Follow the idea.
A concept, in three framesCompare each group.
Use the same rate scale for both periods.
Inspect the mixture.
Group sizes determine their weights.
Read the headline.
The overall rate reflects both rates and weights.
A WORKING DEFINITION
Aggregation and Simpson’s paradox
An aggregate rate combines group rates using population weights. Simpson’s paradox describes a reversal between an aggregate comparison and the comparisons within its groups.
FOLLOW ONE EXAMPLE
Ask who makes up the average.
Period A: 80/100 in the higher-rate group and 20/100 in the lower-rate group, totaling 100/200. Period B: 18/20 and 54/180, totaling 72/200. Both group rates rise ten percentage points; the observed overall rate falls fourteen. Equal 50/50 weights give B 60%.
Work through the investigation →WHERE THE CLAIM STOPS
Keep the assumptions attached.
A reversal in aggregate rates does not establish a causal effect or improvement for every individual. Equal weights describe a chosen comparison, not the observed population.
Inspect this model’s assumptions and definitions
- Group rates are descriptive; they do not establish improvement for every individual or a causal effect.
- Equal weighting answers a standardized question and does not replace observed population counts.
- Both groups remain nonempty and Period A stays fixed in this model.
Definitions used in this instrument
- population
- 200-attempts-each-period-v1
- groups
- higher-and-lower-rate-groups-v1
- rates
- A-80-20-B-90-30-percent
- standard
- equal-group-weights-50-50
SOURCES & SCOPE
Read beyond the model.
Sarkar & Bandyopadhyay (2021), Simpson’s Paradox: A Singularity of Statistical and Inductive Inference ↗
Primary mathematical discussion of aggregation reversals and inference. The two-period counts here are original constructed data, not an empirical result from this paper.
All example data, figures and exact calculations on this page are original constructed teaching material. Source publications provide conceptual background, not the example dataset.
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