Common Errors in Statistics (and How to Avoid Them) (eBook)

PHILLIP I. GOOD, PhD, is Operations Manager of Statcourse.com, a consulting firm specializing in statistical solutions for industry. He has published more than thirty scholarly works, more than six hundred popular articles, and twenty-one books, including Introduction to Statistics Through Resampling Methods and R/S-PLUS and Introduction to Statistics Through Resampling Methods and Microsoft Office Excel, both published by Wiley. JAMES W. HARDIN, PhD, is Research Associate Professor and Director of the Biostatistics Collaborative Unit at the University of South Carolina.

PREFACE xi

PART I FOUNDATIONS 1

1 Sources of Error 3

Prescription, 4

Fundamental Concepts, 5

Ad Hoc, Post Hoc Hypotheses, 7

To Learn More, 11

2 Hypotheses: The Why of Your Research 13

Prescription, 13

What is a Hypothesis?, 14

Found Data, 16

Null Hypothesis, 16

Neyman-Pearson Theory, 17

Deduction and Induction, 21

Losses, 22

Decisions, 23

To Learn More, 25

3 Collecting Data 27

Preparation, 27

Response Variables, 28

Determining Sample Size, 32

Sequential Sampling, 36

One-Tail or Two?, 37

Fundamental Assumptions, 40

Experimental Design, 41

Four Guidelines, 43

Are Experiments Really Necessary?, 46

To Learn More, 47

PART II STATISTICAL ANALYSIS 49

4 Data Quality Assessment 51

Objectives, 52

Review the Sampling Design, 52

Data Review, 53

The Four-Plot, 55

To Learn More, 55

5 Estimation 57

Prevention, 57

Desirable and Not-So-Desirable Estimators, 57

Interval Estimates, 61

Improved Results, 65

Summary, 66

To Learn More, 66

6 Testing Hypotheses: Choosing a Test Statistic 67

First Steps, 68

Test Assumptions, 70

Binomial Trials, 71

Categorical Data, 72

Time-to-Event Data (Survival Analysis), 73

Comparing the Means of Two Sets of Measurements, 76

Comparing Variances, 85

Comparing the Means of k Samples, 89

Subjective Data, 91

Independence Versus Correlation, 91

Higher-Order Experimental Designs, 92

Inferior Tests, 96

Multiple Tests, 97

Before You Draw Conclusions, 97

Summary, 99

To Learn More, 99

7 Miscellaneous Statistical Procedures 101

Bootstrap, 102

Bayesian Methodology, 103

Meta-Analysis, 110

Permutation Tests, 112

To Learn More, 113

PART III REPORTS 115

8 Reporting Your Results 117

Fundamentals, 117

Descriptive Statistics, 122

Standard Error, 127

p-Values, 130

Confidence Intervals, 131

Recognizing and Reporting Biases, 133

Reporting Power, 135

Drawing Conclusions, 135

Summary, 136

To Learn More, 136

9 Interpreting Reports 139

With a Grain of Salt, 139

The Analysis, 141

Rates and Percentages, 145

Interpreting Computer Printouts, 146

To Learn More, 146

10 Graphics 149

The Soccer Data, 150

Five Rules for Avoiding Bad Graphics, 150

One Rule for Correct Usage of Three-Dimensional Graphics, 159

The Misunderstood and Maligned Pie Chart, 161

Two Rules for Effective Display of Subgroup Information, 162

Two Rules for Text Elements in Graphics, 166

Multidimensional Displays, 167

Choosing Graphical Displays, 170

Summary, 172

To Learn More, 172

PART IV BUILDING A MODEL 175

11 Univariate Regression 177

Model Selection, 178

Stratification, 183

Estimating Coefficients, 185

Further Considerations, 187

Summary, 191

To Learn More, 192

12 Alternate Methods of Regression 193

Linear Versus Non-Linear Regression, 194

Least Absolute Deviation Regression, 194

Errors-in-Variables Regression, 196

Quantile Regression, 199

The Ecological Fallacy, 201

Nonsense Regression, 202

Summary, 202

To Learn More, 203

13 Multivariable Regression 205

Caveats, 205

Correcting for Confounding Variables, 207

Keep It Simple, 207

Dynamic Models, 208

Factor Analysis, 208

Reporting Your Results, 209

A Conjecture, 211

Decision Trees, 211

Building a Successful Model, 214

To Learn More, 215

14 Modeling Correlated Data 217

Common Sources of Error, 218

Panel Data, 218

Fixed- and Random-Effects Models, 219

Population-Averaged GEEs, 219

Quick Reference for Popular Panel Estimators, 221

To Learn More, 223

15 Validation 225

Objectives, 225

Methods of Validation, 226

Measures of Predictive Success, 229

Long-Term Stability, 231

To Learn More, 231

GLOSSARY, GROUPED BY RELATED BUT DISTINCT TERMS 233

BIBLIOGRAPHY 237

AUTHOR INDEX 259

SUBJECT INDEX 267

"The new edition incorporates more graphics and examples using more
recent data. ... Good's advice is usually wise, and always
worth considering. Recommended as stimulating reading for the
statistical sophisticate." (Journal of Biopharmaceutical
Statistics, January 2010)