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Statistics for Compensation
In a sentence
A practical guide teaching compensation and HR professionals the descriptive statistical and modeling techniques needed to analyze pay data and make sound organizational decisions.
Statistics for Compensation demystifies the numbers behind pay decisions, giving compensation and human resources professionals a hands-on toolkit of descriptive statistics and model-building techniques grounded in real-world case studies from a fictitious company, BPD. Author John H. Davis draws on decades of practitioner, consulting, and teaching experience to walk readers from basic notions of percent and compound interest through frequency distributions, measures of location and variability, and into powerful regression-based market models—linear, exponential, maturity curve, power, and multiple linear regression. The book's central message is that statistics do not simply answer questions; they raise issues, challenge assumptions, and require aggressive inquisitiveness because behind every data point there is a story. With worked examples, practice problems, and a disciplined five-step model-building framework, the book equips professionals to identify market positions, build salary structures, set salary increase budgets, and defend recommendations with data—all in service of helping organizations attract, retain, motivate, and align the people they need.
Tags
The model
A framework in which analytical design levers (statistical techniques, model building, market analysis) applied to compensation data produce psychological and behavioral states (understanding, comprehension, confidence, aggressive inquisitiveness) that lead to better compensation decisions and organizational outcomes such as sound market positioning and the ability to attract, retain, motivate, and align employees.
Application of Descriptive Statistical Techniquesdesign lever
The deliberate use of descriptive statistical methods—percent, frequency distributions, measures of location and variability, and regression modeling—to organize, summarize, and analyze compensation and HR data.
Disciplined Model-Building Processdesign lever
The five-step, scientific-method-based process of specifying the problem, generating critical factors, identifying relationships, quantifying and analyzing, and evaluating the model to relate pay to explanatory variables.
Market Analysis and Salary Survey Processbehavioral pattern
The applied process of gathering market data, aging it to a common date, creating a market model, and comparing employee pay to develop market position, salary structures, and salary increase budgets.
Aggressive Inquisitivenesspsychological state
The inner drive, natural curiosity, and persistent inclination to explain anomalies, outliers, and the story behind every data point rather than accepting numbers at face value.
Data Comprehension and Understandingpsychological state
The analyst's grasp of what a set of data means—its distribution, central tendency, variability, and relationships—achieved by trading detail for simplicity through summarization.
Assumption Validationbehavioral pattern
The practice of checking assumptions—plotting data, examining correlation matrices for multicollinearity, confirming job matches, and identifying lurking variables—before drawing conclusions.
Analyst Decision Confidencepsychological state
The practitioner's comfort level and confidence in a model and its conclusions, driven by good model evaluation (fit, common sense) and sufficient data, enabling them to defend recommendations.
Quality of Compensation Decisionsoutcome metric
The soundness of decisions and recommendations—on pay levels, structures, budgets, and policies—that result from converting raw data through information into well-reasoned conclusions.
Organizational Talent Outcomesoutcome metric
The organization's ability to attract, retain, motivate, and align the kinds and numbers of people it needs to achieve its goals, supported by fair and competitive pay decisions.
How they connect
- statistical technique application → influences data comprehension
- model building process → predicts market analysis process
- data comprehension → influences analyst confidence
- market analysis process → influences analyst confidence
- analyst confidence → predicts decision quality
- aggressive inquisitiveness → moderates data comprehension
- assumption validation → moderates decision quality
- decision quality → predicts organizational talent outcomes
- statistical technique application → mediates decision quality
The process
The book provides a comprehensive playbook for compensation professionals to make data-driven decisions. The core methodology centers on using descriptive statistics to transform raw internal and external pay data into actionable insights. The overall process begins with foundational data analysis—organizing data into frequency distributions and calculating measures of location and variability to understand its characteristics. This leads to the central activity of model building, where statistical models (such as linear, exponential, maturity curve, or power models) are created to describe the relationship between market pay and internal job value metrics like grade or experience. These market models are the cornerstone of the primary operational process: conducting a comprehensive market analysis. This involves gathering and aging salary survey data, creating the appropriate market model, and then comparing the organization's current pay levels to this model to determine its market position. The output of this analysis directly informs the development of market-based salary structures and the calculation of an initial salary increase budget. The playbook concludes by integrating these analytical results with broader business context. The market-based budget is refined by considering factors like affordability, turnover, and strategic goals to arrive at a final recommended budget. This systematic, model-driven approach enables compensation professionals to move beyond simple data reporting to strategically manage pay, justify recommendations, and ensure compensation programs are both internally equitable and externally competitive.
General Model Building
To provide a systematic, five-step framework for solving problems by creating an objective, abstract representation of reality that relates a problem variable to the critical factors that influence it.
When to use: When faced with a problem that requires understanding why a variable of interest (e.g., pay, turnover) varies and what factors influence it.
Step 1Specify the problem or issue.
Entry: A problem or question has been identified.
Exit: The dependent (y) variable is clearly defined.
In: Business question or problem statement · Out: Defined dependent (y) variable
Step 2Generate critical factors that may impact the problem.
Entry: The dependent variable is defined.
Exit: A list of potential independent (x) variables is created.
In: Defined dependent (y) variable, Subject matter expertise · Out: List of potential independent (x) variables
Step 3Identify the relationship between the factors and the problem.
Entry: Potential independent variables are identified.
Exit: A visual plot of the data is created and the general relationship is identified.
- Is there a relationship?
- What is the nature of the relationship (linear, exponential, etc.)?
In: Raw data for y and x variables · Out: Scatter plot, Initial assessment of the relationship type
Step 4Quantify the relationship and analyze.
Entry: A relationship has been visually identified.
Exit: A mathematical equation for the model is generated.
In: Scatter plot, Raw data · Out: Model equation (e.g., y' = a + bx), Model statistics (e.g., r-squared, SEE)
Step 5Evaluate the model.
Entry: A model equation has been generated.
Exit: A decision is made on the validity and usefulness of the model.
- Is the model a good fit for the data?
- Does the model make logical sense in the business context?
In: Model equation and statistics · Out: Validated model, Understanding of the model's strengths and limitations
Conducting a Market Analysis and Developing a Salary Structure
To systematically analyze external salary survey data and internal employee data to determine the organization's market position, create a market-based pay structure, and develop a data-driven salary increase budget.
When to use: Typically performed annually as part of the compensation planning cycle to prepare for the upcoming salary administration year.
Step 1Gather market data from salary surveys.
Entry: The annual compensation review cycle has begun.
Exit: Relevant market data for benchmark jobs is compiled.
In: List of benchmark jobs, Salary survey sources · Out: Compiled raw market data for benchmark jobs
Step 2Age all survey data to a common date.
Entry: Raw market data has been gathered.
Exit: All market data is adjusted to a consistent and future-oriented effective date.
In: Raw market data, Effective date of each survey's data, Market movement factors · Out: Aged market data
Step 3Create a market model to establish a market policy line.
Entry: Market data has been aged.
Exit: A market model equation and line are established.
- Which model best fits the data trend (Linear, Exponential, Maturity Curve, Power, or Job Pricing)?
In: Aged market data, Internal job value data (e.g., grades, experience) · Out: Market model scatter plot, Market policy line (prediction equation)
Step 4Develop a market-based salary structure.
Entry: A market model has been created.
Exit: A new salary structure with minimums, midpoints, and maximums is defined.
- What is the appropriate range spread for this employee group?
In: Market policy line, Desired range spread percentage · Out: Market-based salary structure
Step 5Compare employee pay to the market model to determine market position.
Entry: A market-based salary structure is developed and current employee pay data is available.
Exit: The organization's market position and the initial catch-up budget are quantified.
In: Market-based salary structure, Current employee pay data · Out: Market position percentage, Initial market-based salary increase budget ('catch-up' amount)
Step 6Develop the final market-based salary increase budget.
Entry: The initial catch-up budget is known.
Exit: A final market-based salary increase budget is calculated.
In: Initial catch-up budget, Anticipated market movement percentage, Company pay policy · Out: Final market-based salary increase budget
Step 7Recommend a final salary increase budget.
Entry: The final market-based budget is calculated.
Exit: A final, comprehensive salary increase budget recommendation is prepared.
In: Final market-based salary increase budget, Data on affordability, turnover, business strategy, etc. · Out: Final recommended salary increase budget
Step 8Adjust the market-based salary structure.
Entry: A final salary increase budget has been approved.
Exit: An official, adjusted salary structure for the new plan year is established.
In: Market-based salary structure, Approved salary increase budget, Current market position · Out: Final, adjusted salary structure for the plan year
Developing Salary Increase Guidelines (Merit Matrix)
To create a merit matrix that provides managers with guidelines for awarding salary increases based on employee performance and position-in-range, while ensuring the total cost aligns with the organization's overall salary increase budget.
When to use: After the overall salary increase budget has been approved and guidelines are needed for managers to allocate raises.
Step 1Create a merit matrix template.
Entry: An overall salary increase budget is approved.
Exit: An empty merit matrix template is created.
In: Performance rating scale, Position-in-range categories · Out: Merit matrix template
Step 2Populate the matrix with total salaries.
Entry: The merit matrix template is created.
Exit: Each cell in the matrix contains the total salary dollars for the corresponding employee group.
In: Employee data (salary, performance rating, position-in-range) · Out: Salary-populated merit matrix
Step 3Propose initial raise percentages for each cell.
Entry: The matrix is populated with total salaries.
Exit: A matrix of proposed raise percentages is created.
In: Compensation philosophy · Out: Matrix of trial raise percentages
Step 4Calculate the total cost of the proposed raises.
Entry: Trial raise percentages have been proposed.
Exit: The total dollar cost of the proposed guidelines is calculated.
In: Salary-populated merit matrix, Matrix of trial raise percentages · Out: Total projected salary increase cost
Step 5Compare the total cost to the budget and iterate.
Entry: The total projected cost is calculated.
Exit: A final set of raise percentages that meets the budget is determined.
- Is the total cost within the approved budget?
In: Total projected salary increase cost, Approved salary increase budget · Out: Final merit matrix guidelines
Building a Multiple Linear Regression Model
To explain or predict a dependent variable (e.g., percent raise) using more than one independent variable (e.g., performance, position-in-range) and to understand the unique, relative impact of each independent variable while controlling for the others.
When to use: When investigating complex issues like pay equity or the drivers of employee raises, where multiple factors are believed to be influential simultaneously.
Step 1Specify the problem and define all variables.
Entry: A complex analytical question has been posed.
Exit: A dependent variable and a set of potential independent variables are defined.
In: Business problem · Out: List of y and x variables
Step 2Gather data and conduct preliminary analysis.
Entry: Variables have been defined.
Exit: Data is gathered and preliminary relationships and multicollinearity risks are identified.
- Are any independent variables highly correlated with each other?
In: Data sources · Out: Scatter plots, Correlation matrix
Step 3Build the model iteratively.
Entry: Preliminary analysis is complete.
Exit: One or more regression models with different combinations of variables are created.
- In what order should variables be entered into the model?
In: Cleaned data set · Out: Regression model outputs
Step 4Evaluate the model at each step.
Entry: A new variable has been added to the model.
Exit: A decision is made on whether to keep the newly added variable.
- Does the new variable significantly improve the model's explanatory power?
- Do the coefficients still make sense?
In: Regression model output · Out: Interim assessment of model validity
Step 5Finalize and interpret the best model.
Entry: Multiple model variations have been tested and evaluated.
Exit: A final, validated regression model is selected and its implications are understood.
In: All tested model outputs · Out: Final model equation, Interpretation of coefficients and relative variable impacts
The story
The reader A compensation or human resources professional responsible for pay who wants to make sound, data-backed decisions and confidently defend recommendations to executives.
External problem
They must analyze internal and external pay data to determine market positions, build salary structures, and set salary increase budgets—often under time pressure and uncertainty.
Internal problem
They feel intimidated by statistics and worried that they lack the analytical competence to prove recommendations with data when executives say 'prove it to us.'
Philosophical problem
Pay decisions should be based on rigorous, transparent analysis rather than guesswork, gut feeling, or blindly following the crowd.
The plan
- Learn the basic notions—percent, compound interest, and how numbers raise issues.
- Summarize and describe data with frequency distributions, measures of location, and measures of variability.
- Follow the five-step model-building process to relate pay to grade, experience, or company size.
- Apply market models to identify market position, build salary structures, and set salary increase budgets.
- Use multiple linear regression to uncover the real drivers of pay and other outcomes while checking assumptions.
Success
- The professional confidently makes data-backed recommendations, defends them to executives, and helps the organization attract, retain, motivate, and align the right people.
At stake
- The professional relies on raw data or intuition, misuses statistics, makes flawed pay decisions, and loses credibility with executives and employees.
Chapter by chapter
ch01Introduction
The introductory chapter sets the stage for understanding statistical analysis, emphasizing the narrative behind data and advocating for an inquisitive approach to interpreting numbers.
- Statistical analysis is essential for making informed decisions in an increasingly data-driven world.
- Each data point conveys a story, emphasizing the need for inquisitiveness and critical thinking in interpretation.
- The journey into statistics begins with a strong foundation in basic concepts, facilitating more advanced analysis.
- A model-building framework can provide structure and clarity in approaching statistical challenges.
ch02Basic Notions
This chapter introduces foundational concepts in percentages, percentage differences, and compound interest, providing essential mathematical tools for effective financial reasoning.
- Percentages are not just numbers; they are crucial for understanding scale and impact in financial contexts.
- Visual representations of percentage data can simplify complex financial information.
- Recognizing and calculating percent differences is key to tracking financial performance over time.
- Compound interest is a powerful tool that can significantly amplify savings if understood and utilized correctly.
ch03Frequency Distributions and Histograms
This chapter elucidates the construction and analysis of frequency distributions and histograms, essential tools for visually representing data distributions and enabling comparisons across datasets.
ch04Measures of Location
This chapter investigates various statistical measures of location, including mode, median, and mean, highlighting their applications and limitations in interpreting data sets.
ch05Measures of Variability
This chapter delves into the critical role of variability in data analysis, illustrating how understanding measures such as standard deviation and range can enhance a professional's decision-making and data interpretation.
- Understanding measures of variability is essential for making informed data-driven decisions.
- Standard deviation is a key indicator that reveals how much individual data points deviate from the mean.
- The coefficient of variation allows for effective comparisons across datasets with differing means or units.
- Rely on measures such as range and P90/P10 to capture the full scope of variability within your data.
ch06Model Building
This chapter explores the intricacies of model building, emphasizing the scientific method and structured processes that illuminate both the significance of models and practical strategies for their development.
ch07Linear Model
This chapter demystifies the linear model, illustrating its foundational role in data analysis and the considerations necessary for effective application and evaluation.
- Linear models are powerful tools but must be applied with diligence to avoid misinterpretations.
- Model fitting should not be a mere mathematical exercise but an exploration of the data's story.
- Overfitting is a significant risk when creating complex models; simplicity can often yield better predictive performance.
- R-squared values alone do not guarantee a model's success; comprehensive evaluation is crucial.
ch08Exponential Model
This chapter explores the structure, application, and evaluation of exponential models, emphasizing their relevance in understanding growth phenomena in various contexts.
- Exponential growth often leads to results that can significantly outpace linear expectations, making accurate modeling essential.
- Logarithms serve as a crucial tool for reversing the effects of exponential growth and understanding underlying relationships.
- Evaluating exponential models requires a robust understanding of statistical principles and metrics like R-squared values.
- Misinterpreting growth patterns can lead to strategic errors—awareness of exponential behaviors can mitigate these risks.
ch09Maturity Curve Model
This chapter elucidates the Maturity Curve Model, a strategic framework that maps the progressive stages of organizational maturity, enabling businesses to assess their current capabilities and identify areas for growth.
ch10Power Model
This chapter presents a framework for understanding and evaluating power dynamics within organizations, crucial for professionals navigating complex relationships.
ch11Market Models and Salary Survey Analysis
This chapter examines the methodologies underlying market-based salary increases and the analytical frameworks that inform salary survey analysis, emphasizing the necessity of aligning compensation with market standards to remain competitive.
- Market alignment in salary structures is vital not only for talent acquisition but also for retention and employee satisfaction.
- The synthesis of rigorous data analysis with strategic compensation planning can create a competitive edge for organizations.
- Organizations must regularly reassess market conditions and revise salary recommendations accordingly to maintain equity.
- A well-defined salary structure not only enhances transparency but also reinforces organizational integrity.
ch12p01Integrated Market Model: Linear (part 1/3)
This chapter introduces the foundational components of building an Integrated Market Model focused on linear compensation analysis, emphasizing the gathering and processing of market data.
- Accurate market data gathering is essential for crafting competitive pay structures that attract and retain talent.
- Aging data to a common date is crucial for making valid comparisons and decisions in compensation planning.
- An Integrated Market Model provides a systematic approach to aligning employee pay with market realities.
- Continuous comparison of actual salaries to the market model fosters a commitment to equity in compensation practices.
ch12p02Integrated Market Model: Linear (part 2/3)
This chapter examines how companies can strategically position their compensation structures within various market percentiles, using statistical methods to ensure competitive and performance-aligned pay.
- Rigorous understanding of market percentiles is essential for setting competitive compensation structures.
- Performance-based adjustments lend transparency and drive motivation within teams when consistently applied.
- Visualization tools, such as histograms and percentile bars, aid in understanding data distributions and scenarios.
- Accurate data calculations are necessary for informing equitable pay decisions and ensuring compliance with market standards.
ch12p03Integrated Market Model: Linear (part 3/3)
This chapter explores the methodology for constructing an effective linear regression model to analyze employee productivity metrics in relation to training, drawing significant insights from graphical data representation and statistical calculations.
ch13Power Model
The chapter explores the power model as a statistical tool for analyzing the relationship between executive pay and company size, particularly suited for data varying by orders of magnitude.
- The power model is essential for accurately depicting the correlation between executive pay and company size, particularly in high-stakes industries.
- A strong correlation value (e.g., 0.921 for log pays and sales) indicates the model's usefulness in setting pay strategies.
- Logarithmic transformations reveal clearer relationships in data that span wide ranges, highlighting the model's necessity.
- The standard error of estimate indicates variability in actual pay, reminding practitioners of the importance of flexibility in compensation structures.
ch14Market Models and Salary Survey Analysis
This chapter articulates the critical methodologies for analyzing market position and creating a market-based salary structure, emphasizing the importance of salary surveys and careful consideration of various internal and external factors.
- The integrated and job pricing market models offer tailored approaches to salary analysis depending on your organization's structure.
- Identifying outliers is crucial; behind each data point is a unique story that can affect compensation strategies.
- A successful salary administration strategy demands more than just hard data; soft contextual factors are equally vital in shaping final recommendations.
- Developing a final salary increase budget requires careful consideration of both market data and internal company policies.
ch15Integrated Market Model: Linear
This chapter presents a systematic approach to developing a market-based salary structure using linear models to ensure internal equity and external competitiveness in employee compensation.
ch16Integrated Market Model: Exponential
This chapter provides a structured method for developing a salary structure and increase budget for the BPD finance department, utilizing survey data and an exponential model to ensure both internal equity and external competitiveness.
- Gathering precise market data is foundational for developing effective compensation structures.
- Aging salary data to a common reference date is critical for maintaining salary relevancy and competitiveness.
- Employing an exponential model for salary predictions promotes equitable pay progression across job grades.
- It is essential to compare employee pay against market models to accurately assess positioning and necessary budgetary adjustments.
ch17Integrated Market Model: Maturity Curve
The chapter outlines a methodical approach to establishing a market-based salary structure utilizing maturity curve data to ensure internal equity and external competitiveness within an organization.
- It is crucial to integrate external market data into salary structures to maintain competitive advantages in talent acquisition and retention.
- Aging salary data to a common date is a foundational step that allows for more accurate and equitable salary comparisons.
- Cubic models are effective tools for capturing the relationship between professional experience and market compensation levels.
- A definitive market-based salary structure enhances transparency and fairness, thereby fostering a culture of trust and motivation within the workforce.
ch18Job Pricing Market Model: Group of Jobs
This chapter presents a structured approach to establishing a market-based salary model for IT positions, emphasizing the importance of aligning employee pay with market data through a clear four-step process.
- Effective job pricing requires a structured analysis of market data to develop competitive salary structures.
- Each employee should have an individualized market-based salary structure that reflects their specific skill and level, not merely a grade system.
- A methodical approach yields a salary increase budget that addresses both current market positions and projected movements.
- Utilizing market pay as a reference helps ensure that the organization offers salaries that attract and retain necessary talent.
ch19Job Pricing Market Model: Power Model
This chapter explores the power model for determining executive compensation, focusing on how external salary data corresponds to organizational size, revealing the complexities behind CEO pay structures.
- The power model for executive compensation capitalizes on the correlation between organizational size and executive pay.
- Significant variation exists in CEO compensation compared to market averages, necessitating justifiable rationale from boards.
- Integration of total compensation components—such as incentives and equity—is crucial for establishing competitive remuneration packages.
- Predictive modeling is essential for organizations to assess and adjust executive pay in a dynamically changing market landscape.
ch20p01Multiple Linear Regression (part 1/2)
Multiple Linear Regression serves as a powerful analytical technique that enhances prediction accuracy by incorporating multiple variables, revealing complex interactions that influence outcomes.
- Multiple Linear Regression provides a comprehensive framework for predicting outcomes when multiple independent variables are present.
- The process of model building in MLR is inherently experimental, involving iterative testing and refinement.
- It is vital to maintain a balance between model complexity and interpretability for effective communication of results.
- Perceptible disparities in pay can often be addressed through rigorous data analysis and transparent communication strategies.
ch20p02Multiple Linear Regression (part 2/2)
Chapter 20 concludes its exploration of multiple linear regression by addressing complex issues like multicollinearity, model fitting, and practical applications within compensation analysis.
Questions this book answers
- Why do we do statistical analysis in compensation, and how does it lead to better decisions?
- How do we summarize, describe, and present raw pay data so it becomes useful information?
- What measures of location and variability best characterize a set of compensation data?
- How do we build models that relate market pay to internal grades, experience, or company size?
- How do we determine an organization's market position, build a salary structure, and set a salary increase budget?
Glossary
- Application of Descriptive Statistical Techniques
- The deliberate and appropriate use of descriptive statistical methods to obtain, organize, summarize, present, interpret, and analyze compensation and HR data.
- Disciplined Model-Building Process
- A structured application of the scientific method to build a model relating a problem variable to critical factors through five explicit steps.
- Market Analysis and Salary Survey Process
- The applied end-to-end process of turning salary survey data into a market position, salary structure, and salary increase budget.
- Aggressive Inquisitiveness
- An inner drive and persistent curiosity to explain why data are the way they are, including anomalies, outliers, and the story behind each data point.
- Data Comprehension and Understanding
- The analyst's grasp of the meaning of a data set—its shape, central tendency, variability, and relationships—after summarization.
- Assumption Validation
- The practice of verifying the assumptions underlying an analysis before drawing conclusions.
- Analyst Decision Confidence
- The practitioner's comfort level in a model and its conclusions, enabling them to recommend and defend decisions.
- Quality of Compensation Decisions
- The soundness, defensibility, and appropriateness of compensation decisions and recommendations derived from analysis.