Introductory Statistics and Analytics (eBook)

Peter C. Bruce is President and Founder of the Institute for Statistics Education at www.statistics.com. He has written multiple journal articles and is the developer of Resampling Stats software. Mr. Bruce is the coauthor of Data Mining for Business Intelligence: Concepts, Techniques, and Applications in Microsoft Office Excel with XLMiner¯®, Second Edition, also published by Wiley.

Preface ix

Acknowledgments xi

Introduction xiii

1 Designing and Carrying Out a Statistical Study 1

1.1 A Small Example, 3

1.2 Is Chance Responsible? The Foundation of Hypothesis Testing, 3

1.3 A Major Example, 7

1.4 Designing an Experiment, 8

1.5 What to Measure--Central Location, 13

1.6 What to Measure--Variability, 16

1.7 What to Measure--Distance (Nearness), 19

1.8 Test Statistic, 21

1.9 The Data, 22

1.10 Variables and Their Flavors, 28

1.11 Examining and Displaying the Data, 31

1.12 Are we Sure we Made a Difference? 39

Appendix: Historical Note, 39

1.13 Exercises, 40

2 Statistical Inference 45

2.1 Repeating the Experiment, 46

2.2 How Many Reshuffles? 48

2.3 How Odd is Odd? 53

2.4 Statistical and Practical Significance, 55

2.5 When to use Hypothesis Tests, 56

2.6 Exercises, 56

3 Displaying and Exploring Data 59

3.1 Bar Charts, 59

3.2 Pie Charts, 61

3.3 Misuse of Graphs, 62

3.4 Indexing, 64

3.5 Exercises, 68

4 Probability 71

4.1 Mendel's Peas, 72

4.2 Simple Probability, 73

4.3 Random Variables and their Probability Distributions, 77

4.4 The Normal Distribution, 80

4.5 Exercises, 84

5 Relationship between Two Categorical Variables 87

5.1 Two-Way Tables, 87

5.2 Comparing Proportions, 90

5.3 More Probability, 92

5.4 From Conditional Probabilities to Bayesian Estimates, 95

5.5 Independence, 97

5.6 Exploratory Data Analysis (EDA), 99

5.7 Exercises, 100

6 Surveys and Sampling 104

6.1 Simple Random Samples, 105

6.2 Margin of Error: Sampling Distribution for a Proportion, 109

6.3 Sampling Distribution for a Mean, 111

6.4 A Shortcut--the Bootstrap, 113

6.5 Beyond Simple Random Sampling, 117

6.6 Absolute Versus Relative Sample Size, 120

6.7 Exercises, 120

7 Confidence Intervals 124

7.1 Point Estimates, 124

7.2 Interval Estimates (Confidence Intervals), 125

7.3 Confidence Interval for a Mean, 126

7.4 Formula-Based Counterparts to the Bootstrap, 126

7.5 Standard Error, 132

7.6 Confidence Intervals for a Single Proportion, 133

7.7 Confidence Interval for a Difference in Means, 136

7.8 Confidence Interval for a Difference in Proportions, 139

7.9 Recapping, 140

Appendix A: More on the Bootstrap, 141

Resampling Procedure--Parametric Bootstrap, 141

Formulas and the Parametric Bootstrap, 144

Appendix B: Alternative Populations, 144

Appendix C: Binomial Formula Procedure, 144

7.10 Exercises, 147

8 Hypothesis Tests 151

8.1 Review of Terminology, 151

8.2 A-B Tests: The Two Sample Comparison, 154

8.3 Comparing Two Means, 156

8.4 Comparing Two Proportions, 157

8.5 Formula-Based Alternative--t-Test for Means, 159

8.6 The Null and Alternative Hypotheses, 160

8.7 Paired Comparisons, 163

Appendix A: Confidence Intervals Versus Hypothesis Tests, 167

Confidence Interval, 168

Relationship Between the Hypothesis Test and the Confidence Interval, 169

Comment, 170

Appendix B: Formula-Based Variations of Two-Sample Tests, 170

Z-Test With Known Population Variance, 170

Pooled Versus Separate Variances, 171

Formula-Based Alternative: Z-Test for Proportions, 172

8.8 Exercises, 172

9 Hypothesis Testing--2 178

9.1 A Single Proportion, 178

9.2 A Single Mean, 180

9.3 More Than Two Categories or Samples, 181

9.4 Continuous Data, 187

9.5 Goodness-of-Fit, 187

Appendix: Normal Approximation; Hypothesis Test of a Single Proportion, 190

Confidence Interval for a Mean, 190

9.6 Exercises, 191

10 Correlation 193

10.1 Example: Delta Wire, 194

10.2 Example: Cotton Dust and Lung Disease, 195

10.3 The Vector Product and Sum Test, 196

10.4 Correlation Coefficient, 199

10.5 Other Forms of Association, 204

10.6 Correlation is not Causation, 205

10.7 Exercises, 206

11 Regression 209

11.1 Finding the Regression Line by Eye, 210

11.2 Finding the Regression Line by Minimizing Residuals, 212

11.3 Linear Relationships, 213

11.4 Inference for Regression, 217

11.5 Exercises, 221

12 Analysis of Variance--ANOVA 224

12.1 Comparing More Than Two Groups: ANOVA, 225

12.2 The Problem of Multiple Inference, 228

12.3 A Single Test, 229

12.4 Components of Variance, 230

12.5 Two-Way ANOVA, 240

12.6 Factorial Design, 246

12.7 Exercises, 248

13 Multiple Regression 251

13.1 Regression as Explanation, 252

13.2 Simple Linear Regression--Explore the Data First, 253

13.3 More Independent Variables, 257

13.4 Model Assessment and Inference, 261

13.5 Assumptions, 267

13.6 Interaction, Again, 270

13.7 Regression for Prediction, 272

13.8 Exercises, 277

Index 283

"The book is an excellent primary textbook for courses in preliminary statistics as well as a supplement for courses in upper-level statistics and related fields, such as biostatistics and econometrics. The book is also a general reference for readers interested in revisiting the value of statistics." (Zentralblatt MATH, 1 April 2015)