Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable. This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov chain data. While most chapters focus on statistical theory and applications, three chapters deal exclusively with computational issues. Detailed worked examples appear throughout the book, and each chapter includes an extensive problem set. Written at an elementary to intermediate level, Exact Analysis of Discrete Data is accessible to anyone having taken a basic course in statistics or biostatistics, bringing to them valuable material previously buried in specialized journals.
1 Discrete distributions 1
2 One-sided univariate analysis 29
3 Two-sided univariate analysis 55
4 Computing fundamentals 87
5 Elements of conditional analysis 117
6 Two 2 x 2 tables 159
7 Assessing inference 189
8 Several 2 x 2 tables : I 227
9 Several 2 x 2 tables : II 253
10 The 2 x K table 279
11 Polynomial algorithms : I 323
12 Polynomial algorithms : II 349
13 Multinomial models 377
14 Matched and dependent data 415
15 Reflections on exactness 449
