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NONPARAMETRİK TESTLERDE EN UYGUN SİMÜLASYON SAYISINA GÖRE İSTATİSTİKSEL GÜÇ VE I. TİP HATA OLASILIKLARI

STATISTICAL POWER AND PROBABILITIES OF TYPE I ERROR IN TERMS OF SUITABLE NUMBER OF SIMULATIONS IN NONPARAMETRIC TESTS

Journal Name:

  • The Journal of Academic Social Science Studies

Publication Year:

  • 2013
DOI: 
http://dx.doi.org/10.9761/JASSS_668

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
Recently, simulation techniques have been widely used in social and medical sciences as well as natural and applied sciences. One of the most common fields of application of these simulation techniques is determination of statistical powers and probabilities of type I error of both parametric and nonparametric tests. Simulation number plays a vital role in such deterministic studies. In case of number of simulations not being sufficient for a clear analysis, then study findings may be inconsistent and instable. In contrast, if number of simulations exceeds the suitable number then it means waste of time. In this study, the effects of different numbers of simulations on determination process of statistical powers and probabilities of type I error of nonparametric tests were discussed. Furthermore, optimum numbers of simulations for determining statistical powers and probabilities of type I error were suggested for future researchers. In this context, one of the nonparametric tests which is used for testing data obtained from two samples, namely Wald Wolfowitz runs test was applied and results were generalized for all nonparametric tests. In study, four equal and small sample sizes were used, these were as follows: (5, 5), (10, 10), (15, 15) and (20, 20). Simulation runs were performed for twenty different numbers of simulation. Significance levelα was assumed as 0, 05 for each sample size. Study was performed by taking the prerequisites of normality and homogeneity of variance into account. According to results; if researchers perform 80.000 simulation runs for a sample size of 5, 60.000 for a sample size of 10 and 50.000 for a sample size of 15 and 40.000 for a sample size of 20 they will have the optimum numbers of simulations in practice.
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Abstract (Original Language): 
Son yıllarda, fen bilimlerinin yanı sıra, sosyal ve beşeri bilimler ile sağlık bilimlerinde de simülasyon tekniklerinden oldukça sık faydalanılmaktadır.Simülasyon tekniklerinin en fazla kullanıldığı yerlerden biri de parametrik ve nonparametrik testlerin I. tip hata olasılıkları ve istatistiksel güçlerinin belirlenmesidir.Bu amaçla yapılan çalışmalarda simülasyon sayısı çok önemlidir.Eğer uygulanan simülasyon sayısı yeterli sayıda olmazsa elde edilen sonuçlar tutarlı ve kararlı olmayabilir.Çok fazla sayıda belirlenen simülasyon sayısı ise boşuna zaman kaybına neden olur. Bu çalışmada, farklı simülasyon sayılarının, nonparametrik testlerin, I. tip hata olasılıkları ve istatistiksel güçlerinin tahmininde göstereceği farklılıklar ele alınmış ve araştırmacılara, I. tip hata olasılığı ve testin gücü bakımından kullanmaları gereken optimum düzeyde simülasyon sayıları önerilmiştir. Bu amaçla iki örnekten elde edilen verileri test etmekte kullanılan nonparametrik testlerden Wald Wolfowitz dizi sayıları testinden faydalanılmış ve elde edilen sonuçlar tüm nonparametrik testler için genellenmiştir. Çalışmada dört eşit ve küçük örnek hacmi kullanılmıştır.Kullanılan örnek hacimleri; (5, 5), (10, 10), (15, 15) ve (20, 20) örnek hacimleridir.Simülasyon denemeleri yirmi farklı simülasyon sayısı için gerçekleştirilmiştir. Çalışmada α önem seviyesi, her bir örnek büyüklüğü için 0, 05 olarak kabul edilmiştir. Çalışma normallik ve varyansların homojenliği ön şartları altında yapılmıştır. Çalışmadan elde edilen sonuçlara göre; araştırmacılar, çalışmalarında kullanacakları örnek hacmi 5 ise 80.000, 10 ise 60.000, 15 ise 50.000 ve 20 ise de 40.000 simülasyon gerçekleştirirlerse bu simülasyon sayıları uygulamada yeterlidir.
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