STATISTICAL POWER AND PROBABILITIES OF TYPE I ERROR IN TERMS OF SUITABLE NUMBER OF SIMULATIONS IN NONPARAMETRIC TESTS
NONPARAMETRİK TESTLERDE EN UYGUN SİMÜLASYON SAYISINA GÖRE İSTATİSTİKSEL GÜÇ VE I. TİP HATA OLASILIKLARI

Author : Ötüken SENGER
Number of pages : 1315-1326

Abstract

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 level? 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.

Keywords

Number of simulation, type I error, power of test, normal distribution, homogeneity of variance.

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