Statistics Quest

Capstone project · Human resources and reward · about 200 minutes

Employee compensation and pay equity review

Review pay at a 600-person company: describe a skewed salary distribution, separate the unadjusted gender gap from the adjusted one, handle job level as a possible mediator rather than a neutral control, test the sensitivity of the result, and give HR careful, costed recommendations.

The brief

Qasr Horizon Trading (a fictional company with 600 employees in six departments) has committed to an annual pay-equity review. The board's remuneration committee meets in three weeks and has asked the HR analytics team — you — for an independent analysis.

The questions

  1. How is base pay distributed, and what does a “typical” salary look like?
  2. How large is the gender pay gap before any adjustment, and how much remains once legitimate pay factors are taken into account?
  3. Is the company's job-level structure itself part of the story?
  4. What should HR do, and what would it cost?

Stakeholders. The chief human resources officer owns the response and the budget. The remuneration committee needs a defensible number. Legal counsel warns against wording that claims more (or less) than the analysis supports. Employee representatives will read the summary and will ask why “the gap” in their newsletter (the raw one) differs from yours.

Constraints. Monthly base salary is the primary pay measure (bonuses are reviewed separately); the analysis must avoid naming or singling out individuals; HR has signalled that any remediation budget should be justified with an interval, not only a point estimate.

The data. salaries has one row per employee: department, job level (L1–L5), years of experience, gender as recorded in the HR system, education, last performance rating, monthly base salary and last year's bonus (SAR). It is synthetic: generated to behave like real HR data, with effects planted to be found. Its numbers say nothing about any real employer.

What this review can and cannot do. It is a statistical description of pay patterns in observational data. Neither the raw gap nor any adjusted gap can by itself prove or disprove discrimination, and the adjusted gap depends on which controls you choose. It is not legal advice: which pay factors count as legitimate, and what a gap means legally, depend on the jurisdiction and on advice from qualified employment counsel.

Dataset

Employee salaries at a fictional company

600 rows · one row = one employee · synthetic data

EmployeeDepartmentJob levelExperience (years)GenderEducationPerformance ratingMonthly base salary (SAR)Annual bonus (SAR)
Q0001TechnologyL3 Senior Specialist17.5MaleBachelor3202600
Q0002FinanceL1 Associate2.4MaleDiploma390809740.39
Q0003LegalL2 Specialist11FemaleBachelor2130003293.69
Q0004SalesL2 Specialist12.7FemaleBachelor3124600
Q0005SalesL1 Associate1.8MaleBachelor377400
Q0006FinanceL3 Senior Specialist16.8FemaleMaster41694033514.43

Included with a Formula Quest membership

This capstone has 5 stages and 19 graded tasks, ending with a written report.

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