# Illuminating Statistical Analysis Using Scenarios and Simulations

## Books

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.

• 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

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