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
