Exact Analysis of Discrete Data: 1st Edition (Hardback) book cover

Exact Analysis of Discrete Data

1st Edition

By Karim F. Hirji

Chapman and Hall/CRC

1,066 pages | 140 B/W Illus.

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pub: 2005-11-18
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Description

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.

Reviews

"The book’s infrastructure makes it a good candidate as a teaching resource. The chapters offer detailed worked example. Furthermore, each chapter includes exercises . . . some practitioners in discrete data analysis also will find this book useful."

– In Technometrics, August 2008, Vol. 50, No. 3

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.

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General