ABSTRACT
In many elementary statistics courses, the subject matter is somewhat arbitrarily divided into two categories, called descriptive and inductive statistics. Descriptive statistics usually relates only to the calculation of or presentation of figures to summarize or to characterize a set of data. The mathematical statistician may claim that it is the users’ problem to decide on the legitimacy of the assumptions. Frequently in practice, the assumptions that are deemed reasonable by empirical evidence or past experience are not the desired ones, that is, those for which standard statistical techniques have been developed. Power calculations for any test require knowledge of the probability distribution of the test statistic under the alternative, but the alternatives in nonparametric problems are often extremely general. Before embarking on a systematic treatment of new concepts, some basic notation and definitions must be agreed upon and the groundwork prepared for development.
