Normal Olmayan Dağılımlı Populasyonlardan Alınan Örneklerde Hesaplanan Çeşitli Test İstatistiklerinin I. Tip Hata Olasılıkları Bakımından Karşılaştırılması

Abstract

Bu çal ışmada, çeşitli varyanslara sahip Beta 4,14 ve Ki-Kare 5 da ğı l ı m ı gösteren populasyonlardan al ı nan 3 veya 4 gruplu örneklerden yararlan ı larak F, Marascuilo, Welch, Brown-Forsythe ve Alexander-Govern test istatistiklerinin 100 000 simülasyon denemesi sonunda gerçekle şen I. tip hata olas ı l ı klar ı bak ı m ı ndan karşı laşt ı nlmas ı yap ı lm ışt ı r. Simülasyon denemeleri sonunda, normal da ğı l ı m ön şart ı n ı n yerine gelmemesinin da ğı l ı m şeklinin , F testini etkilemedi ğ i, populasyon varyanslar ı homojenken veya aşı r ı heterojen değ ilken örnek genişlikleri dengeli olmak şart ı yla, F testinin güvenilir sonuçlar verdi ğ i görülmü ştür. Diğer alternatif testlerin, genel olarak da ğı l ı m şeklinden ve örnek genişlikleri ile bu örneklerin dengeli olup olmad ı klar ı ndan oldukça etkilendikleri sonucuna var ı lm ışt ı r.

Keywords

• I. tip hata
• varyanslar ı n homojenliğ i
• varyans analizi
• normal olmayan da ğı l ı mlar

Comparison of Some Test Statistics About Realized Type I Error Rate in the Non-Normal Populations

Abstract

In this study, F, Marascuilo, Welch, Brown-Forsythe and Alexander-Govern tests were compared on realized type I error rates via three or four samples which are taken from Beta 4,14 and Chi-Square 5 populations by simulation technique. At the end of 100 000 simulation trials it was determined that the violation of normality assumption was not as important as homogeneity of variance for F test but it was important for the other tests. It was concluded that other alternative tests were highly affected by the distribution shape, sample size and being balanced or unbalanced of observations in samples.

Keywords

• type I error
• homogeneity of variance
• Non-normal distributions

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