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Introduction to Biostatistical Applications in Health Research with Microsoft (R) Office Excel
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#### Table of Contents

PREFACE ix ACKNOWLEDGEMENTS xi NOTICES xiii ABOUT THE COMPANION WEBSITE xv PART ONE BASIC CONCEPTS 1 1 THINKING ABOUT CHANCE 3 1.1 Properties of Probability / 3 1.2 Combinations of Events / 7 1.2.1 Intersections / 8 1.2.2 Unions / 13 1.3 Bayes' Theorem / 15 2 DESCRIBING DISTRIBUTIONS 18 2.1 Types of Data / 19 2.2 Describing Distributions Graphically / 19 2.2.1 Graphing Discrete Data / 20 2.2.2 Graphing Continuous Data / 22 2.3 Describing Distributions Mathematically / 26 2.3.1 Parameter of Location / 27 2.3.2 Parameter of Dispersion / 31 2.4 Taking Chance into Account / 38 2.4.1 Standard Normal Distribution / 39 3 EXAMINING SAMPLES 49 3.1 Nature of Samples / 50 3.2 Estimation / 51 3.2.1 Point Estimates / 51 3.2.2 The Sampling Distribution / 56 3.2.3 Interval Estimates / 60 3.3 Hypothesis Testing / 64 3.3.1 Relationship between Interval Estimation and Hypothesis Testing / 72 PART TWO UNIVARIABLE ANALYSES 75 4 UNIVARIABLE ANALYSIS OF A CONTINUOUS DEPENDENT VARIABLE 79 4.1 Student's t-Distribution / 81 4.2 Interval Estimation / 84 4.3 Hypothesis Testing / 86 5 UNIVARIABLE ANALYSIS OF AN ORDINAL DEPENDENT VARIABLE 90 5.1 Nonparametric Methods / 90 5.2 Estimation / 94 5.3 Wilcoxon Signed-Rank Test / 95 5.4 Statistical Power of Nonparametric Tests / 97 6 UNIVARIABLE ANALYSIS OF A NOMINAL DEPENDENT VARIABLE 99 6.1 Distribution of Nominal Data / 100 6.2 Point Estimates / 101 6.2.1 Proportions / 101 6.2.2 Rates / 104 6.3 Sampling Distributions / 108 6.3.1 Binomial Distribution / 108 6.3.2 Poisson Distribution / 112 6.4 Interval Estimation / 114 6.5 Hypothesis Testing / 117 PART THREE BIVARIABLE ANALYSES 121 7 BIVARIABLE ANALYSIS OF A CONTINUOUS DEPENDENT VARIABLE 123 7.1 Continuous Independent Variable / 123 7.1.1 Regression Analysis / 125 7.1.2 Correlation Analysis / 149 7.2 Ordinal Independent Variable / 165 7.3 Nominal Independent Variable / 166 7.3.1 Estimating the Difference between the Groups / 166 7.3.2 Taking Chance into Account / 167 8 BIVARIABLE ANALYSIS OF AN ORDINAL DEPENDENT VARIABLE 175 8.1 Ordinal Independent Variable / 176 8.2 Nominal Independent Variable / 184 9 BIVARIABLE ANALYSIS OF A NOMINAL DEPENDENT VARIABLE 189 9.1 Continuous Independent Variable / 190 9.1.1 Estimation / 191 9.1.2 Hypothesis Testing / 198 9.2 Nominal Independent Variable / 200 9.2.1 Dependent Variable Not Affected by Time: Unpaired Design / 201 9.2.2 Hypothesis Testing / 208 9.2.3 Dependent Variable Not Affected by Time: Paired Design / 218 9.2.4 Dependent Variable Affected by Time / 223 PART FOUR MULTIVARIABLE ANALYSES 227 10 MULTIVARIABLE ANALYSIS OF A CONTINUOUS DEPENDENT VARIABLE 229 10.1 Continuous Independent Variables / 230 10.1.1 Multiple Regression Analysis / 231 10.1.2 Multiple Correlation Analysis / 247 10.2 Nominal Independent Variables / 248 10.2.1 Analysis of Variance / 249 10.2.2 Posterior Testing / 258 10.3 Both Continuous and Nominal Independent Variables / 265 10.3.1 Indicator (Dummy) Variables / 266 10.3.2 Interaction Variables / 267 10.3.3 General Linear Model / 273 11 MULTIVARIABLE ANALYSIS OF AN ORDINAL DEPENDENT VARIABLE 281 11.1 Nonparametric Analysis of Variance / 282 11.2 Posterior Testing / 288 12 MULTIVARIABLE ANALYSIS OF A NOMINAL DEPENDENT VARIABLE 293 12.1 Continuous And/or Nominal Independent Variables / 294 12.1.1 Maximum Likelihood Estimation / 294 12.1.2 Logistic Regression Analysis / 297 12.1.3 Cox Regression Analysis / 306 12.2 Nominal Independent Variables / 307 12.2.1 Stratified Analysis / 308 12.2.2 Relationship between Stratified Analysis and Logistic Regression / 318 12.2.3 Life Table Analysis / 322 APPENDIX A: FLOWCHARTS 335 APPENDIX B: STATISTICAL TABLES 341 APPENDIX C: STANDARD DISTRIBUTIONS 377 APPENDIX D: EXCEL PRIMER 380 INDEX 385

#### About the Author

Robert P. Hirsch, PhD, is on the faculty for the Foundation for the Advanced Education in the Sciences within the Graduate School at the National Institutes of Health. He is also a retired Professor of Epidemiology and Biostatistics and Adjunct Professor of Statistics at The George Washington University. Dr. Hirsch is the author of numerous books in the field of health research and practice.

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