Introduction to Biostatistical Applications in Health Research with Microsoft Office Excel

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