Lab 05 / Relationships
When every group wins but the total loses
Can B do better in both groups but worse overall?
Adjust the mix of two synthetic groups and see how different weights can reverse an aggregate comparison. Change one control at a time, then open the values under the chart before interpreting the picture.
View the values behind this chart
Loading the deterministic simulation...
SEEDInterpret the result
The paired explanation covers the mechanism, assumptions, and cases where this simulation should not be generalized.
01 / Question
What this display answers
An overall rate is a weighted average of group-specific rates. Two options can use different group weights, so an option that is ahead inside every group can still trail in the aggregate.
The reversal is arithmetic, not proof that the grouped result is causal. Choosing what to condition on requires subject-matter reasoning about how groups arise.
02 / Reading
What to notice
- At a high novice share for B, confirm that B is five points ahead in both visible groups but behind overall.
- Lower B's novice share until the reversal disappears.
- Increase the within-group edge. A sufficiently large advantage can overcome the composition difference.
03 / Mechanism
The model behind it
Option A always has 20% novice cases. Option B's mix is controlled. Baseline completion rates are 60% for novice cases and 90% for returning cases.
The model uses fractional expected counts to keep rates exact while weights move.
04 / Limits
Where the result stops
A grouping variable can be a confounder, mediator, or collider; stratification is not automatically the correct analysis.
Neither the grouped nor aggregate association establishes a causal effect without a suitable design.