Permutation, Parametric, and Bootstrap Tests of Hypotheses

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Springer Science & Business Media, Jan 27, 2006 - Mathematics - 316 pages
This text is intended to provide a strong theoretical background in testing hypotheses and decision theory for those who will be practicing in the real worldorwhowillbeparticipatinginthetrainingofreal-worldstatisticiansand biostatisticians. In previous editions of this text, my rhetoric was somewhat tentative. I was saying, in e?ect, “Gee guys, permutation methods provide a practical real-world alternative to asymptotic parametric approximations. Why not give them a try?” But today, the theory, the software, and the hardware have come together. Distribution-free permutation procedures are the primary method for testing hypotheses. Parametric procedures and the bootstrap are to be reserved for the few situations in which they may be applicable. Four factors have forced this change: 1. Desire by workers in applied ?elds to use the most powerful statistic for their applications. Such workers may not be aware of the fundamental lemma of Neyman and Pearson, but they know that the statistic they wanttouse—acomplexscoreoraratioofscores,doesnothaveanalready well-tabulated distribution. 2. Pressure from regulatory agencies for the use of methods that yield exact signi?cance levels, not approximations. 3. A growing recognition that most real-world data are drawn from mixtures of populations. 4. A growing recognition that missing data is inevitable, balanced designs the exception. Thus, it seems natural that the theory of testing hypothesis and the more general decision theory in which it is embedded should be introduced via the permutation tests. On the other hand, certain relatively robust param- ric tests such as Student’s t continue to play an essential role in statistical practice.
 

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Contents

A Wide Range of Applications
1
Optimal Procedures
13
Testing Hypotheses
33
Distributions 67
66
Multiple Tests
79
Experimental Designs
85
Multifactor Designs
119
Categorical Data
143
Coping with Disaster
195
Exchangeability
215
Increasing Computational Efficiency
233
Theory of Testing Hypotheses
255
Exchangeable Observations
268
Bibliography
279
Author Index
303
Subject Index
309

Multivariate Analysis
169
Clustering in Time and Space
189

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About the author (2006)

PHILLIP I. GOOD, PhD, is Operations Manager of Information Research, a consulting firm specializing in statistical solutions for private and public organizations and has published eighteen books.

JAMES W. HARDIN, PhD, is Associate Research Professor in the Department of Epidemiology and Biostatistics at the University of South Carolina.

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