A Foundational Understanding of Basic Quantitative Methods in Compensation

A foundational understanding of basic quantitative principles is a necessity for HR and compensation professionals involved in salary planning. Mathematics is used constantly when managing compensation within an organization, so understanding how mathematics can be applied to ensure an accurate analysis of salary survey data is critical in the development, administration, and monitoring of salary plans. In short, learning how to analyze salary data is a vital skill for HR and compensation analysts to master.  

Compensation analysts are heavily relied on to analyze compensation and survey data to help streamline the compensation management process in an organization. Their insights and conclusions on collected survey data will ultimately help guide the direction and development of an organization’s compensation plan, in addition to being key in attracting, retaining, and motivating top talent. 

As part of our ongoing series in helping professionals understand the ins and outs of becoming a Compensation Analyst, we will focus here on a few foundational quantitative methods that are commonly used in compensation as it pertains to analyzing survey data. In this blog, we will examine the following: 

• The importance of mastering basic quantitative principles to accomplish essential tasks, such as compensation management, salary administration, and accurate interpretation of survey data. 

• Understanding which tasks require a grasp of these foundational quantitative skills. 

• A cursory look at the most common, basic quantitative methods in compensation planning and management — the mathematics needed for success — and how they are used in salary administration.

 

The Importance of Mastering Basic Quantitative Principles in Compensation Management

First and foremost, salary administration is a complex process requiring mastery of many analytical and quantitative skills in order to administer and manage compensation competently and successfully. A significant part of being a compensation analyst is understanding when to apply these skills and how to effectively incorporate these findings into a specific organization’s current compensation strategy.  

One of the main tasks of a compensation analyst is to assess and perform analysis on collected compensation data and prepare wage and salary data to facilitate compensation management functions of an organization. You can imagine that quite a few of these tasks require basic quantitative principles. 

Here are a few examples of tasks that commonly require the mastery of core foundational quantitative skills: 

• Analyzing and interpreting salary survey data 

• Building and managing a salary structure 

• Implementing salary increases 

• Accounting for geographic pay differentials 

With our Distance Learning Center (DLC) you can soon become an expert in successfully applying these quantitative skills. ERI SalaryExpert gives professionals the opportunity to enrich their skill set with the Compensation Analyst Credential (CAC), plus additional continuing education courses. This online credential teaches the basics of salary planning and administration, allowing you to diversify your skill set and demonstrate your knowledge of compensation management and salary administration. 

 

Common Quantitative Principles Used in Salary Administration and Compensation Planning 

In salary administration and compensation planning, there are a few core quantitative principles needed for compensation analysts to complete their tasks accurately and effectively. 

Interpreting Salary Surveys 

Compensation analysts are exposed to many salary surveys, making learning how to analyze salary data accurately an essential skill. With salary surveys being widely used in salary administration to conduct essential tasks, such as setting pay, examinations must render an accurate analysis from the myriad salary surveys that are available. This entails measuring the average, median, and mode. 

Average

Measuring the average pay of the positions surveyed is one of the most important aspects of analyzing data. The following three averages are the most common averages used in compensation analysis: 

• Arithmetic mean: The most common form of average, it is simply the sum of all the observations divided by the total number of observations.

 

When is this used? A common example of arithmetic mean is finding the average pay for a specific job found among all utilized salary surveys. 

• Geometric mean growth rate: This average is used when you need to look at trends in the average salary for a particular job over time, especially when salary values build on each other. This is used when trying to find the average annual salary increase for a job over a span of years, accounting for compounding. An example would be calculating the salary increase from 2019 to 2023, where the average salary for a job was $50,000 in 2019 and $58,000 in 2023: 

(58,000/50,000​)1/4 ​− 1= (1.16)1/4 – 1 ≈ 1.0377 – 1 =0.0377.  

Therefore, 3.77% per year would be the annual salary increase from 2019 to 2023 for this job. 

• Weighted average: This average is used to calculate the overall average salary for a job, accounting for the number of incumbents reported by each survey. Each survey’s reported average salary is multiple by the number of incumbents, summed across all reporting surveys, and then divided by the total number of incumbents. 

Weighted average = Total salary dollars across all companies / Total number of incumbents  

When is this used? Weighted averages are used to represent the true average across an entire population, rather than a simple average that gives equal weight to each data point regardless of size. This ensures larger organizations with more incumbents in a role have a proportionate impact on the final average. 

Median

Since the average can be significantly affected by high or low values, computing the median is often favored, giving compensation analysts a more accurate measure of the middle of a salary distribution if it has outliers.  

The median is the middle value in a data set when the values are arranged in order. The median is often referred to as the midpoint of a distribution, such as the following data set with 50 as the median: 

[25, 38, 38, 50, 60, 68, 95] 

Mode

The mode is used by compensation analysts to find the most frequently occurring salary in a survey. The mode can be identified by rearranging the salaries in groups, allowing analysts to clearly see which value occurs most frequently. For example, the data set below has a mode of 38: 

[25, 38, 38, 50, 60, 68, 95] 

 

Establishing and Administering Salary Structures 

Now that you understand some of the basic, core mathematical tools used in analyzing salary surveys, let’s turn to learning quantitative methods to establish salary structures and perform salary administration. 

A salary structure is composed of an organization’s hierarchy of jobs, which is based on grades, ranking, or job evaluation points, and their associated pay ranges. Salary structures are also used by HR and compensation coordinators as a framework to determine how much an organization’s employees should be paid. An organization’s salary structure can also be seen as the physical representation of their compensation strategy in action, making the maintenance of salary structures a critical component of compensation management.  

The proper maintenance of an organization’s salary structure can translate to several positive outcomes: 

• Staying competitive as an employer, attracting and retaining top talent 

• Maintaining accurate information on an organization’s expenses  

• Incorporating the space and opportunity for pay raises  

The proper development, administration, and monitoring of salary structures are critical responsibilities for compensation analysts. When creating salary structures, there are a number of quantitative methods that compensation analysts must utilize:  

• Market index: This is the company's current pay rate for a job compared to the market rate for the job, expressed as a ratio. The market index is calculated as follows:

 

• Compa ratios: This is the company's current pay rate for a job compared to the range midpoint for the job. This is how you determine a compa ratio:

 

• Pay grades: These are groups of jobs ranked and grouped based on similar market value or internal worth, typically resulting in fewer groups than total individual jobs. Each pay grade contains jobs with similar compensation levels, even if the duties differ. 

• Salary range: This is the spread of pay given to a job or group of jobs, defined by the minimum and the maximum. Salary ranges allow an employer to recognize differences among employees performing the same or similar job but at different performance or experience levels. 

Note: Pay grades and salary ranges are used as tools, usually represented through functioning graphs, to manage the financial progression of employees within an organization. Often, determining the market index and compa ratios helps compensation analysts develop pay grades and salary ranges in a salary structure.  

From here, the salary structure is used as a framework to help define, regularly review, and manage the salary administration process. 

Implementing Salary Increases

As part of continuous monitoring and management of an organization’s salary structure, compensation analysts encounter common tasks, such as implementing salary increases. When implementing a salary increase, compensation analysts have to create a salary formation formula. 

For example, let’s assume that an organization has the following salary structure: y = 8.34x + $2,400. The salary structure is based on a point evaluation system, with 100 representing the bottom and 900 representing the top of the structure. Salaries at the bottom of the structure are increasing at a 6% rate. Salaries at the top of the structure are increasing at a 12% rate. To determine the new salary formation formula, there are a couple of steps to take: 

First, calculate the salary increase for the bottom and top of the structure separately.  

Calculate the bottom of the structure as follows: 

y = 8.34x + $2,400 

y = (8.34) (100) + $2,400 

y = 834 + $2,400 

y = $3,234 

$3,234 x 1.06 = $3,428.04 

Calculate the top of the structure as follows: 

y = 8.34x + $2,400 

y = (8.34) (900) + $2,400 

y = 7,506 + $2,400 

y = $9,906 

$9,906 x 1.12 = $11,094.72 

Then, solve the two equations simultaneously to find the new structure by calculating the slope, using this equation: y = mx + b 

$11,094.72 = (m)(900) + b 

- $3,428.04 = (m)(100) + b 

$7,666.68 = (m)(800) 

m = 9.583 

Substitute “m” into one of the original equations to solve for “b”: 

$3,428.04 = (m)(100) + b $3,428.04 = (9.583)(100) + b 

$3,428.04 = 958.3 + b 

$2,470 = b 

Here is the new structure equation: 

y = 9.583x + $2,470 

 

Accounting for Geographic Differentials

For organizations of a larger scale, accounting for geographic differentials plays an important role in determining salary and cost-of-living adjustments. Disparate locations may have widely different pay for the same jobs due to various factors, such as the supply and demand of labor or even differing state legislation.  

Geographic differentials are represented through percentages to compute differentials between two or more areas. Let’s say the national average salary for an executive secretary is $65,00,000, and California’s salary index is 22% above the national average. To determine the salary of an executive secretary in California, multiply the national average salary of the job by the specific salary index for the location. For this example, finding the salary for an executive secretary in California is computed as follows: 

$65,000 x 1.22 = $79,200 

 

ERI SalaryExpert as Your Resource Center 

ERI SalaryExpert’s Compensation Analyst Credential (CAC) designation is a smart choice for continuing education and career development. From the ease of your computer, you can become an expert in the field of compensation, mastering foundational concepts, such as basic quantitative principles in compensation management. Through ERI’s Distance Learning Center (DLC), you will have access to a library of resources for HR and compensation training. At the tip of your fingers, ERI SalaryExpert is your trusted resource center to spearhead your achievements and success.  

If you have any questions about the Compensation Analyst Credential (CAC) designation or other resources provided by ERI’s Distance Learning Center, please email [email protected]