The mixture changes the headline.

INVESTIGATIONS / MEASUREMENT & FRAMING

Constructed example

Can every group improve while the headline gets worse?

The groups improved. The mix changed. The headline tells another story.

YOUR TASK / CONSTRUCTED EXAMPLE

Review the headline before explaining it

You’re reviewing a fictional performance comparison between two periods. Interpret the overall rate, then open the groups and examine their changing shares.

A first judgment.
An evidence trail.
Your decision.

Begin with a provisional judgment

Loading the supplied example…

What can the headline alone tell you?A lower overall rate suggests both groups did worseThe mix of groups could explain the changeI need the group results before explaining it

Keep a private first thought (optional)

Your first reasoning

Private writing stays out of links and default downloads. A reopened link does not restore it.

This records a provisional judgment and the starting configuration. It does not change a mathematical setting or save automatically.

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%

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

—Period A · observedpercent

—Period B · observedpercent

—B minus Apercentage points

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.

Try the instrument →

Save this experiment

Explore the model and compare working versions

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.

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 →