RADAR Learning Lab: When the Average Lies

Simpson’s Paradox in AI Evaluation

This packet turns Simpson’s Paradox into a practical AI-evaluation habit. Learners first encounter a small, visible reversal, then work through a record-level evaluation with unequal case mix, and finally complete a capstone in which a deployment dashboard recommends the wrong model.

The central discipline is simple:

An aggregate result can be calculated correctly and still answer the wrong decision question.

The RADAR check

Step	Practice
R - Read the claim	State exactly what the metric is being used to claim.
A - Audit the denominator and mix	Check who, what, and how much each group contributes to the total.
D - Disaggregate	Calculate performance within meaningful strata.
A - Adjust to a common population	Standardize only when the target mix is relevant and defensible.
R - Recommend and record uncertainty	Make a decision, document limitations, and specify the next evaluation.

Learning path

Module 1: The Winner Changes When We Slice the Data

Level: Beginner

Learners compare two systems using aggregate success rates, then receive the routine-versus-complex breakdown. The overall winner loses inside both case types. Learners calculate a common-mix rate and write a corrected recommendation.

Learning goals:

• Recognize a strict aggregate reversal.
• Explain how unequal case mix changes a weighted average.
• Distinguish Simpson’s Paradox from a simple subgroup disparity.
• Replace an aggregate-only claim with a decision-relevant comparison.

Module 2: Evaluation Under Unequal Case Mix

Level: Advanced

Learners analyze 2,000 synthetic evaluation records across Easy, Medium, and Hard requests. They calculate aggregate and stratified success and hallucination rates, standardize both models to a common production mix, examine uncertainty, and redesign the evaluation.

Learning goals:

• Build a denominator-aware evaluation table.
• Standardize results to a declared target population.
• Interpret uncertainty and small-cell risk.
• Separate predictive comparison from causal claims.
• Propose a matched or paired follow-up evaluation.

Capstone: The Dashboard Says Ship It

Level: Applied synthesis

A candidate model appears dramatically better on the executive dashboard. Its evaluation set, however, contains far fewer High-severity cases. Learners audit accuracy, unsafe recommendations, latency, human overrides, confidence, and reviewer scores; identify the reversal; and write an executive deployment memo.

The evidence supports holding full deployment and running a matched, production-weighted, human-in-the-loop evaluation before launch.

Packet contents

Guides

• Guides/RADAR_When_the_Average_Lies_Facilitator_Guide.pdf
  • 18-page facilitation guide
  • lesson plans, pacing, prompts, answer keys, SQL/Python starter patterns, capstone rubric, and references
• Guides/RADAR_When_the_Average_Lies_Learner_Workbook.pdf
  • 13-page printable learner packet
  • worksheets for both modules, the capstone memo, self-check, reflection, and reference card

Workbooks

• Workbooks/RADAR_Simpsons_Paradox_Learner_Data_Workbook.xlsx
  • formatted data tabs and learner workspaces
• Workbooks/RADAR_Simpsons_Paradox_Instructor_Key.xlsx
  • formula-driven answer keys, standardized metrics, calibration analysis, and capstone rubric

Data

• Data/module1_summary.csv
• Data/module2_records.csv
• Data/module2_target_mix.csv
• Data/capstone_records.csv
• Data/capstone_target_mix.csv

All records are synthetic. Binary fields use 1 for true/yes and 0 for false/no. Record-level files are shuffled so learners must aggregate rather than rely on row order.

Quick start for facilitators

1. Give learners the learner PDF and learner workbook only.
2. In Module 1, show the aggregate dashboard before revealing the subgroup table.
3. Require every reported rate to include its numerator, denominator, and percentage.
4. In Module 2, have learners calculate aggregate results first, then stratified results, then standardized results.
5. Use the capstone as an individual or team assessment. Require an executive memo plus a proposed evaluation redesign.
6. Keep the instructor workbook separate. It contains formulas and expected answers.

Strict definition used in this packet

This packet reserves Simpson’s Paradox for a directional reversal: one option appears better in the aggregate, while the competing option is better within every meaningful stratum shown. A model performing worse for one subgroup is important, but it is not automatically Simpson’s Paradox.

Causal caution

Disaggregation does not tell learners which variables should be controlled for. A grouping variable may be a confounder, mediator, collider, proxy, or merely a convenient slice. Standardization in these labs is used to compare systems under a declared deployment mix, not to prove a causal effect.

Data notes and expected checks

• Module 1 aggregate winner: Atlas
• Module 1 within-stratum and common-mix winner: Beacon
• Module 2 aggregate winner: Atlas
• Module 2 within-difficulty and production-standardized winner: Beacon
• Capstone aggregate dashboard winner: Candidate
• Capstone within-severity and production-standardized winner: Current

These checks are included here for packet QA. Remove or conceal this section when distributing the README directly to learners.

Reuse guidance

The packet is designed to be adapted to other AI evaluation settings. Preserve three pieces when changing the scenario:

1. The aggregate and subgroup denominators must be visible.
2. The target population must be declared rather than smuggled in through a weighted average.
3. The recommendation must record uncertainty and specify what evidence would change the decision.

---

Source: modules/when-the-average-lies-simpsons-paradox-in-ai-evaluation/source-packet/README.md