Modified T tests for positively skewed distributions and comparisons

The aim of this study is to introduce Chen? s Test for testing the null hypotheses of population mean with drawn samples from positively skewed distributions and to compare it with other tests. In this context, firstly, prior studies are mentioned. In the second section, Student t Test, Johnson?s Modified Square t Test, Johnson?s Modified Linear t Test, Sutton? s Composite Test (Sutton? s Decision Rule) and Chen? s Test are discussed. In the third section, it is informed concerning positively skewed distributions and experiment design which are used in the simulation study. These distributions are Exponential distribution, Gamma distribution, Chi-Square distribution, Lognormal distribution, Weibull distribution and Beta distribution. In the fourth section, by drawing stated samples from each distribution, for each test, the reject (experimental type I error) rates for null hypothesis which is actually true and the reject (power of the test) rates for null hypothesis which is actually false are calculated. Experimental type I error rates are compared with nominal a and experimental power of the test rates are compared with each other.At the end of simulation study, in some situations, Sutton? s Composite Test (Sutton? s Decision Rule) with respect to experimental type I error rates gives close results with Chen? s Test. Otherwise, it is determined that Chen? s Test is more powerful than other tests.When sample size is increased a few, it is determined that experimental type I error rates concerning Chen? s Test are more close to nominal a than experimental type I error rates concerning Sutton? s Composite Test .As a result, Chen? s Test gives better results than other tests with respect to both reject (experimental type I error) rates for null hypothesis which is actually true and the reject (power of the test) rates for null hypothesis which is actually false.