Nonparametric Statistical Inference
This book was first published in 1971 and last revised in 1992. During the span of over 30 years, it seems fair to say that the book has made a meaningful contribution to the teaching and learning of nonparametric statistics. We have been gratified by the interest and the comments from our readers, reviewers, and users. These comments and our own experiences have resulted in many corrections, improvements, and additions.
We have two main goals in this revision: We want to bring the material covered in this book into the 21st century, and we want to make the material more user friendly.
With respect to the first goal, we have added new materials concerning the quantiles, the calculation of exact power and simulated power, sample size determination, other goodness-of-fit tests, and multiple comparisons. These additions will be discussed in more detail later. We have added and modified examples and included exact solutions done by hand and modern computer solutions using MINITAB,* SAS, STATXACT, and SPSS. We have removed most of the computer solutions to previous examples using BMDP, SPSSX, Execustat, or IMSL, because they seem redundant and take up too much valuable space. We have added a number of new references but have made no attempt to make the references comprehensive on some current minor refinements of the procedures covered. Given the sheer volume of the literature, preparing a comprehensive list of references on the subject of nonparametric statistics would truly be a challenging task. We apologize to the authors whose contributions could not be included in this edition.
With respect to our second goal, we have completely revised a number of sections and reorganized some of the materials, more fully integrated the applications with the theory, given tabular guides for applications of tests and confidence intervals, both exact and approximate, placed more emphasis on reporting results using P values, added some new problems, added many new figures and titled all figures and tables, supplied answers to almost all the problems, increased the number of numerical examples with solutions, and written concise but detailed summaries for each chapter.We think the problem answers should be a major plus, something many readers have requested over the years. We have also tried to correct errors and inaccuracies from previous editions.
In Chapter 1, we have added Chebyshev’s inequality, the Central Limit Theorem, and computer simulations, and expanded the listing of probability functions, including the multinomial distribution and the relation between the beta and gamma functions. Chapter 2 has been completely reorganized, starting with the quantile function and the empirical distribution function (edf), in an attempt to motivate the reader to see the importance of order statistics. The relation between rank and the edf is explained. The tests and confidence intervals for quantiles have been moved to Chapter 5 so that they are discussed along with other one-sample and paired-sample procedures, namely, the sign test and signed rank test for the median. New discussions of exact power, simulated power, and sample size determination, and the discussion of rank tests in Chapter 5 of the previous edition are also included here. Chapter 4, on goodness-of-fit tests, has been expanded to include Lilliefors’s test for the exponential distribution,computation of normal probability plots, and visual analysis of goodness of fit using P-P and Q-Q plots.
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