett ve Levene istatistiklerinin kritik de ğ erleri de belirlenmi ştir. Bu değerlerin belirlenmesi için 1000000 deneme yap ı lmışt ı r. Sonuçta, Bartlett testinin I. Tip hata bak ı mı ndan daha iyi olduğu vurgulanm ışt ı r.

Anahtar Kelimeler

• Bartlett testi
• Levene testi
• I. Tip hata
• varyanslar ı n homojenliği

References

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