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Contents Part I: General Concept and Techniques Chapter 1: Measurement 1.1 What is biostatistics? 1.2 Organization of data 1.3 Types of measurements 1.4 Data quality Chapter 2: Types of studies 2.1 Surveys 2.2 Comparative studies Chapter 3: Frequency distributions 3.1 Stemplots 3.2 Frequency tables 3.3 Additional frequency charts Chapter 4: Summary statistics 4.1 Central location: mean 4.2 Central location: median 4.3 Central location: mode 4.4 Comparison of the mean, median, and mode 4.5 Spread: quartiles 4.6 Boxplots 4.7 Spread: the variance and standard deviation 4.8 Selecting summary statistics Chapter 5: Probability concepts 5.1 What is probability? 5.2 Types of random variables 5.3 Discrete random variables 5.4 Continuous random variables 5.5 More rules and properties of probability Chapter 6: Binomial probability distributions 6.1 Binomial random variables 6.2 Calculating binomial probabilities 6.3 Cumulative probabilities 6.4 Probability calculators 6.5 Expected value and variance of a binomial random variable 6.6 Using the binomial pmf to help make judgments Chapter 7: Normal probability distributions 7.1 Characteristics of Normal distributions 7.2 Determining Normal probabilities 7.3 Finding values that correspond to Normal probabilities 7.4 Assessing departures from Normality Chapter 8: Introduction to statistical inference 8.1 Concepts 8.2 Sampling behavior of a mean 8.3 Sampling behavior of a proportion Chapter 9: Basis of hypothesis testing 9.1 The null and alternative hypotheses 9.2 Test statistic 9.3 P-value 9.4 Statistical significance 9.5 One-sample z test (summary) 9.6 Power and sample size Chapter 10: Basis of confidence intervals 10.1 Introduction to confidence intervals 10.2 Confidence interval for µ, s known 10.3 Sample size requirements 10.4 Relationship between hypothesis testing and confidence intervals Part II: Quantitative response variable Chapter 11: Inference about a mean 11.1 Estimated standard error of the mean 11.2 Student¿s t distributions 11.3 One-sample t test 11.4 Confidence interval for µ 11.5 Paired samples 11.6 Conditions for inference 11.7 Sample size and power Chapter 12: Comparing independent means 12.1 Paired and independent samples 12.2 Exploratory and descriptive statistics 12.3 Inference about the mean difference 12.4 Equal variance t procedure (optional) 12.5 Conditions for inference 12.6 Sample size and power Chapter 13: Comparing several means (one-way ANOVA) 13.1 Descriptive statistics 13.2 The Problem of Multiple Comparisons 13.3 Analysis of variance (ANOVA) 13.4 Post hoc comparisons 13.5 The equal variance assumption 13.6 Introduction to non-parametric tests Chapter 14: Correlation and Regression 14.1 Data 14.2 Scatterplots 14.3 Correlation 14.4 Regression Chapter 15: Multiple Linear Regression 15.1 The general idea 15.2 The multiple linear regression model 15.3 Categorical explanatory variables in regression models 15.4 Regression coefficients 15.5 ANOVA for multiple linear regression 15.6 Examining multiple regression conditions Part III: Categorical response variable Chapter 16: Inference about a proportion 16.1 Proportions 16.2 The sampling distribution of a proportion 16.3 Hypothesis test, Normal approximation 16.4 Hypothesis test, binomial method 16.5 Confidence interval for population proportion p 16.6 Sample size and power Chapter 17: Comparing two proportions 17.1 Data 17.2 Proportion difference (risk difference) 17.3 Hypothesis test 17.4 Proportion ratio (relative risk) 17.5 Systematic sources of error 17.6 Power and sample size Chapter 18: Cross-tabulated counts 18.1 Types of samples 18.2 Describing naturalistic and cohort samples 18.3 Chi-square test of association 18.4 Test for trend 18.4 Case-control samples 18.5 Matched-pairs Chapter 19: Stratified 2-by-2 Tables 19.1 Preventing confounding 19.2 Simpson¿s paradox 19.3 Mantel-Haenszel methods 19.4 Interaction Appendices A. Table of 2000 Random Digits B. Cumulative probabilities for a Standard Normal random variable (z Table) C. t Table D. F Table E. ?2 Table F. Two-tails of z Preface Basic Biostatistics is an introductory text that presents statistical ideas and techniques for students and workers in public health and biomedical research. The book is designed to be accessible to students with modest mathematical backgrounds. No more than high school algebra is needed to understand this book. With this said, I hope to get past the notion that biostatistics is just an extension of math. Biostatistics is much more than that¿it is a combination of mathematics and careful reasoning. Do not let the former interfere with the later. Biostatistical analysis is more than just number crunching. It considers how research questions are generated, studies are designed, data are collected, and results are interpreted. Analysis of data, with a more or less statistical flavor, should play many roles. Basic Biostatistics pays particular attention to exploratory and descriptive analyses. Whereas many introductory biostatistics texts give this topic intermittent attention, this text gives it ongoing consideration. Both exploratory and confirmatory data analysis deserves our attention. Biostatistics entails formulating research questions and designing processes for exploring and testing theories. I hope students who come to the study of biostatistics asking ¿What¿s the right answer?¿ leave asking ¿Was that the right question?¿ Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise. Several additional points bear emphasis: Point 1: Practice, practice, practice. In studying biostatistics, you are developing a new set of reasoning skills. What is true of developing other skills is true of developing biostatistical skills¿the only way to get better is to practice with the proper awareness and attention. To this end, illustrative examples and exercises are incorporated throughout the book. I¿ve tried to make illustrations and exercises relevant. Many have historical importance. Carefully following the reasoning of illustrations and exercises is an opportunity to learn. (¿Never regard study as a duty, but as the enviable opportunity to learn.¿) Answers to odd-numbered exercises are provided in the back of the book. Instructors may requests answers to even-numbered exercises from the publisher. Point 2: Structure of book. The structure of this book may differ from that of other texts. Chapters are intentionally brief and limited in scope. This allows for flexibility in the order of coverage. The book is organized into three main parts. Part I (Chapters 1 ¿ 10) addresses basic concepts and techniques. Students should complete these chapters (or a comparable introductory course) before moving on to Part II and III. Part II (Chapters 11 ¿ 15) covers analytic techniques for quantitative response variables. Part III (Chapters 16 ¿ 19) covers techniques for categorical responses. Chapters in these sections can be covered in different orders, at the discretion of the instructor. One instructor may choose to cover these chapters in sequence, while another may cover Chapter 11 and Chapter 16 simultaneously (as an example), since these chapters both address one-sample problems. (Chapter 11 covers one-sample problems for quantitative response variables; Chapter 16 covers one-sample problems for binary response variables.) As another example, one could cover the chapters on categorical responses (Chapters 16 ¿ 19) before covering the chapters on quantitative response (Chapter 11 ¿ 15), if this was the focus of the course. Point 3: Hand calculations and computational support. While I believe there is still benefit in learning to calculate statistics by hand, students are encouraged to use statistical software to supplement hand calculations. Use of software tools can free us from some of the tedium of numerical manipulations, leaving more time to think about practical implications of results. The only way humans can do BETTER than computers is to take a chance of doing WORSE. So we have got to take seriously the need for steady progress toward teaching routine procedures to computers rather than to people. That will leave the teachers of people with only things hard to teach, but this is our proper fate. The book is not tied to any particular software package, but does make frequent use of these three programs: StaTable, SPSS, and WinPepi. ? StaTable is a freeware program that provides access to twenty-five commonly used statistical distributions. It is runs on Windows®, Palm®, and Web-browser (Java) platforms. This program eliminates the need to look-up probabilities in hard-copy tables. It also allows for more precise interpolations for probabilities, especially for continuous random variables. The website for this book will include a link to the StaTable website. ? SPSS - SPSS is commercial software package with versions that run on Windows® and Macintosh® computers. A student version of the program can be purchased at campus bookstores and online at www.journeyed.com. Another economical alternative is lease SPSS for short-term use through the website www.e-academy.com. ? WinPepi stands for WINdows Programs for EPIdemiologists. This is a series of computer programs written by Joe Abramson of the Hebrew University-Hadassah School of Public Health and Community Medicine (Jerusalem, Israel) and Paul Gahlinger (University of Utah, Salt Lake City, Utah). The programs are designed for use in the practice of biostatistics, but are also excellent learning aids. WinPepi is free and can be downloaded from the website for this book.
Library of Congress Subject Headings for this publication:
Medical statistics.
Biometry.
Public health -- Statistical methods.
Biometry -- methods.
Public Health Practice.