Illuminating Statistical Analysis Using Scenarios and Simulations

Features an integrated approach of statistical scenarios and simulations to aid readers in developing key intuitions needed to understand the wide ranging concepts and methods of statistics and inference Illuminating Statistical Analysis Using Scenarios and Simulations presents the basic concepts of statistics and statistical inference using the dual mechanisms of scenarios and simulations. This approach helps readers develop key intuitions and deep understandings of statistical analysis. Scenario-specific sampling simulations depict the results that would be obtained by a very large number of individuals investigating the same scenario, each with their own evidence, while graphical depictions of the simulation results present clear and direct pathways to intuitive methods for statistical inference. These intuitive methods can then be easily linked to traditional formulaic methods, and the author does not simply explain the linkages, but rather provides demonstrations throughout for a broad range of statistical phenomena. In addition, induction and deduction are repeatedly interwoven, which fosters a natural "need to know basis" for ordering the topic coverage. Examining computer simulation results is central to the discussion and provides an illustrative way to (re)discover the properties of sample statistics, the role of chance, and to (re)invent corresponding principles of statistical inference. In addition, the simulation results foreshadow the various mathematical formulas that underlie statistical analysis. In addition, this book: • Features both an intuitive and analytical perspective and includes a broad introduction to the use of Monte Carlo simulation and formulaic methods for statistical analysis • Presents straight-forward coverage of the essentials of basic statistics and ensures proper understanding of key concepts such as sampling distributions, the effects of sample size and variance on uncertainty, analysis of proportion, mean and rank differences, covariance, correlation, and regression • Introduces advanced topics such as Bayesian statistics, data mining, model cross-validation, robust regression, and resampling • Contains numerous example problems in each chapter with detailed solutions as well as an appendix that serves as a manual for constructing simulations quickly and easily using Microsoft® Office Excel® Illuminating Statistical Analysis Using Scenarios and Simulations is an ideal textbook for courses, seminars, and workshops in statistics and statistical inference and is appropriate for self-study as well. The book also serves as a thought-provoking treatise for researchers, scientists, managers, technicians, and others with a keen interest in statistical analysis. Jeffrey E. Kottemann, Ph.D., is Professor in the Perdue School at Salisbury University. Dr. Kottemann has published articles in a wide variety of academic research journals in the fields of business administration, computer science, decision sciences, economics, engineering, information systems, psychology, and public administration. He received his Ph.D. in Systems and Quantitative Methods from the University of Arizona.

Preface ix Acknowledgements xi Part I Sample Proportions and the Normal Distribution 1 1 Evidence and Verdicts 3 2 Judging Coins I 5 3 Brief on Bell Shapes 9 4 Judging Coins II 11 5 Amount of Evidence I 19 6 Variance of Evidence I 23 7 Judging Opinion Splits I 27 8 Amount of Evidence II 31 9 Variance of Evidence II 35 10 Judging Opinion Splits II 39 11 It Has Been the Normal Distribution All Along 45 12 Judging Opinion Split Differences 49 13 Rescaling to Standard Errors 53 14 The Standardized Normal Distribution Histogram 55 15 The z-Distribution 59 16 Brief on Two-Tail Versus One-Tail 65 17 Brief on Type I Versus Type II Errors 69 Part II Sample Means and the Normal Distribution 75 18 Scaled Data and Sample Means 77 19 Distribution of Random Sample Means 79 20 Amount of Evidence 81 21 Variance of Evidence 83 22 Homing in on the Population Mean I 87 23 Homing in on the Population Mean II 91 24 Homing in on the Population Mean III 93 25 Judging Mean Differences 95 26 Sample Size, Variance, and Uncertainty 99 27 The t-Distribution 105 Part III Multiple Proportions and Means: The X2- and F-Distributions 111 28 Multiple Proportions and the X2-Distribution 113 29 Facing Degrees of Freedom 119 30 Multiple Proportions: Goodness of Fit 121 31 Two-Way Proportions: Homogeneity 125 32 Two-Way Proportions: Independence 127 33 Variance Ratios and the F-Distribution 131 34 Multiple Means and Variance Ratios: ANOVA 137 35 Two-Way Means and Variance Ratios: ANOVA 143 Part IV Linear Associations: Covariance, Correlation, and Regression 147 36 Covariance 149 37 Correlation 153 38 What Correlations Happen Just by Chance? 155 39 Judging Correlation Differences 161 40 Correlation with Mixed Data Types 165 41 A Simple Regression Prediction Model 167 42 Using Binomials Too 171 43 A Multiple Regression Prediction Model 175 44 Loose End I (Collinearity) 179 45 Loose End II (Squaring R) 183 46 Loose End III (Adjusting R-Squared) 185 47 Reality Strikes 187 Part V Dealing with Unruly Scaled Data 193 48 Obstacles and Maneuvers 195 49 Ordered Ranking Maneuver 199 50 What Rank Sums Happen Just by Chance? 201 51 Judging Rank Sum Differences 203 52 Other Methods Using Ranks 205 53 Transforming the Scale of Scaled Data 207 54 Brief on Robust Regression 209 55 Brief on Simulation and Resampling 211 Part VI Review and Additional Concepts 213 56 For Part I 215 57 For Part II 221 58 For Part III 227 59 For Part IV 233 60 For Part V 243 Appendices 247 A Data Types and Some Basic Statistics 249 B Simulating Statistical Scenarios 253 C Standard Error as Standard Deviation 271 D Data Excerpt 273 E Repeated Measures 277 F Bayesian Statistics 281 G Data Mining 287 Index 295