A Comparison of Usual t-Test Statistic and Modified t-Test Statistics on Skewed Distribution Functions

摘要

When the sample size n is small, the random variable T ={the square root of}n(X - )/S is said to follow a central t distribution with degrees of freedom (n - 1), where X is the sample mean and S is the sample standard deviation, provided that the data X N (, ~2). The random variable T can be used as a test statistic to hypothesize the population mean . Some argue that the t-test statistic is robust against the normality of the distribution and claim that the normality assumption is not necessary. In this article we will use simulation to study whether the t-test is really robust if the population distribution is not normally distributed. In particular, we will study how the skewness of a probability distribution will affect the confidence interval as well as the t-test statistic.