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<p>Preface xiii</p> <p><b>Chapter 1 Introduction 1</b></p> <p>1.1 Why do Statistical Analysis? 2</p> <p>Example Analysis 3</p> <p>1.2 Statistics 5</p> <p>1.3 Numbers Raise Issues 6</p> <p>1.4 Behind Every Data Point, There Is a Story 8</p> <p>1.5 Aggressive Inquisitiveness 9</p> <p>1.6 Model Building Framework 9</p> <p>Example Model 10</p> <p>1.7 Data Sets 10</p> <p>1.8 Prerequisites 11</p> <p><b>Chapter 2 Basic Notions 13</b></p> <p>2.1 Percent 14</p> <p>Graphical Displays of Percents 16</p> <p>2.2 Percent Difference 21</p> <p>2.3 Compound Interest 23</p> <p>Future Value 24</p> <p>Present Value 26</p> <p>Translating 27</p> <p>Practice Problems 28</p> <p><b>Chapter 3 Frequency Distributions and Histograms 31</b></p> <p>3.1 Definitions and Construction 41</p> <p>Rules for Categories 43</p> <p>3.2 Comparing Distributions 48</p> <p>Absolute Comparison and Relative Comparison 48</p> <p>Comparing More Than Two Distributions 50</p> <p>3.3 Information Loss and Comprehension Gain 51</p> <p>3.4 Category Selection 51</p> <p>3.5 Distribution Shapes 54</p> <p>Uniform Distribution 55</p> <p>Bell-Shaped Distribution 55</p> <p>Normal Distribution 56</p> <p>Skewed Distribution 59</p> <p>Bimodal Distribution 60</p> <p>Practice Problems 62</p> <p><b>Chapter 4 Measures of Location 67</b></p> <p>4.1 Mode 67</p> <p>4.2 Median 68</p> <p>4.3 Mean 70</p> <p>4.4 Trimmed Mean 73</p> <p>4.5 Overall Example and Comparison 73</p> <p>Comparison 75</p> <p>4.6 Weighted and Unweighted Average 76</p> <p>Which Measure to Use? 78</p> <p>Application of Weighted Averages to Salary Increase Guidelines 80</p> <p>4.7 Simpson’s Paradox 82</p> <p>4.8 Percentile 85</p> <p>Reverse Percentile 88</p> <p>4.9 Percentile Bars 90</p> <p>Practice Problems 92</p> <p><b>Chapter 5 Measures of Variability 95</b></p> <p>5.1 Importance of Knowing Variability 95</p> <p>5.2 Population and Sample 96</p> <p>Examples of Populations 96</p> <p>Examples of Samples and Populations 96</p> <p>5.3 Types of Samples 97</p> <p>5.4 Standard Deviation 98</p> <p>Interpretations and Applications of Standard Deviation 100</p> <p>5.5 Coefficient of Variation 107</p> <p>Interpretations and Applications of Coefficient of Variation 108</p> <p>5.6 Range 109</p> <p>Interpretations and Applications of Range 109</p> <p>5.7 P90/P10 110</p> <p>Interpretations and Applications of P90/P10 111</p> <p>5.8 Comparison and Summary 112</p> <p>Practice Problems 115</p> <p><b>Chapter 6 Model Building 119</b></p> <p>6.1 Prelude to Models 119</p> <p>6.2 Introduction 120</p> <p>6.3 Scientific Method 122</p> <p>6.4 Models 123</p> <p>6.5 Model Building Process 126</p> <p>Plotting Points 128</p> <p>Functional Forms 132</p> <p>Method of Least Squares 136</p> <p>Practice Problems 138</p> <p><b>Chapter 7 Linear Model 141</b></p> <p>7.1 Examples 141</p> <p>7.2 Straight Line Basics 143</p> <p>Interpretations of Intercept and Slope 144</p> <p>Using the Equation 145</p> <p>7.3 Fitting the Line to the Data 147</p> <p>What We Are Predicting 148</p> <p>Interpretations of Intercept and Slope 149</p> <p>7.4 Model Evaluation 149</p> <p>Appearance 150</p> <p>Coefficient of Determination 150</p> <p>Correlation 152</p> <p>Standard Error of Estimate 154</p> <p>Common Sense 154</p> <p>7.5 Summary of Interpretations and Evaluation 155</p> <p>7.6 Cautions 155</p> <p>7.7 Digging Deeper 158</p> <p>7.8 Keep the Horse before the Cart 160</p> <p>Practice Problems 164</p> <p><b>Chapter 8 Exponential Model 167</b></p> <p>8.1 Examples 167</p> <p>8.2 Logarithms 168</p> <p>Antilogs 170</p> <p>Scales 170</p> <p>Why Logarithms? 171</p> <p>8.3 Exponential Model 172</p> <p>8.4 Model Evaluation 176</p> <p>Appearance 176</p> <p>Coefficient of Determination 177</p> <p>Correlation 177</p> <p>Standard Error of Estimate 177</p> <p>Common Sense 178</p> <p>Summary of Evaluation 178</p> <p>Practice Problems 178</p> <p><b>Chapter 9 Maturity Curve Model 181</b></p> <p>9.1 Maturity Curves 181</p> <p>9.2 Building the Model 184</p> <p>Cubic Model 184</p> <p>Cubic Model Evaluation 186</p> <p>Spline Model 187</p> <p>Spline Model Evaluation 188</p> <p>9.3 Comparison of Models 190</p> <p>Practice Problems 190</p> <p><b>Chapter 10 Power Model 193</b></p> <p>10.1 Building the Model 193</p> <p>10.2 Model Evaluation 197</p> <p>Appearance 197</p> <p>Coefficient of Determination 198</p> <p>Correlation 198</p> <p>Standard Error of Estimate 198</p> <p>Common Sense 199</p> <p>Summary of Evaluation 199</p> <p>Practice Problems 200</p> <p><b>Chapter 11 Market Models and Salary Survey Analysis 201</b></p> <p>11.1 Introduction 201</p> <p>11.2 Commonalities of Approaches 203</p> <p>11.3 Final Market-Based Salary Increase Budget 205</p> <p>Initial Market-Based Salary Increase Budget and Market Position 205</p> <p>Final Market-Based Salary Increase Budget 206</p> <p>Raises Given Throughout the Year 206</p> <p>Raises Given on a Common Date 208</p> <p>11.4 Other Factors Influencing the Final Salary Increase Budget Recommendation 210</p> <p>Assumptions 211</p> <p>11.5 Salary Structure 211</p> <p>Practice Problems 213</p> <p><b>Chapter 12 Integrated Market Model: Linear 215</b></p> <p>12.1 Gather Market Data 215</p> <p>12.2 Age Data to a Common Date 217</p> <p>12.3 Create an Integrated Market Model 217</p> <p>Interpretations 219</p> <p>12.4 Compare Employee Pay with Market Model 222</p> <p>Practice Problems 228</p> <p><b>Chapter 13 Integrated Market Model: Exponential 233</b></p> <p>Practice Problems 246</p> <p><b>Chapter 14 Integrated Market Model: Maturity Curve 251</b></p> <p>Practice Problems 261</p> <p><b>Chapter 15 Job Pricing Market Model: Group of Jobs 265</b></p> <p>Practice Problems 272</p> <p><b>Chapter 16 Job Pricing Market Model: Power Model 277</b></p> <p>Practice Problems 280</p> <p><b>Chapter 17 Multiple Linear Regression 283</b></p> <p>17.1 What It Is 283</p> <p>17.2 Similarities and Differenceswith Simple Linear Regression 284</p> <p>17.3 Building the Model 285</p> <p>First x-Variable 292</p> <p>Second x-Variable 295</p> <p>Standardized Coefficient 298</p> <p>Third x-Variable 300</p> <p>Multicollinearity 301</p> <p>17.4 Model Evaluation 305</p> <p>Regression Coefficients 305</p> <p>Standardized Coefficients 306</p> <p>Coefficient of Determination 306</p> <p>Standard Error of Estimate 306</p> <p>Multicollinearity 306</p> <p>Simplicity 307</p> <p>Common Sense 307</p> <p>Acceptability 307</p> <p>Reality 307</p> <p>Decision 307</p> <p>17.5 Mixed Messages in Evaluating A Model 308</p> <p>r² Versus Common Sense 308</p> <p>r² Versus Simplicity 308</p> <p>Simplicity Versus Acceptability 308</p> <p>17.6 Summary of Regressions 308</p> <p>17.7 Digging Deeper 310</p> <p>Summary 315</p> <p>Practice Problems 317</p> <p>Appendix 319</p> <p>A.1 Value Exchange Theory 319</p> <p>Achieving Organization Goals 319</p> <p>Value Exchange 319</p> <p>A Fair Value Exchange Is a Good Deal 320</p> <p>A.2 Factors Determining a Person’s Pay 321</p> <p>System Factors 322</p> <p>Individual Factors 323</p> <p>A.3 Types of Numbers 324</p> <p>Definitions and Properties 324</p> <p>Histograms with All Four Types of Measurements 327</p> <p>A.4 Significant Figures 330</p> <p>A.5 Scientific Notation 331</p> <p>A.6 Accuracy and Precision 332</p> <p>Which Is More Important? 333</p> <p>A.7 Compound Interest–Additional 333</p> <p>Other Formulas 333</p> <p>A.8 Rule of 72 334</p> <p>Derivation of the Rule of 72 335</p> <p>A.9 Normal Distribution 336</p> <p>Central Limit Theorem 337</p> <p>Distribution of Salary Survey Data 338</p> <p>A.10 Linear Regression Technical Note 338</p> <p>A.11 Formulas for Regression Terms 340</p> <p>A.12 Logarithmic Conversion 340</p> <p>A.13 Range Spread Relationships 340</p> <p>Overlap 343</p> <p>A.14 Statistical Inference in Regression 344</p> <p>t-Statistic and Its Probability 347</p> <p>F-Statistic and Its Probability 348</p> <p>Mixed Messages in Evaluating a Model 349</p> <p>A.15 Additional Multiple Linear Regression Topics 349</p> <p>Adjusted r2 349</p> <p>Coding of Indicator Variables 350</p> <p>Interaction Terms 351</p> <p>GLOSSARY 357</p> <p>REFERENCES 369</p> <p>ANSWERS TO PRACTICE PROBLEMS 371</p> <p>INDEX 433</p>

<p>“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.”  (<i>Workspan,</i> 1 January 2013)</p> "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) <p> </p>

<b>JOHN H. DAVIS, PhD</b>, 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.

<b>An insightful, hands-on focus on the statistical methods used by compensation and human resources professionals in their everyday work</b> <p>Across various industries, compensation professionals work to organize and analyze aspects of employment that deal with elements of pay, such as deciding base salary, bonus, and commission provided by an employer to its employees for work performed. Acknowledging the numerous quantitative analyses of data that are a part of this everyday work, <i>Statistics for Compensation</i> provides a comprehensive guide to the key statistical tools and techniques needed to perform those analyses and to help organizations make fully informed compensation decisions.</p> <p>This self-contained book is the first of its kind to explore the use of various quantitative methods—from basic notions about percents to multiple linear regression—that are used in the management, design, and implementation of powerful compensation strategies. Drawing upon his extensive experience as a consultant, practitioner, and teacher of both statistics and compensation, the author focuses on the usefulness of the techniques and their immediate application to everyday compensation work, thoroughly explaining major areas such as:</p> <ul> <li> <p>Frequency distributions and histograms</p> </li> <li> <p>Measures of location and variability</p> </li> <li> <p>Model building</p> </li> <li> <p>Linear models</p> </li> <li> <p>Exponential curve models</p> </li> <li> <p>Maturity curve models</p> </li> <li> <p>Power models</p> </li> <li> <p>Market models and salary survey analysis</p> </li> <li> <p>Linear and exponential integrated market models</p> </li> <li> <p>Job pricing market models</p> </li> </ul> <p>Throughout the book, rigorous definitions and step-by-step procedures clearly explain and demonstrate how to apply the presented statistical techniques. Each chapter concludes with a set of exercises, and various case studies showcase the topic's real-world relevance. The book also features an extensive glossary of key statistical terms and an appendix with technical details. Data for the examples and practice problems are available in the book and on a related FTP site.</p> <p><i>Statistics for Compensation</i> is an excellent reference for compensation professionals, human resources professionals, and other practitioners responsible for any aspect of base pay, incentive pay, sales compensation, and executive compensation in their organizations. It can also serve as a supplement for compensation courses at the upper-undergraduate and graduate levels.</p>

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