Power Efficiency of Sign Test and Wilcoxon Signed Rank Test Relative to T-Test

Abstract

Many statistical tests require that your data follow a normal distribution. Sometimes this is not the case. In some instances it is possible to transform the data to make them follow a normal distribution; in others this is not possible or the sample size might be so small that it is difficult to ascertain whether or not the data a normally distributed. In such cases it is necessary to use a statistical test that does not require the data to follow a particular distribution. In the present study, we compared the power efficiency of one sample t-test, sign test and Wilcoxon signed rank test for small samples from normal, uniform, beta and exponential distributions for which the type I error, power of the test and power efficiency were computed. The comparison indicates that, the Wilcoxon signed rank test and sign test are as good as the t-test in a situation where the underlying distribution of the population is uncertain. For increasing sample size and increasing value of population mean, the non parametric tests achieved almost the same power with the t-test in all the selected distributions.

Keyword: One Sample, T-test, Sign test, Wilcoxon signed rank test, Type I error, Power of the test and Power efficiency