ABSTRACT
An important problem in statistics relates to obtaining information about the form of the population from which a sample is drawn. The shape of this distribution might be the focus of the investigation. Alternatively, some inference concerning a particular aspect of the population may be of primary interest. In this latter case, in classical statistics, information about the form generally must be postulated or incorporated in the null hypothesis to perform an exact parametric type of inference. For example, suppose we have a small number of observations from an unknown population with unknown variance and the hypothesis of interest concerns the value of the population mean. The traditional parametric test, based on Student’s t distribution, is derived under the assumption of a normal population. The exact distribution theory and probabilities of both types of errors depend on this population form. Therefore it might be desirable to check on the 104reasonableness of the normality assumption before forming any conclusions based on the t distribution. If the normality assumption appears not to be justified, some type of nonparametric inference for location might be more appropriate with a small sample size.
