The effect of skewness and kurtosis on the one-sample<i>T</i>test and the impact of knowledge of the population standard deviation

Abstract

The test statistic for the t-test on one population mean is derived under the assumption that the sample was randomly chosen from a normal population and that the population standard deviation is unknown and must be estimated from the sample. However, it is clear that in practice this test is often performed on populations that are far from normal. This paper offers new insights into the effect of both skewness and kurtosis on the size (probability of a Type I error) of the one-sample t test and discusses the effect of sample size on the robustness of the test. In addition, the authors consider the impact that knowledge of the population standard deviation (or an a priori estimate believed to be sufficiently close to the true value) would have on the test.