Lab 08 / Relationships
Why extremes drift inward
What happens when we retest only the highest first scores?
Create two noisy synthetic measurements, select the most extreme first results, and compare the same selected group on retest. 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 guide explains the mechanism, assumptions, and cases where this display should not be generalized.
What this display answers
When two measurements are imperfectly correlated, an extreme first result usually combines a persistent component with unusually favorable or unfavorable noise. Selecting on that first extreme also selects on its noise.
On retest, new noise is unlikely to be equally extreme in the same direction. The selected group's average therefore moves toward the population center even when nothing intervenes.
What to notice
- Start with correlation 0.55 and select the highest 10%. Compare first and retest means.
- Raise correlation toward 0.95. More of the first ranking persists and the inward movement usually shrinks.
- Select a less extreme 30%. The first selected mean starts closer to the center.
The model behind it
Two standardized normal measurements have a controlled correlation and are scaled to center 50 with standard deviation 10.
Only cases with the highest first score are displayed. No treatment or event is applied between measurements.
Where the result stops
Regression to the mean is a group expectation, not a guarantee that every selected case moves inward.
A contemporaneous comparison group and a credible design are needed before attributing observed change to an intervention.