1st Edition

A Course in Categorical Data Analysis

By Thomas Leonard Copyright 1999
    204 Pages
    by Chapman & Hall

    204 Pages
    by Chapman & Hall

    Categorical data-comprising counts of individuals, objects, or entities in different categories-emerge frequently from many areas of study, including medicine, sociology, geology, and education. They provide important statistical information that can lead to real-life conclusions and the discovery of fresh knowledge. Therefore, the ability to manipulate, understand, and interpret categorical data becomes of interest-if not essential-to professionals and students in a broad range of disciplines.

    Although t-tests, linear regression, and analysis of variance are useful, valid methods for analysis of measurement data, categorical data requires a different methodology and techniques typically not encountered in introductory statistics courses. Developed from long experience in teaching categorical analysis to a multidisciplinary mix of undergraduate and graduate students, A Course in Categorical Data Analysis presents the easiest, most straightforward ways of extracting real-life conclusions from contingency tables. The author uses a Fisherian approach to categorical data analysis and incorporates numerous examples and real data sets. Although he offers S-PLUS routines through the Internet, readers do not need full knowledge of a statistical software package.

    In this unique text, the author chooses methods and an approach that nurtures intuitive thinking. He trains his readers to focus not on finding a model that fits the data, but on using different models that may lead to meaningful conclusions. The book offers some simple, innovative techniques not highighted in other texts that help make the book accessible to a broad, interdisciplinary audience. A Course in Categorical Data Analysis enables readers to quickly use its offering of tools for drawing scientific, medical, or real-life conclusions from categorical data sets.

    SAMPLING DISTRIBUTIONS
    Experimental Design for a Population Proportion
    Further Properties of the Binomial Distribution
    Statistical Procedures for the Binomial Distribution
    The Poisson Distribution
    Statistical Procedures for the Poisson Distribution
    The Multinomial distribution
    Sir Ronald Fisher's Conditioning Result
    More General Sampling Models
    Generalizing the Binomial Distribution
    The Discrete Exponential Family of Distributions
    Generalizing the Multinomial Distribution
    TWO BY TWO CONTINGENCY TABLES
    Conditional Probability and Independence
    Independence of Rows and Columns
    Investigating Independence, Given Observational Data
    Edwards' Theorem
    Log Contrasts and the Multinomial Distribution
    The Log Measure of Association Test
    The Product Binomial Model
    The Independent Poisson Model
    Fisher's Exact Test
    Power Properties of our Test Procedures
    SIMPSON'S PARADOX AND 23 TABLES
    Probability Theory
    The Cornish Pixie/Irish Leprechaun Example
    Interpretation of Simpson's Paradox
    The Three-Directional Approach
    Measure of Association Analysis for 23 Tables
    Medical Example
    Testing Equality for two 2 x 2 Tables
    The Three-directional Approach of the Analysis 23 Tables
    THE MADISON DRUG ALCOHOL ABUSE STUDY
    Experimental Design
    Statistical Results (phase 3) of Study
    Further Validation of Results
    GOODMAN'S FULL RANK INTERACTION ANALYZED FOR TWO WAY TABLES
    Introductory Example
    Methodological Developments
    Numerical Example
    Methodological Developments
    Business School Example
    Methodological Developments
    Advertising Example
    Testing for Equality of Unconditional Cell Probabilities
    Analysis of Berkeley Admissions Data
    Further Data Sets
    FURTHER EXAMPLES AND EXTENSIONS
    Hypertension, Obesity, and Alcohol Consumption
    The Bristol Cervical Screening Data
    The Multiple Sclerosis Data
    The Dundee Dental Health Data
    CONDITIONAL INDEPENDENCE MODELS FOR TWO-WAY TABLES
    Fixed Zeros and Missing Observations
    Incomplete Tables
    Perfectly Fitting Further Cells
    Complete Tables
    Further Data Sets
    LOGISTIC REGRESSION
    Review of General Methodology
    Analyzing Your Data Using S-PLUS
    Analysis of Mice Exposure Data
    Analysis of Space Shuttle Failure Data
    Further Data Sets
    FURTHER REGRESSION MODELS
    Regression Models for Poisson Data
    The California Eqrthquake Data
    A Generalization of Logistic Regression
    Logistic Regression for Matched Case-Control Studies
    Further Data
    FINAL TOPICS
    Continuous Random Variables
    Logistic Discrimination Analysis
    Testing The Slope and Quadratic Term
    Extensions
    Three-Way Contingency Tables
    INDEX

    Biography

    Leonard, Thomas

    "…presents an interesting and alternative view of categorical data analysis (CDA)…This book would be appropriate for upper undergraduates or master's level courses in statistics for non-majors who need an overview of CDA without going into great detail and theory…represents a fresh perspective on CDA. It is well worth a look, both by practitioners who use these methods in their research and by instructors who plan to teach courses on this subject … The author has extensive teaching experience at the University of Wisconsin-Madison and at the University of Edinburgh, and the choice of topics in this book reflects that experience … Each chapter is followed by useful exercises that should aid in developing an understanding of the presented material … Its many biological and medical examples, some developed in detail, make it especially useful for students with interests in the health sciences."
    --C. B. Borkowf, National Cancer Institute, Bethesda, MD, in Biometrics, December 2000

    "This book offers something different…what a wealth of detail and insight he develops! Copious numerical examples are discussed alongside the theory, and each of these are interpreted in the context of the study that generated the data…a welcome addition to the literature."
    --J. M. Juritz, Short Book Reviews of the ISI, April 2000

    "…a unique work in the implementation of techniques and methodologies needed…are not usually found in introductory statistics courses…Highly recommended for upper-division undergraduates and graduate students, faculty, and professionals."
    --D. J. Gougeon, University of Scranton in CHOICE


    "This book would be appropriate for upper undergraduate or master's level courses in statistics for non-majors who need an overview of CDA without going into great detail and theory. Its many biological and medical examples, some developed in detail, make it especially useful for students with interests in the health sciences."
    C.B. Borkowf, National Cancer Institute, Bethesda, maryland, USA
    "…the excellent discussion of Simpson's paradox, could be included in more general survey courses."
    C.B. Borkowf, National Cancer Institue, Bethesda, Maryland, USA
    "…this book represents a fresh perspective on CDA. It is well worth a look, both by practitioners who use these methods in their research and by instructors who plan to teach courses on this subject."
    C.B. Borkowf, National Cancer Institute, Bethesda, Maryland, USA
    "... this is a very useful little book that serves as an excellent introduction to S-PLUS commands..."
    -Journal of the Royal Statistical Society
    This ia a very useful handbook…accessible introduction and quick reference to S-PLUS."
    -Short Book Reviews of the ISI
    "…written in a clear and lucid style…an excellent candidate for a beginning level graduate textbook on statistical methods…a useful reference for practitioners."
    -Zentralblatt für Mathematik