Statistical Symbols Symbols are listed in order of their appearance in the text. X A single element normally distributed population lies from the population mean; or the N Number of elements in a population number of standard errors by which n Number of elements in a sample a random sample mean lies from the population mean p The probability of an event occur- ring. In reports of statistical signifi- µx– The mean of the random sampling cance, p is the probability that the distribution of means result could have been obtained by σx– Standard error or standard error of chance—i.e., the probability that a the mean (standard deviation of the type I error is being made random sampling distribution of q The probability of an event not means) [SEM or SE] occurring; equal to (1 – p) sx– Estimated standard error (estimat- ƒ Frequency ed standard error of the mean) C Centile (or percentile) rank; or t The number of estimated standard confidence level errors by which a random sample mean lies from the population mean Mo Mode df Degrees of freedom Mdn Median α The criterion level at which the µ Population mean null hypothesis will be accepted or – rejected; the probability of making X Sample mean a type I error ∑ The sum of b Probability of making a type II error x Deviation score c2 Chi-square; a test of proportions σ2 Population variance r Correlation coefficient S2 Sample variance r Rho; Spearman rank order correla- σ Population standard deviation (SD) tion coefficient S Sample standard deviation (SD) r2 Coefficient of determination z The number of standard deviations b Regression coefficient; the slope of by which a single element in a the regression line High-Yield TM Biostatistics, Epidemiology, & Public Health FOURTH EDITION High-Yield TM Biostatistics, Epidemiology, & Public Health FOURTH EDITION Anthony N. Glaser, MD, PhD Clinical Assistant Professor of Family Medicine Department of Family Medicine Medical University of South Carolina Charleston, South Carolina Acquisitions Editor: Susan Rhyner Product Manager: Catherine Noonan Marketing Manager: Joy Fisher-Williams Vendor Manager: Bridgett Dougherty Manufacturing Manager: Margie Orzech Design Coordinator: Teresa Mallon Compositor: S4Carlisle Publishing Services Fourth Edition Copyright © 2014, 2005, 2001, 1995 Lippincott Williams & Wilkins, a Wolters Kluwer business. 351 West Camden Street Two Commerce Square Baltimore, MD 21201 2001 Market Street Philadelphia, PA 19103 Printed in China All rights reserved. This book is protected by copyright. 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Glaser, MD, PhD, clinical assistant professor, Medical University of South Carolina. — 4th edition. pages cm Earlier title: High-yield biostatistics. Includes bibliographical references and index. ISBN 978-1-4511-3017-1 1. Medical statistics. 2. Biometry. I. Title. R853.S7G56 2014 570.1'5195—dc23 2012039198 DISCLAIMER Care has been taken to confirm the accuracy of the information present and to describe generally accepted practices. However, the authors, editors, and publisher are not responsible for errors or omissions or for any consequences from application of the information in this book and make no warranty, expressed or implied, with respect to the currency, completeness, or accuracy of the contents of the publication. Application of this information in a particular situation remains the professional responsibility of the p ractitioner; the clini- cal treatments described and recommended may not be considered absolute and universal r ecommendations. 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Lippincott Williams & Wilkins customer service representatives are available from 8:30 am to 6:00 pm, EST. 9 8 7 6 5 4 3 2 1 To my wife, Marlene Contents Statistical Symbols .........................................................................................inside front cover Preface .....................................................................................................................................ix 1 Descriptive Statistics ...........................................1 Populations, Samples, and Elements .......................................................................................1 Probability ................................................................................................................................1 Types of Data ............................................................................................................................2 Frequency Distributions ..........................................................................................................3 Measures of Central Tendency .................................................................................................8 Measures of Variability .............................................................................................................9 Z Scores ..................................................................................................................................12 2 Inferential Statistics .......................................... 15 Statistics and Parameters .......................................................................................................15 Estimating the Mean of a Population ....................................................................................19 t Scores ..................................................................................................................................21 3 Hypothesis Testing ............................................ 24 Steps of Hypothesis Testing ...................................................................................................24 z-Tests ....................................................................................................................................28 The Meaning of Statistical Significance .................................................................................28 Type I and Type II Errors .......................................................................................................28 Power of Statistical Tests ........................................................................................................29 Directional Hypotheses ..........................................................................................................31 Testing for Differences between Groups ................................................................................32 Post Hoc Testing and Subgroup Analyses ..............................................................................33 Nonparametric and Distribution-Free Tests ..........................................................................34 4 Correlational and Predictive Techniques ................ 36 Correlation .............................................................................................................................36 Regression ..............................................................................................................................38 Survival Analysis ....................................................................................................................40 Choosing an Appropriate Inferential or Correlational Technique ........................................43 5 Asking Clinical Questions: Research Methods .......... 45 Simple Random Samples ........................................................................................................46 vii viii Contents Stratified Random Samples ....................................................................................................46 Cluster Samples .....................................................................................................................46 Systematic Samples ................................................................................................................46 Experimental Studies .............................................................................................................46 Research Ethics and Safety ....................................................................................................51 Nonexperimental Studies .......................................................................................................53 6 Answering Clinical Questions I: Searching for and Assessing the Evidence ....................................... 59 Hierarchy of Evidence ............................................................................................................60 Systematic Reviews ................................................................................................................60 7 Answering Clinical Questions II: Statistics in Medical Decision Making ............................................... 68 Validity ...................................................................................................................................68 Reliability ...............................................................................................................................69 Reference Values ....................................................................................................................69 Sensitivity and Specificity ......................................................................................................70 Receiver Operating Characteristic Curves .............................................................................74 Predictive Values ....................................................................................................................75 Likelihood Ratios ...................................................................................................................77 Prediction Rules .....................................................................................................................80 Decision Analysis ...................................................................................................................81 8 Epidemiology and Population Health .................... 86 Epidemiology and Overall Health .........................................................................................86 Measures of Life Expectancy .................................................................................................88 Measures of Disease Frequency .............................................................................................88 Measurement of Risk .............................................................................................................92 9 Ultra-High-Yield Review ...................................101 References ............................................................................................................................105 Index ....................................................................................................................................107