The mixture changes the headline.

INSTRUMENTS / MEASUREMENT & FRAMING

Constructed example

Change the mix. Keep the rates.

Change an input. Inspect every step. Keep a fixed record.

01 / THE QUESTION

Does a falling average mean every group did worse?

Two periods. Two groups. Each group has a higher success rate in Period B, yet the combined rate falls from 50% to 36% in the opening example.

Keep a first thought

Your first interpretation

Optional. Included only when you explicitly save; excluded from shared links.

Constructed data · every relationship and outcome is supplied.

02 / OPEN THE MODEL

Comparison weights

0%50%100%

Higher-rate group

A80%

B90%

A: 80/100 · B: 18/20

Lower-rate group

A20%

B30%

A: 20/100 · B: 54/180

Overall · actual population

A50%

B36%

A: 100/200 · B: 72/200

All bars use the same 0–100% scale. Period B group rates stay fixed at 90% and 30% while its population mix changes.

Group rates stay fixed.Population weights change the headline ↓

Higher-rate group in Period B 20 / 200 attempts

Higher-rate: 20Lower-rate: 180

50Period A · observedpercent

36Period B · observedpercent

-14B minus Apercentage points

Follow the idea.

A concept, in three frames

Compare 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.

HOLD ONE VERSION STILL

What changes when you change the model?

Keep the current inputs beside your next adjustment.

Ask who makes up the average.

An overall rate weights each group by its share of the population. More attempts in the lower-rate group can pull the headline down even when both group rates rise.

Read the investigation →

Save this experiment

MODEL & LIMITS

What this model leaves open

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.

InputsWhat is supplied?
DefinitionWhat is counted?
InferenceWhat follows?

Inspect the exact workings

Original constructed counts · 200 attempts in each period
Group	A success / total	A rate	B success / total	B rate
Higher-rate	80/100	80%	18/20	90%
Lower-rate	20/100	20%	54/180	30%
Observed total	100/200	50%	72/200	36%

Actual B weights: 20/200 and 180/200. Standardized B = ½ × 90% + ½ × 30% = 60%. Choosing equal weights changes the question, not the original counts.

Assumptions, sources and evidence status

Original constructed fixture: constructed-aggregation-v1. aggregation-v1. No empirical observations are represented by these example counts.

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.

Read the definition and primary background sources →