| Statistical methods based on ranks, methods usually referred to as nonparametric or distribution-free, have been and continue to be pervasive in the literature of mathematical and applied statistics. Some describe these methods as true competitors of normal-theory methods, others describe them as inefficient methods which waste the information inherent in the actual data.;Chapter 2 details the work of the earliest period of nonparametric statistics. The efforts of this period range from intuitive analysis of sample data to sophisticated procedures which anticipate the modern period.;Chapter 3 traces the mathematical development of nonparametric statistics from 1936 up to around 1960, a period that saw the mathematical development of the familiar nonparametric competitors of popular parametric methods, i.e., the development of Spearman's Rho, Friedman's test, Kendall's Tau, Wilcoxon's tests, and the Kruskal-Wallis test.;Chapter 4 traces the debate--parametric vs. nonparametric--from the time (1908) Student promulgated the normal-theory distribution that bears his name, up to the present day. We show that the controversy over the use of methods based on normal distribution assumptions led to the development of nonparametric statistics. It is seen that after that development, the question of interest was whether, in the case of non-normal populations, one would better retain the power and size of a statistical test using parametric or nonparametric methods. An examination of sampling studies, on this question, indicates the use of parametric methods.;In this study we trace the development of nonparametric statistics from its earliest appearance up to the point when the best known methods had been developed (about 1960). Noting that nonparametric statistics has been surrounded by controversy from its beginning up to the present, we also trace the debate over the relative merits of these methods and parametric (normal-theory) methods.;In Chapter 5 we summarize our findings in the form of implications for statistical education, particularly at the introductory level. We recommend the use of nonparametric methods when data is in ranks. We further suggest that nonparametric methods be presented as rank transformation (of parametric statistics) procedures. |
