Basic Statistics: A Primer for the Biomedical Sciences

Description

New Edition of a Classic Guide to Statistical Applications in the Biomedical Sciences In the last decade, there have been significant changes in the way statistics is incorporated into biostatistical, medical, and public health research. Addressing the need for a modernized treatment of these statistical applications, Basic Statistics, Fourth Edition presents relevant, up-to-date coverage of research methodology using careful explanations of basic statistics and how they are used to address practical problems that arise in the medical and public health settings. Through concise and easy-to-follow presentations, readers will learn to interpret and examine data by applying common statistical tools, such as sampling, random assignment, and survival analysis. Continuing the tradition of its predecessor, this new edition outlines a thorough discussion of different kinds of studies and guides readers through the important, related decision-making processes such as determining what information is needed and planning the collections process. The book equips readers with the knowledge to carry out these practices by explaining the various types of studies that are commonly conducted in the fields of medical and public health, and how the level of evidence varies depending on the area of research. Data screening and data entry into statistical programs is explained and accompanied by illustrations of statistical analyses and graphs. Additional features of the Fourth Edition include: A new chapter on data collection that outlines the initial steps in planning biomedical and public health studies A new chapter on nonparametric statistics that includes a discussion and application of the Sign test, the Wilcoxon Signed Rank test, and the Wilcoxon Rank Sum test and its relationship to the Mann-Whitney U test An updated introduction to survival analysis that includes the Kaplan Meier method for graphing the survival function and a brief introduction to tests for comparing survival functions Incorporation of modern statistical software, such as SAS, Stata, SPSS, and Minitab into the presented discussion of data analysis Updated references at the end of each chapter Basic Statistics, Fourth Edition is an ideal book for courses on biostatistics, medicine, and public health at the upper-undergraduate and graduate levels. It is also appropriate as a reference for researchers and practitioners who would like to refresh their fundamental understanding of statistical techniques. Basic Statistics CONTENTS Preface to the Fourth Edition 1 Initial Steps 1.1 Reasons for Studying Biostatistics 1.2 Initial Steps in Designing a Biomedical Study 1.2.1 Setting Objectives 1.2.2 Making a Conceptual Model of the Disease Process 1.2.3 Estimating the Number of Persons with the Risk Factor or Disease 1.3 Common Types of Biomedical Studies 1.3.1 Surveys 1.3.2 Experiments 1.3.3 Clinical Trials 1.3.4 Field Trials 1.3.5 Prospective Studies 1.3.6 Case/Control Studies 1.3.7 Other Types of Studies 1.3.8 Rating Studies by the Level of Evidence 1.3.9 CONSORT Problems References 2 Populations and Samples 2.1 Basic Concepts 2.2 Definitions of Types of Samples 2.2.1 Simple Random Samples 2.2.2 Other Types of Random Samples 2.2.3 Reasons for Using Simple Random Samples 2.3 Methods of Selecting Simple Random Samples 2.3.1 Selection of a Small Simple Random Sample 2.3.2 Tables of Random Numbers 2.3.3 Sampling With and Without Replacement 2.4 Application of Sampling Methods in Biomedical Studies 2.4.1 Characteristics of a Good Sampling Plan 2.4.2 Samples for Surveys 2.4.3 Samples for Experiments 2.4.4 Samples for Prospective Studies 2.4.5 Samples for Case/Control Studies Problems References 3 Collecting and Entering Data 3.1 Initial Steps 3.1.1 Decide What Data You Need 3.1.2 Deciding How to Collect the Data 3.1.3 Testing the Collection Process 3.2 Data Entry 3.3 Screening the Data 3.4 Code Book Problems References 4 Frequency Tables and Their Graphs 4.1 Numerical Methods of Organizing Data 4.1.1 An Ordered Array 4.1.2 Stem and Leaf Tables 4.1.3 The Frequency Table 4.1.4 Relative Frequency Tables 4.2 Graphs 4.2.1 The Histogram: Equal Class Intervals 4.2.2 The Histogram: Unequal Class Intervals 4.2.3 Areas Under the Histogram 4.2.4 The Frequency Polygon 4.2.5 Histograms with Small Class Intervals 4.2.6 Distribution Curves Problems References 5 Measures of Location and Variability 5.1 Measures of Location 5.1.1 The Arithmetic Mean 5.1.2 The Median 5.1.3 Other Measures of Location 5.2 Measures of Variability 5.2.1 The Variance and the Standard Deviation 5.2.2 Other Measures of Variability 5.3 Sampling Properties of the Mean and Variance 5.4 Considerations in Selecting Appropriate Statistics 5.4.1 Relating Statistics and Study Objectives 5.4.2 Relating Statistics and Data Quality 5.4.3 Relating Statistics to the Type of Data 5.5 A Common Graphical Method for Displaying Statistics Problems References 6 The Normal Distribution 6.1 Properties of the Normal Distribution 6.2 Areas Under the Normal Curve 6.2.1 Computing the Area Under a Normal Curve 6.2.2 Linear Interpolation 6.2.3 Interpreting Areas as Probabilities 6.3 Importance of the Normal Distribution 6.4 Examining Data for Normality 6.4.1 Using Histograms and Box Plots 6.4.2 Using Normal Probability Plots or Quantile-Quantile Plots 6.5 Transformations 6.5.1 Finding a Suitable Transformation 6.5.2 Assessing the Need for a Transformation Problems References 7 Estimation of Population Means: Confidence Intervals 7.1 Confidence Intervals 7.1.1 An Example 7.1.2 Definition of Confidence Interval 7.1.3 Choice of Confidence Level 7.2 Sample Size Needed for a Desired Confidence Interval 7.3 The t Distribution 7.4 Confidence Interval for the Mean Using the t Distribution 7.5 Estimating the Difference Between Two Means: Unpaired Data 7.5.1 The Distribution of X1 – X2 7.5.2 Confidence Intervals for μ1 – μ2: Known Variance 7.5.3 Confidence Intervals for μ1 – μ2: Unknown Variance 7.6 Estimating the Difference Between Two Means: Paired Comparison Problems References 8 Tests of Hypotheses on Population Means 8.1 Tests of Hypotheses for a Single Mean 8.1.1 Test for a Single Mean When σ Is Known 8.1.2 One-sided Tests When σ Is Known 8.1.3 Summary of Procedures for Test of Hypotheses 8.1.4 Test for a Single Mean When σ Is Unknown 8.2 Tests for Equality of two Means: Unpaired Data 8.2.1 Testing for Equality of Means When σ Is Known 8.2.2 Testing for Equality of Means When σ Is Unknown 8.3 Testing for Equality of Means: Paired Data 8.4 Concepts Used in Statistical Testing 8.4.1 Decision to Accept or Reject 8.4.2 Two Kinds of Error 8.4.3 An Illustration of β 8.5 Sample Size 8.6 Confidence Intervals Versus Tests 8.7 Correcting for Multiple Testing 8.8 Reporting the Results Problems References 9 Variances: Estimation and Tests 9.1 Point Estimates for Variances and Standard Deviations 9.2 Testing Whether Two Variances Are Equal: F Test 9.3 Approximate t Test 9.4 Other Tests Problems References 10 Categorical Data: Proportions 10.1 Single Population Proportion 10.1.1 Graphical Displays of Proportions 10.2 Samples from Categorical Data 10.3 The Normal Approximation to the Binomial 10.3.1 Use of the Normal Approximation to the Binomial 10.3.2 Continuity Correction 10.4 Confidence Intervals for a Single Population Proportion 10.5 Confidence Intervals for the Difference in Two Proportions 10.6 Tests of Hypothesis for Population Proportions 10.6.1 Tests of Hypothesis for a Single Population Proportion 10.6.2 Testing the Equality of Two Population Proportions 10.7 Sample Size for Testing Two Proportions 10.8 Data Entry and Analysis Using Statistical Programs Problems References 11 Categorical Data: Analysis of Two-way Frequency Tables 11.1 Different Types of Tables 11.1.1 Tables Based on a Single Sample 11.1.2 Tables Based on Two Samples 11.1.3 Tables Based on Matched or Paired Samples 11.1.4 Relationship Between Type of Study Design and Type of Table 11.2 Relative Risk and Odds Ratio 11.2.1 Relative Risk 11.2.2 Odds Ratios 11.3 Chi-Square Tests for Frequency Tables: Two-by-Two Tables 11.3.1 Chi-Square Test for a Single Sample: Two-by-Two Tables 11.3.2 Chi-Square Test for Two Samples: Two-by-Two Tables 11.3.3 Chi-Square Test for Matched Samples: Two-by-Two Tables 11.3.4 Assumptions for the Chi-Square Test 11.3.5 Necessary Sample Size: Two-by-Two Tables 11.3.6 The Continuity Correction: Two-by-Two Tables 11.4 Chi-Square Tests for Larger Tables 11.4.1 Chi-Square for Larger Tables: Single Sample 11.4.2 Interpreting a Significant Test 11.4.3 Chi-Square Test for Larger Tables; More Than Two Samples or Outcomes 11.4.4 Necessary Sample Size for Large Tables 11.5 Remarks Problems References 12 Regression and Correlation 12.1 The Scatter Diagram: Single Sample 12.2 Linear Regression: Single Sample 12.2.1 Least-Squares Regression Line 12.2.2 Interpreting the Regression Coefficients 12.2.3 Plotting the Regression Line 12.2.4 The Meaning of the Least-Squares Line 12.2.5 The Variance of the Residuals 12.2.6 Model Underlying Single-Sample Linear Regression 12.2.7 Confidence Intervals in Single-Sample Linear Regression 12.2.8 Tests of Hypotheses for Regression Line from a Single Samde 12.3 The Correlation Coefficient for Two Variables From a Single Sample 12.3.1 Calculation of the Correlation Coefficient 12.3.2 The Meaning of the Correlation Coefficient 12.3.3 The Population Correlation Coefficient 12.3.4 Confidence Intervals for the Correlation Coefficient 12.3.5 Test of Hypothesis That p = 0 12.3.6 Interpreting the Correlation Coefficient 12.4 Linear Regression Assuming the Fixed-X Model 12.4.1 Model Underlying the Fixed-X Linear Regression 12.4.2 Linear Regression Using the Fixed-X Model 12.5 Other Topics in Linear Regression 12.5.1 Use of Transformations in Linear Regression 12.5.2 Effect of Outliers from the Regression Line 12.5.3 Multiple Regression Problems References 13 Nonparametric Statistics 13.1 The Sign Test 13.1.1 Sign Test for Large Samples 13.1.2 Sign Test When the Sample Size Is Small 13.2 The Wilcoxon Signed Ranks Test 13.2.1 Wilcoxon Signed Ranks Test for Large Samples 13.2.2 Wilcoxon Signed Ranks Test for Small Samples 13.3 The Wilcoxon-Mann-Whitney Test 13.3.1 Wilcoxon Rank Sum Test for Large Samples 13.3.2 Wilcoxon Rank Sum Test for Small Samples 13.4 Spearman's Rank Correlation Problems References 14 Introduction to Survival Analysis 14.1 Survival Analysis Data 14.1.1 Describing Time to an Event 14.1.2 Example of Measuring Time to an Event 14.2 Survival Functions 14.2.1 The Death Density Function 14.2.2 The Cumulative Death Distribution Function 14.2.3 The Survival Function 14.2.4 The Hazard Function 14.3 Computing Estimates of f(t), S(t), and h(t) 14.3.1 Clinical Life Tables 14.3.2 Kaplan-Meier Estimate 14.4 Comparison of Clinical Life Tables and the Kaplan-Meier Method 14.5 Additional Analyses Using Survival Data 14.5.1 Comparing the Equality of Survival Functions 14.5.2 Regression Analysis of Survival Data Problems References Appendix A: Statistical Tables Appendix B: Answers to Selected Problems Appendix C: Computer Statistical Program Resources C.1 Computer Systems for Biomedical Education and Research C.2 A Brief Indication of Statistics Computer Program Advances and Some Relevant Publications Since 2000 C.3 Choices of Computer Statistical Software Bibliography Index