Introductory Statistics and Analytics

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