Compensation Equity Analysis

Most HR teams compare average salaries by gender in a spreadsheet and call it an audit. This analysis does what a proper audit requires: compare compensation across groups while controlling for legitimate pay factors, test whether the remaining gaps are statistically significant, and document the method so it can be reviewed.

Worked Example (Made-Up Data): Raw Gap Versus Same-Level Gap

Question: How does mean pay (average pay) by gender change when we compare all staff with staff at the same job level?

Inputs: Made-up data, seed 17. Each row is one person, with a group, a job level, and a pay amount. The script builds in the same base pay for both groups at each level: $50,000 at the lower level and $80,000 at the higher level. A random amount (normal, standard deviation $4,000) is added to each pay. Men are 10 at the lower level and 30 at the higher level. Women are 30 at the lower level and 10 at the higher level. No pay gap within a level is built in.

Method: Find the mean for each group. Then find the mean within each job level. The gap is women's mean minus men's mean. This sums up the sample. It does not test if the gap could be due to chance.

import numpy as np

# Simulated data, seed 17. Each row is one employee.
rng = np.random.default_rng(17)
rows = []
for group, counts in [('men', {'lower': 10, 'higher': 30}),
                      ('women', {'lower': 30, 'higher': 10})]:
    for level, count in counts.items():
        base = 50000 if level == 'lower' else 80000
        salaries = base + rng.normal(0, 4000, count)
        rows.extend((group, level, float(salary)) for salary in salaries)

array = np.array(rows, dtype=object)
groups = array[:, 0]
levels = array[:, 1]
salaries = array[:, 2].astype(float)
men_mean = salaries[groups == 'men'].mean()
women_mean = salaries[groups == 'women'].mean()
raw_diff = women_mean - men_mean
raw_pct = 100 * raw_diff / men_mean
n_men = (groups == 'men').sum()
n_women = (groups == 'women').sum()
print(f"Employees: {len(rows)} (men: {n_men}, women: {n_women})")
print(f"Mean pay, men: ${men_mean:,.2f}")
print(f"Mean pay, women: ${women_mean:,.2f}")
print(f"Raw difference (women minus men): ${raw_diff:,.2f} "
      f"({raw_pct:.2f}% of men's mean)")
for level in ('lower', 'higher'):
    mask = levels == level
    male_avg = salaries[mask & (groups == 'men')].mean()
    female_avg = salaries[mask & (groups == 'women')].mean()
    print(f"{level.title()} level means: men ${male_avg:,.2f}; "
          f"women ${female_avg:,.2f}; "
          f"difference ${female_avg - male_avg:,.2f}")

Printed output:

Employees: 80 (men: 40, women: 40)
Mean pay, men: $71,747.07
Mean pay, women: $56,574.46
Raw difference (women minus men): $-15,172.61 (-21.15% of men's mean)
Lower level means: men $48,322.78; women $48,787.95; difference $465.16
Higher level means: men $79,555.17; women $79,934.01; difference $378.84

Result: Across all 80 staff, women's mean pay is $15,172.61 lower, which is 21.15% of the men's mean. Within each job level the group means are close: women are $465.16 above men at the lower level and $378.84 above at the higher level. Because equal pay at each level is built in, there is no within-level gap for the script to find. Those two small differences are chance. With a $4,000 spread and groups of 10 and 30, the standard error of each difference is about $1,460, so a difference of a few hundred dollars is well within noise. The whole raw gap comes from the mix of job levels: 30 of the 40 men are at the higher level and 30 of the 40 women are at the lower level.

Limit: The data are made up and have only two job levels. This demo does not test if the gap could be due to chance, include other parts of pay, or show if a real firm pays fairly. Real data can differ in every one of these ways.

Sources

• Simpson E (1951). The Interpretation of Interaction in Contingency Tables. Journal of the Royal Statistical Society Series B. doi 10.1111/j.2517-6161.1951.tb00088.x.

Simpson described the reversal of a group gap once the groups are split in 1951. This paper is cited for who and when. No number on this page comes from it.

Why a Spreadsheet Average Is Not a Pay Equity Audit

The raw pay gap is the simple difference in average pay between two groups. It can be misleading for your organization's internal audit, because it doesn't account for legitimate pay factors.

A proper compensation equity analysis asks a more specific question: after controlling for job role, experience, education, performance, and location, do statistically significant pay gaps remain? The gap can grow or shrink after adjustment, depending on how the groups differ in the pay factors used in the check. The adjusted gap is the one that speaks to whether the company is paying differently for the same work.

You upload a CSV from your HRIS, specify the compensation column and the grouping variables, and get a statistical comparison. A spreadsheet of averages does not show how a gap was tested. A statistical analysis with a documented method, significance testing, and effect sizes can be reviewed.

How a Proper Pay Equity Analysis Works

A sound audit has two layers:

Layer 1: Unadjusted group comparison: compare mean and median compensation between groups (male vs. female, or across ethnic groups) without any controls. This is the "headline number", the same kind of figure as a publicly reported pay gap. You produce it with a t-test (two groups) or ANOVA (three or more groups). Even though it doesn't control for pay factors, this number matters: it is the figure people will compare their own experience against.

Layer 2: Controlled comparison: the same analysis, but run within comparable groups. Instead of comparing all men to all women, compare men and women within the same job level, department, and experience band. If you have enough granularity in your data, this approach controls for legitimate pay factors without requiring multivariate regression. Within each group, a remaining gap is not explained by the factors you stratified on, but it may still reflect factors you did not include.

The first layer tells you what the gap looks like. The second layer tells you how much of it remains within comparable groups. Neither one on its own decides whether pay is fair: when several factors matter at once, use a regression that adjusts for them together, and have legal or compensation specialists review any unexplained gap before drawing conclusions.

What Data Do You Need?

A CSV export from your HRIS combining compensation and demographic data. Some companies need to merge payroll data with demographics from a separate HRIS export.

Required columns

• base_salary (or annual_compensation, total_comp): the numeric outcome you're testing
• gender (or ethnicity, race): the protected characteristic you're analyzing

Columns for a controlled analysis

• job_title or job_level: defines comparable groups (people doing similar work)
• department: additional grouping to create tighter comparisons
• years_of_experience or seniority: a common legitimate pay factor
• education_level, if your compensation model considers education
• performance_rating: most recent cycle rating
• location: for companies with geographic pay differentials

Sample size guidance

• Overall and per group: use a power check, a way to find how many people are needed. The count rests on the gap to find, pay spread, group mix, and test choice.
• For within-group analysis: you need enough employees per comparable group (job level + department + gender) to run statistical tests. Small groups should be combined, or their results read with care. The worked example above shows how groups of 10 can swing by a few hundred dollars from chance alone.

How to Read the Report

Group means and medians: the raw numbers. Mean salary for men, mean salary for women, and the difference in both absolute dollars and percentage terms. The median is often more informative than the mean for compensation data, because a few highly paid executives can pull the mean up without reflecting the typical employee's experience.

Box plots: visual comparison of the salary distributions by group. Overlapping boxes suggest similar compensation; clearly separated boxes suggest a gap worth testing. The plot shows the shape of the gap, but significance comes from the statistical test, not from how the boxes look. Look for outliers (the dots beyond the whiskers): a few extremely high or low salaries can distort the means.

ANOVA F-test (for 3+ groups), if you're comparing pay across multiple ethnic groups, departments, or job levels, the F-statistic and p-value tell you whether at least one group differs significantly. The p-value is the probability of seeing differences at least this large if there were no real pay difference between the groups. A p-value below 0.05 is statistically significant evidence against "no difference", not proof that a gap is real or what caused it; a p-value above 0.05 is not proof of equal pay either. Significance alone isn't enough: look at the effect size (eta-squared), and read it apart from the p-value.

Tukey HSD post-hoc comparisons: after ANOVA finds a significant overall difference, Tukey identifies which specific pairs differ. This is critical for pay equity: "Compensation differs significantly across ethnic groups" is a finding. A pair-by-pair result that names which two groups differ, by how many dollars, and with what interval, is an actionable finding.

Confidence intervals: for each comparison, the report shows the estimated size of the gap with upper and lower bounds. A confidence interval that excludes zero goes with a significant result. The width tells you about precision: a narrow interval gives you a specific remediation target, and a wide interval means you need more data or tighter comparable groups.

Effect size (Cohen's d): measures practical significance, separate from statistical significance. In compensation analysis, even a small effect size can translate to meaningful dollar amounts when multiplied across the workforce.

What to Do With the Results

Immediate

• Document the findings: keep the evidence of your pay equity analysis, not just results. Save the report with its methodology, data sources, and date of analysis.
• Flag significant gaps: for each significant comparison, calculate the total cost to close the gap. If 45 women in job level 3 are underpaid by an average of $3,500, the remediation cost is $157,500 (45 x $3,500), a concrete number for budget discussions. These counts are a hypothetical example.
• Check for confounders: if the gender gap is significant overall but not within any single job level, as in the worked example above, the gap is consistent with occupational segregation (more women in lower-paying roles) rather than unequal pay for equal work, though non-significance within a level is not proof of equal pay. Both are problems, but they require different solutions.

Strategic

• Run it on a regular schedule: build pay equity analysis into your annual compensation cycle, ideally before merit increases so you can use the budget to close gaps.
• Layer in regression: the ANOVA-based approach compares groups. For a more granular analysis that controls for multiple factors simultaneously, follow up with a regression analysis using salary as the dependent variable and gender/ethnicity as an independent variable alongside the legitimate pay factors. The coefficient on the protected characteristic is the adjusted gap.
• Explore intersectionality: the gap may be larger for specific intersections (e.g., Hispanic women in technical roles) than for any single dimension. Run separate analyses for key intersections.
• Check pay drivers with correlation analysis: use correlation analysis to understand which factors (seniority, education, performance) most strongly predict pay in your organization. If performance ratings barely correlate with compensation, your pay-for-performance policy isn't working as intended.

When to Use Something Else

• Comparing exactly two groups (e.g., male vs. female): A t-test gives a simpler, directional result with a confidence interval for the pay gap. It's mathematically equivalent to ANOVA with two groups but produces cleaner output for a two-group comparison.
• Heavily skewed compensation data: If executive compensation creates extreme outliers, a Kruskal-Wallis test compares medians without assuming a normal distribution. Compensation data is often right-skewed, making this a useful robustness check.
• Controlling for multiple factors simultaneously: ANOVA compares groups one factor at a time. For a proper multivariate analysis (controlling for experience, education, and performance all at once), you need regression. Start with ANOVA for the headline comparison, then follow up with regression for the adjusted gap.
• Full pay equity platform: If you need continuous monitoring, integration with your HRIS, and automated remediation recommendations, a dedicated pay equity platform may fit better. This analysis is a statistical comparison of one export.