Exact Analysis of Discrete Data

Exact Analysis of Discrete Data

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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.show more

Product details

  • Hardback | 552 pages
  • 184 x 254 x 34mm | 1,102.24g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 140 black & white illustrations
  • 1584880708
  • 9781584880707

Table of contents

DISCRETE DISTRIBUTIONS Introduction Discrete Random Variables Probability Distributions Polynomial Based Distributions Binomial Distribution Poisson Distribution Negative Binomial Distribution Hypergeometric Distribution A General Representation The Multinomial Distribution The Negative Trinomial Suffcient Statistics The Polynomial Form ONE-SIDED UNIVARIATE ANALYSIS Introduction One Parameter Inference Tail Probability and Evidence Exact Evidence Function Mid-p Evidence Function Asymptotic Evidence Function Matters of Significance Confidence Intervals Illustrative Examples Design and Analysis Exercises TWO-SIDED UNIVARIATE ANALYSIS Introduction Two-Sided Inference Twice the Smaller Tail Method Examples The Likelihood Function The Score Method Additional Illustrations Likelihood Ratio and Wald Methods Three More Methods Comparative Computations The ABC of Reporting Additional Comments At the Boundary Equivalent Statistics COMPUTING FUNDAMENTALS Introduction Computing Principles Combinatorial Coeocients Polynomial Storage and Evaluation Computing Distributions Roots of Equations Iterative Methods ELEMENTS OF CONDITIONAL ANALYSIS Introduction Design and Analysis Modes of Inference The 2 x 2 Table The One Margin Fixed Design The Overall Total Fixed Design The Nothing Fixed Design A Retrospective Design The Inverse Sampling Design Unconditional Analysis Conditional Analysis Comparing Two Rates Points to Ponder Derivation of Test Statistics TWO 2 x 2 TABLES Introduction Sources of Variability On Stratification Data Examples Statistical Models Conventional Analysis Conditional Analysis An Example A Second Example On Case-Control Sampling Anatomy of Interactions ASSESSING INFERENCE Introduction Exact Unconditional Analysis Randomized Inference Exact Power Exact Coverage The Fisher and Irwin Tests Some Features Desirable Features On Unconditional Analysis Why the Mid-p? SEVERAL 2 x 2 TABLES: I Introduction Three Models Exact Distributions The COR Model Conditional Independence Trend In Odds Ratios Recommendations SEVERAL 2 x 2 TABLES: II Introduction Models for Combining Risk Testing for Homogeneity Test Statistics A Worked Example Checking the TOR Model An Incidence Density Study Other Study Designs Exact Power Additional Issues Derivation THE 2 x K TABLE Introduction An Ordered Table An Unordered Table Test Statistics An Illustration Checking Linearity Other Sampling Designs Incidence Density Data An Inverse Sampling Design Additional Topics Extensions Derivation POLYNOMIAL ALGORITHMS: I Introduction Exhaustive Enumeration Monte-Carlo Simulation Recursive Multiplication Exponent Checks Applications The Fast Fourier Transform POLYNOMIAL ALGORITHMS: II Introduction Bivariate Polynomials A Conditional Polynomial Backward Induction Conditional Values Applications Trivariate Polynomials An Extension Network Algorithms Power Computation Practical Implementation MULTINOMIAL MODELS Introduction Compositions and Partitions A Single Multinomial Trinary Response Models Conditional Polynomials Several 3 x K Tables J x K Tables MATCHED AND DEPENDENT DATA Introduction Matched Designs Paired Binary Outcomes Markov Chain Models REFLECTIONS ON EXACTNESS Introduction Inexact Terminology Bayesians and Frequentists Design and Analysis Status Quo Exactness Practical Inexactness Formal Exactness In Praise of Exactness References Index Each chapter also contains Relevant Literature and Exercises sections.show more