INTRODUCTORY BIOSTATISTICS INTRODUCTORY BIOSTATISTICS Second Edition CHAP T. LE Distinguished Professor of Biostatistics Director of Biostatistics and Bioinformatics Masonic Cancer Center University of Minnesota LYNN E. EBERLY Associate Professor of Biostatistics School of Public Health University of Minnesota Copyright © 2016 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging‐in‐Publication Data Names: Le, Chap T., 1948– | Eberly, Lynn E. Title: Introductory biostatistics. Description: Second edition / Chap T. Le, Lynn E. Eberly. | Hoboken, New Jersey : John Wiley & Sons, Inc., 2016. | Includes bibliographical references and index. Identifiers: LCCN 2015043758 (print) | LCCN 2015045759 (ebook) | ISBN 9780470905401 (cloth) | ISBN 9781118595985 (Adobe PDF) | ISBN 9781118596074 (ePub) Subjects: LCSH: Biometry. | Medical sciences–Statistical methods. Classification: LCC QH323.5 .L373 2016 (print) | LCC QH323.5 (ebook) | DDC 570.1/5195–dc23 LC record available at http://lccn.loc.gov/2015043758 Set in 10/12pt Times by SPi Global, Pondicherry, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 To my wife, Minhha, and my daughters, Mina and Jenna with love C.T.L. To my husband, Andy, and my sons, Evan, Jason, and Colin, with love; you bring joy to my life L.E.E. Contents Preface to the second edition xiii Preface to the First edition xv About the Companion Website xix 1 Descriptive Methods for Categorical Data 1 1.1 Proportions 1 1.1.1 Comparative Studies 2 1.1.2 Screening Tests 5 1.1.3 Displaying Proportions 7 1.2 Rates 10 1.2.1 Changes 11 1.2.2 Measures of Morbidity and Mortality 13 1.2.3 Standardization of Rates 15 1.3 Ratios 18 1.3.1 Relative Risk 18 1.3.2 Odds and Odds Ratio 18 1.3.3 Generalized Odds for Ordered 2 × k Tables 21 1.3.4 Mantel–Haenszel Method 25 1.3.5 Standardized Mortality Ratio 28 1.4 Notes on Computations 30 Exercises 32 2 Descriptive Methods for Continuous Data 55 2.1 Tabular and Graphical Methods 55 2.1.1 One‐Way Scatter Plots 55 2.1.2 Frequency Distribution 56 2.1.3 Histogram and Frequency Polygon 60 viii CONTENTS 2.1.4 Cumulative Frequency Graph and Percentiles 64 2.1.5 Stem and Leaf Diagrams 68 2.2 Numerical Methods 69 2.2.1 Mean 69 2.2.2 Other Measures of Location 72 2.2.3 Measures of Dispersion 73 2.2.4 Box Plots 76 2.3 Special Case of Binary Data 77 2.4 Coefficients of Correlation 78 2.4.1 Pearson’s Correlation Coefficient 80 2.4.2 Nonparametric Correlation Coefficients 83 2.5 Notes on Computations 85 Exercises 87 3 Probability and Probability Models 103 3.1 Probability 103 3.1.1 Certainty of Uncertainty 104 3.1.2 Probability 104 3.1.3 Statistical Relationship 106 3.1.4 Using Screening Tests 109 3.1.5 Measuring Agreement 112 3.2 Normal Distribution 114 3.2.1 Shape of the Normal Curve 114 3.2.2 Areas Under the Standard Normal Curve 116 3.2.3 Normal Distribution as a Probability Model 122 3.3 Probability Models for Continuous Data 124 3.4 Probability Models for Discrete Data 125 3.4.1 Binomial Distribution 126 3.4.2 Poisson Distribution 128 3.5 Brief Notes on the Fundamentals 130 3.5.1 Mean and Variance 130 3.5.2 Pair‐Matched Case–Control Study 130 3.6 Notes on Computations 132 Exercises 134 4 estimation of Parameters 141 4.1 Basic Concepts 142 4.1.1 Statistics as Variables 143 4.1.2 Sampling Distributions 143 4.1.3 Introduction to Confidence Estimation 145 4.2 Estimation of Means 146 4.2.1 Confidence Intervals for a Mean 147 4.2.2 Uses of Small Samples 149 4.2.3 Evaluation of Interventions 151 4.3 Estimation of Proportions 153