Statistics for Compensation: A Practical Guide to Compensation Analysis

Preface xiii

Chapter 1 Introduction 1

1.1 Why do Statistical Analysis? 2

Example Analysis 3

1.2 Statistics 5

1.3 Numbers Raise Issues 6

1.4 Behind Every Data Point, There Is a Story 8

1.5 Aggressive Inquisitiveness 9

1.6 Model Building Framework 9

Example Model 10

1.7 Data Sets 10

1.8 Prerequisites 11

Chapter 2 Basic Notions 13

2.1 Percent 14

Graphical Displays of Percents 16

2.2 Percent Difference 21

2.3 Compound Interest 23

Future Value 24

Present Value 26

Translating 27

Practice Problems 28

Chapter 3 Frequency Distributions and Histograms 31

3.1 Definitions and Construction 41

Rules for Categories 43

3.2 Comparing Distributions 48

Absolute Comparison and Relative Comparison 48

Comparing More Than Two Distributions 50

3.3 Information Loss and Comprehension Gain 51

3.4 Category Selection 51

3.5 Distribution Shapes 54

Uniform Distribution 55

Bell-Shaped Distribution 55

Normal Distribution 56

Skewed Distribution 59

Bimodal Distribution 60

Practice Problems 62

Chapter 4 Measures of Location 67

4.1 Mode 67

4.2 Median 68

4.3 Mean 70

4.4 Trimmed Mean 73

4.5 Overall Example and Comparison 73

Comparison 75

4.6 Weighted and Unweighted Average 76

Which Measure to Use? 78

Application of Weighted Averages to Salary Increase Guidelines 80

4.7 Simpson’s Paradox 82

4.8 Percentile 85

Reverse Percentile 88

4.9 Percentile Bars 90

Practice Problems 92

Chapter 5 Measures of Variability 95

5.1 Importance of Knowing Variability 95

5.2 Population and Sample 96

Examples of Populations 96

Examples of Samples and Populations 96

5.3 Types of Samples 97

5.4 Standard Deviation 98

Interpretations and Applications of Standard Deviation 100

5.5 Coefficient of Variation 107

Interpretations and Applications of Coefficient of Variation 108

5.6 Range 109

Interpretations and Applications of Range 109

5.7 P90/P10 110

Interpretations and Applications of P90/P10 111

5.8 Comparison and Summary 112

Practice Problems 115

Chapter 6 Model Building 119

6.1 Prelude to Models 119

6.2 Introduction 120

6.3 Scientific Method 122

6.4 Models 123

6.5 Model Building Process 126

Plotting Points 128

Functional Forms 132

Method of Least Squares 136

Practice Problems 138

Chapter 7 Linear Model 141

7.1 Examples 141

7.2 Straight Line Basics 143

Interpretations of Intercept and Slope 144

Using the Equation 145

7.3 Fitting the Line to the Data 147

What We Are Predicting 148

Interpretations of Intercept and Slope 149

7.4 Model Evaluation 149

Appearance 150

Coefficient of Determination 150

Correlation 152

Standard Error of Estimate 154

Common Sense 154

7.5 Summary of Interpretations and Evaluation 155

7.6 Cautions 155

7.7 Digging Deeper 158

7.8 Keep the Horse before the Cart 160

Practice Problems 164

Chapter 8 Exponential Model 167

8.1 Examples 167

8.2 Logarithms 168

Antilogs 170

Scales 170

Why Logarithms? 171

8.3 Exponential Model 172

8.4 Model Evaluation 176

Appearance 176

Coefficient of Determination 177

Correlation 177

Standard Error of Estimate 177

Common Sense 178

Summary of Evaluation 178

Practice Problems 178

Chapter 9 Maturity Curve Model 181

9.1 Maturity Curves 181

9.2 Building the Model 184

Cubic Model 184

Cubic Model Evaluation 186

Spline Model 187

Spline Model Evaluation 188

9.3 Comparison of Models 190

Practice Problems 190

Chapter 10 Power Model 193

10.1 Building the Model 193

10.2 Model Evaluation 197

Appearance 197

Coefficient of Determination 198

Correlation 198

Standard Error of Estimate 198

Common Sense 199

Summary of Evaluation 199

Practice Problems 200

Chapter 11 Market Models and Salary Survey Analysis 201

11.1 Introduction 201

11.2 Commonalities of Approaches 203

11.3 Final Market-Based Salary Increase Budget 205

Initial Market-Based Salary Increase Budget and Market Position 205

Final Market-Based Salary Increase Budget 206

Raises Given Throughout the Year 206

Raises Given on a Common Date 208

11.4 Other Factors Influencing the Final Salary Increase Budget Recommendation 210

Assumptions 211

11.5 Salary Structure 211

Practice Problems 213

Chapter 12 Integrated Market Model: Linear 215

12.1 Gather Market Data 215

12.2 Age Data to a Common Date 217

12.3 Create an Integrated Market Model 217

Interpretations 219

12.4 Compare Employee Pay with Market Model 222

Practice Problems 228

Chapter 13 Integrated Market Model: Exponential 233

Practice Problems 246

Chapter 14 Integrated Market Model: Maturity Curve 251

Practice Problems 261

Chapter 15 Job Pricing Market Model: Group of Jobs 265

Practice Problems 272

Chapter 16 Job Pricing Market Model: Power Model 277

Practice Problems 280

Chapter 17 Multiple Linear Regression 283

17.1 What It Is 283

17.2 Similarities and Differenceswith Simple Linear Regression 284

17.3 Building the Model 285

First x-Variable 292

Second x-Variable 295

Standardized Coefficient 298

Third x-Variable 300

Multicollinearity 301

17.4 Model Evaluation 305

Regression Coefficients 305

Standardized Coefficients 306

Coefficient of Determination 306

Standard Error of Estimate 306

Multicollinearity 306

Simplicity 307

Common Sense 307

Acceptability 307

Reality 307

Decision 307

17.5 Mixed Messages in Evaluating A Model 308

r² Versus Common Sense 308

r² Versus Simplicity 308

Simplicity Versus Acceptability 308

17.6 Summary of Regressions 308

17.7 Digging Deeper 310

Summary 315

Practice Problems 317

Appendix 319

A.1 Value Exchange Theory 319

Achieving Organization Goals 319

Value Exchange 319

A Fair Value Exchange Is a Good Deal 320

A.2 Factors Determining a Person’s Pay 321

System Factors 322

Individual Factors 323

A.3 Types of Numbers 324

Definitions and Properties 324

Histograms with All Four Types of Measurements 327

A.4 Significant Figures 330

A.5 Scientific Notation 331

A.6 Accuracy and Precision 332

Which Is More Important? 333

A.7 Compound Interest–Additional 333

Other Formulas 333

A.8 Rule of 72 334

Derivation of the Rule of 72 335

A.9 Normal Distribution 336

Central Limit Theorem 337

Distribution of Salary Survey Data 338

A.10 Linear Regression Technical Note 338

A.11 Formulas for Regression Terms 340

A.12 Logarithmic Conversion 340

A.13 Range Spread Relationships 340

Overlap 343

A.14 Statistical Inference in Regression 344

t-Statistic and Its Probability 347

F-Statistic and Its Probability 348

Mixed Messages in Evaluating a Model 349

A.15 Additional Multiple Linear Regression Topics 349

Adjusted r2 349

Coding of Indicator Variables 350

Interaction Terms 351

GLOSSARY 357

REFERENCES 369

ANSWERS TO PRACTICE PROBLEMS 371

INDEX 433