Order Statistics And Their Use In Testing And Estimation Tests Based On Range And Studentized Range Of Samples From A Normal Population

A companion volume to the authors' previous well-received work, the CRC Handbook of Tables for the Use of Order Statistics in Estimation, this handbook discusses testing whether a hypothesis is true or false. Together, these volumes are your complete reference to theory and important tables relating to order statistics and their applications. Once a researcher completes an experiment, the resulting data is assumed to have come from a normal distribution with its mean and variance unknown. The researcher is then presented with a hypothesis testing problem. The use of order statistics and related functions offers a simple, powerful, and interesting approach to solving this problem. This volume presents an introduction to the use of order statistics and explains the various problems and their applications. The role of order statistics in solving these problems is examined, several important statistics are introduced, and their use in addressing testing of hypothesis problems is highlighted. The book also includes numerous tables that facilitate the methods of hypothesis testing using order statistics. Examples are given of the use of these tables in multiple comparison tests, with attention to error rates and sample sizes, and in the analog range of analysis of variance.

The analysis of variance (ANOYA) models have become one of the most widely used tools of modern statistics for analyzing multifactor data. The ANOYA models provide versatile statistical tools for studying the relationship between a dependent variable and one or more independent variables. The ANOYA mod els are employed to determine whether different variables interact and which factors or factor combinations are most important. They are appealing because they provide a conceptually simple technique for investigating statistical rela tionships among different independent variables known as factors. Currently there are several texts and monographs available on the sub ject. However, some of them such as those of Scheffe (1959) and Fisher and McDonald (1978), are written for mathematically advanced readers, requiring a good background in calculus, matrix algebra, and statistical theory; whereas others such as Guenther (1964), Huitson (1971), and Dunn and Clark (1987), although they assume only a background in elementary algebra and statistics, treat the subject somewhat scantily and provide only a superficial discussion of the random and mixed effects analysis of variance.

An English translation now joins the Russian and Spanish versions. It is based on the newly revised fifth edition of the German version of the book. The original edition has become very popular as a learning and reference source with easy to follow recipes and cross references for scientists in fields such as engineering, chemistry and the life sciences. Little mathematical background is required of the reader and some important topics, like the logarithm, are dealt with in the preliminaries preceding chapter one. The usefulness of the book as a reference is enhanced by a number of convenient tables and by references to other tables and methods, both in the text and in the bibliography. The English edition contains more material than the German original. I am most grateful to all who have in conversations, letters or reviews suggested improvements in or criticized earlier editions. Comments and suggestions will continue to be welcome. We are especially grateful to Mrs. Dorothy Aeppli of St. Paul, Minnesota, for providing numerous valuable comments during the preparation of the English manuscript. The author and the translator are responsible for any remaining faults and imperfections. I welcome any suggestions for improvement. My greatest personal gratitude goes to the translator, Mr. Zenon Reynaro wych, whose skills have done much to clarify the text, and to Springer-Verlag.

Renowned statistician R.G. Miller set the pace for statistics students with Beyond ANOVA: Basics of Applied Statistics. Designed to show students how to work with a set of "real world data," Miller's text goes beyond any specific discipline, and considers a whole variety of techniques from ANOVA to empirical Bayes methods; the jackknife, bootstrap methods; and the James-Stein estimator. This reissue of Miller's classic book has been revised by professors at Stanford University, California. As before, one of the main strengths of Beyond ANOVA is its promotion of the use of the most straightforward data analysis methods-giving students a viable option, instead of resorting to complicated and unnecessary tests. Assuming a basic background in statistics, Beyond ANOVA is written for undergraduates and graduate statistics students. Its approach will also be valued by biologists, social scientists, engineers, and anyone who may wish to handle their own data analysis.