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Simpson's paradox in archive digitization pilot rates

Written answer1 delivery2 min 10 s in total$0.14 in total

The request

Simpson's paradox in archive digitization pilot rates

Read the full request

Analyze this fictional archive digitization pilot directly as text, with no files, code, tools or external research. "Success" means a page passed a predefined quality check. Workflow X: easy pages 81 successes out of 90; difficult pages 2 out of 10. Workflow Y: easy pages 19 out of 20; difficult pages 64 out of 80. A manager says "X succeeds on 83% overall and Y on 83%, so they perform equally; there can be no advantage within either difficulty group." Report the four within-group rates and both pooled rates. Explain what the supplied numbers establish and what they do not establish causally. Calculate directly standardized rates for a target mix of 50% easy and 50% difficult pages; identify any difference in percentage points. Explain how the observed page mix produces the pooled comparison. State whether random assignment, comparable pages within strata, or other confounders have been established by this table. Do not invent sample records, uncertainty estimates or causal evidence. Finish with one precise sentence correcting the manager.

The journey

  1. Read the requestTurned it into a list of things it would have to prove before calling the work done.
  2. Did the workPlanned the pieces, built them and checked the result as it went.
  3. DeliveredThe answer is written below.

The result

Within-difficulty rates: X easy = 81/90 = 90%; X difficult = 2/10 = 20%. Y easy = 19/20 = 95%; Y difficult = 64/80 = 80%. Pooled results: X = 83/100 = 83%; Y = 83/100 = 83%. Observed difficulty mixes: X was 90% easy and 10% difficult; Y was 20% easy and 80% difficult. With a 50% easy/50% difficult target mix, the directly standardized rates are X = 0.5(90%) + 0.5(20%) = 55%, and Y = 0.5(95%) + 0.5(80%) = 87.5%. The directed contrast is Y − X = 32.5 percentage points. The equal pooled rates arise from aggregation over different observed mixes: X had mostly easy pages, while Y had mostly difficult pages. The table establishes these descriptive success rates and mix differences, but it does not establish random assignment, comparable pages within strata, or the absence of confounding. Therefore, causal claims about workflow advantage are unsupported. Although both workflows have an observed pooled success rate of 83%, Y performs better within both difficulty groups and has a 32.5-percentage-point advantage after standardizing both workflows to a 50% easy, 50% difficult mix.
Time2 min 10 s
Cost$0.14
Finished2026-10-03

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