Statistics for Compensation

JOHN H. DAVIS, PhD, is a Certified Compensation Professional and President of Davis Consulting, where he has consulted on salary surveys, statistics, base pay programs, incentive programs, and performance management programs for numerous Fortune 1000–size organizations. He has taught undergraduate and graduate statistics courses and, for the past three decades, has taught thousands of compensation and human resources professionals statistics and its application to common problems in their fields.

• Preface xiiiChapter 1 Introduction 11.1 Why do Statistical Analysis? 2Example Analysis 31.2 Statistics 51.3 Numbers Raise Issues 61.4 Behind Every Data Point, There Is a Story 81.5 Aggressive Inquisitiveness 91.6 Model Building Framework 9Example Model 101.7 Data Sets 101.8 Prerequisites 11Chapter 2 Basic Notions 132.1 Percent 14Graphical Displays of Percents 162.2 Percent Difference 212.3 Compound Interest 23Future Value 24Present Value 26Translating 27Practice Problems 28Chapter 3 Frequency Distributions and Histograms 313.1 Definitions and Construction 41Rules for Categories 433.2 Comparing Distributions 48Absolute Comparison and Relative Comparison 48Comparing More Than Two Distributions 503.3 Information Loss and Comprehension Gain 513.4 Category Selection 513.5 Distribution Shapes 54Uniform Distribution 55Bell-Shaped Distribution 55Normal Distribution 56Skewed Distribution 59Bimodal Distribution 60Practice Problems 62Chapter 4 Measures of Location 674.1 Mode 674.2 Median 684.3 Mean 704.4 Trimmed Mean 734.5 Overall Example and Comparison 73Comparison 754.6 Weighted and Unweighted Average 76Which Measure to Use? 78Application of Weighted Averages to Salary Increase Guidelines 804.7 Simpson’s Paradox 824.8 Percentile 85Reverse Percentile 884.9 Percentile Bars 90Practice Problems 92Chapter 5 Measures of Variability 955.1 Importance of Knowing Variability 955.2 Population and Sample 96Examples of Populations 96Examples of Samples and Populations 965.3 Types of Samples 975.4 Standard Deviation 98Interpretations and Applications of Standard Deviation 1005.5 Coefficient of Variation 107Interpretations and Applications of Coefficient of Variation 1085.6 Range 109Interpretations and Applications of Range 1095.7 P90/P10 110Interpretations and Applications of P90/P10 1115.8 Comparison and Summary 112Practice Problems 115Chapter 6 Model Building 1196.1 Prelude to Models 1196.2 Introduction 1206.3 Scientific Method 1226.4 Models 1236.5 Model Building Process 126Plotting Points 128Functional Forms 132Method of Least Squares 136Practice Problems 138Chapter 7 Linear Model 1417.1 Examples 1417.2 Straight Line Basics 143Interpretations of Intercept and Slope 144Using the Equation 1457.3 Fitting the Line to the Data 147What We Are Predicting 148Interpretations of Intercept and Slope 1497.4 Model Evaluation 149Appearance 150Coefficient of Determination 150Correlation 152Standard Error of Estimate 154Common Sense 1547.5 Summary of Interpretations and Evaluation 1557.6 Cautions 1557.7 Digging Deeper 1587.8 Keep the Horse before the Cart 160Practice Problems 164Chapter 8 Exponential Model 1678.1 Examples 1678.2 Logarithms 168Antilogs 170Scales 170Why Logarithms? 1718.3 Exponential Model 1728.4 Model Evaluation 176Appearance 176Coefficient of Determination 177Correlation 177Standard Error of Estimate 177Common Sense 178Summary of Evaluation 178Practice Problems 178Chapter 9 Maturity Curve Model 1819.1 Maturity Curves 1819.2 Building the Model 184Cubic Model 184Cubic Model Evaluation 186Spline Model 187Spline Model Evaluation 1889.3 Comparison of Models 190Practice Problems 190Chapter 10 Power Model 19310.1 Building the Model 19310.2 Model Evaluation 197Appearance 197Coefficient of Determination 198Correlation 198Standard Error of Estimate 198Common Sense 199Summary of Evaluation 199Practice Problems 200Chapter 11 Market Models and Salary Survey Analysis 20111.1 Introduction 20111.2 Commonalities of Approaches 20311.3 Final Market-Based Salary Increase Budget 205Initial Market-Based Salary Increase Budget and Market Position 205Final Market-Based Salary Increase Budget 206Raises Given Throughout the Year 206Raises Given on a Common Date 20811.4 Other Factors Influencing the Final Salary Increase Budget Recommendation 210Assumptions 21111.5 Salary Structure 211Practice Problems 213Chapter 12 Integrated Market Model: Linear 21512.1 Gather Market Data 21512.2 Age Data to a Common Date 21712.3 Create an Integrated Market Model 217Interpretations 21912.4 Compare Employee Pay with Market Model 222Practice Problems 228Chapter 13 Integrated Market Model: Exponential 233Practice Problems 246Chapter 14 Integrated Market Model: Maturity Curve 251Practice Problems 261Chapter 15 Job Pricing Market Model: Group of Jobs 265Practice Problems 272Chapter 16 Job Pricing Market Model: Power Model 277Practice Problems 280Chapter 17 Multiple Linear Regression 28317.1 What It Is 28317.2 Similarities and Differenceswith Simple Linear Regression 28417.3 Building the Model 285First x-Variable 292Second x-Variable 295Standardized Coefficient 298Third x-Variable 300Multicollinearity 30117.4 Model Evaluation 305Regression Coefficients 305Standardized Coefficients 306Coefficient of Determination 306Standard Error of Estimate 306Multicollinearity 306Simplicity 307Common Sense 307Acceptability 307Reality 307Decision 30717.5 Mixed Messages in Evaluating A Model 308r2 Versus Common Sense 308r2 Versus Simplicity 308Simplicity Versus Acceptability 30817.6 Summary of Regressions 30817.7 Digging Deeper 310Summary 315Practice Problems 317Appendix 319A.1 Value Exchange Theory 319Achieving Organization Goals 319Value Exchange 319A Fair Value Exchange Is a Good Deal 320A.2 Factors Determining a Person’s Pay 321System Factors 322Individual Factors 323A.3 Types of Numbers 324Definitions and Properties 324Histograms with All Four Types of Measurements 327A.4 Significant Figures 330A.5 Scientific Notation 331A.6 Accuracy and Precision 332Which Is More Important? 333A.7 Compound Interest–Additional 333Other Formulas 333A.8 Rule of 72 334Derivation of the Rule of 72 335A.9 Normal Distribution 336Central Limit Theorem 337Distribution of Salary Survey Data 338A.10 Linear Regression Technical Note 338A.11 Formulas for Regression Terms 340A.12 Logarithmic Conversion 340A.13 Range Spread Relationships 340Overlap 343A.14 Statistical Inference in Regression 344t-Statistic and Its Probability 347F-Statistic and Its Probability 348Mixed Messages in Evaluating a Model 349A.15 Additional Multiple Linear Regression Topics 349Adjusted r2 349Coding of Indicator Variables 350Interaction Terms 351GLOSSARY 357REFERENCES 369ANSWERS TO PRACTICE PROBLEMS 371INDEX 433

“As an experienced compensation manager for a publicly traded Fortune 500 company, I have found this book to be an all-inclusive, highly useful and infor­mative desk reference. It certainly has been extremely valuable in helping me to contribute to successful strategic decisions at my company.”  (Workspan, 1 January 2013)"The book can serve as a text for students specializing in compensation or human resources, or as a reference for practitioners. He provides worked examples throughout." (Booknews, 1 June 2011)