Pay Equity Analysis Methodology: WLS Regression Explained for HR Leaders

When regulators, courts, or your board ask whether your organization pays men and women equally for equal work, the answer cannot be a simple comparison of averages. Raw pay gaps — the difference in median or mean pay between men and women — do not account for legitimate differences in role, experience, location, or performance. To determine whether a pay gap is unjustified, you need a statistical method that controls for these factors.

That method is Weighted Least Squares (WLS) regression, and it is the accepted standard in pay equity analysis.

Why Simple Averages Are Not Enough

Suppose your organization has a median gender pay gap of 8%. That number, on its own, tells you very little. It might reflect the fact that more men hold senior roles. It might reflect geographic pay differences. It might reflect tenure distributions. Or it might reflect genuine pay discrimination.

A raw pay gap is a starting point, not an answer. The EU Pay Transparency Directive requires employers with a gender pay gap exceeding 5% to determine whether the gap can be explained by "objective, gender-neutral criteria." Regression analysis is how you make that determination.

What Is Regression Analysis?

Regression analysis is a statistical technique that models the relationship between a dependent variable (in this case, pay) and one or more independent variables (the factors that legitimately influence pay). The goal is to isolate the effect of gender on pay after accounting for everything else that should affect compensation.

In plain terms, regression answers the question: if two employees are identical in role, level, tenure, location, and performance, but differ in gender, is there a statistically significant difference in their pay?

Why WLS, Not OLS?

Most people with a statistics background are familiar with Ordinary Least Squares (OLS) regression. WLS is a refinement of OLS that addresses a common problem in compensation data: heteroscedasticity.

Heteroscedasticity means that the variance of pay is not constant across all groups. In practice, senior roles tend to have much wider pay ranges than junior roles. A software engineer at Level 2 might earn between $85,000 and $95,000, while a VP of Engineering might earn between $200,000 and $350,000. If you run OLS on this data, the model gives equal weight to every observation, which means the high-variance senior roles can disproportionately influence the results.

WLS corrects for this by assigning weights to each observation based on the precision of the data. Groups with less variance get more weight; groups with more variance get less. This produces more reliable estimates of pay gaps within each employee category.

What Variables Are Controlled For?

The choice of control variables is one of the most important decisions in a pay equity analysis. These are the factors that legitimately explain pay differences. Typical control variables include:

Job family and level. The single most important factor. A senior engineer should earn more than a junior engineer, regardless of gender. Job architecture — families, levels, and grades — provides the framework for comparing like with like.

Tenure. Length of service often correlates with pay, either through annual increases, step progressions, or accumulated merit raises. Controlling for tenure helps distinguish between pay gaps caused by discrimination and gaps caused by different lengths of service.

Geographic location. Market rates vary by city, state, and country. An employee in San Francisco should not be compared directly with an employee in Bucharest without a location adjustment.

Performance ratings. If your organization uses performance-based pay, controlling for performance ensures that higher pay for higher performers is not incorrectly attributed to gender.

Education and credentials. In some roles, advanced degrees or professional certifications command a pay premium. Including these as controls prevents confounding.

Hours or employment type. Full-time and part-time employees should typically be analyzed separately, or hours should be included as a control variable.

What Should NOT Be Controlled For

Not every variable belongs in the model. Some factors can themselves be influenced by discrimination, and controlling for them would mask the very gaps you are trying to detect.

Negotiation outcomes should generally not be used as a control. If men negotiate more aggressively and women are penalized for negotiating, including negotiation as a control would hide a discriminatory pattern.

Subjective assessments without clear criteria should be used cautiously. If performance ratings themselves contain gender bias, controlling for them introduces bias into the model.

The principle is straightforward: control for factors that are objective, gender-neutral, and established before the pay decision. Do not control for factors that may themselves be products of bias.

How to Interpret the Results

A WLS regression produces several outputs that matter for pay equity analysis:

The gender coefficient. This is the estimated effect of gender on pay after controlling for all other variables. If the coefficient is -0.04, it means that women earn approximately 4% less than men with otherwise identical characteristics. This is your adjusted pay gap.

Statistical significance. A p-value below 0.05 (the conventional threshold) means you can be 95% confident that the observed gap is not due to random chance. A statistically significant adjusted gap is the strongest indicator of a systemic pay equity issue.

R-squared (R²). This tells you how much of the variation in pay is explained by your model. An R² of 0.85 means your control variables explain 85% of pay differences. A very low R² might indicate missing variables or poor job architecture.

Individual residuals. Beyond the overall gender coefficient, you can examine individual employees whose actual pay deviates significantly from their predicted pay. These outliers are often the most actionable findings — specific individuals who may be underpaid relative to their peers.

Why Methodology Matters for Legal Defensibility

If your organization is ever challenged on pay equity — whether by a regulator, a court, or in a joint pay assessment under the EU Directive — the methodology behind your analysis will be scrutinized.

A defensible analysis requires:

• A recognized statistical method. WLS regression is accepted by employment attorneys, regulators, and courts in both the EU and the US. It is the methodology used by the US Department of Labor's Office of Federal Contract Compliance Programs (OFCCP) and is consistent with EU guidance on pay gap analysis.

• Appropriate control variables. Your choice of variables must be justifiable. Including too few variables risks overstating gaps; including too many (especially biased ones) risks understating them.

• Documentation. The full methodology — model specification, variable definitions, data cleaning steps, and results — should be documented in a format that can withstand legal review.

• Reproducibility. Another qualified analyst should be able to replicate your results given the same data and methodology.

When to Engage Experts

While the principles of WLS regression are straightforward, the execution involves judgment calls that benefit from experience. Deciding which variables to include, how to handle missing data, how to define employee categories, and how to interpret edge cases requires both statistical expertise and knowledge of employment law.

For organizations conducting their first pay equity analysis, or those facing a reporting obligation under the EU Directive, working with a provider that combines statistical rigor with regulatory knowledge significantly reduces the risk of errors or gaps that could undermine the analysis.

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