r=0 (pure luck) · r=1 (no regression)
z-score 2.00
Predicted true 121.0
Regression amount -9.0
% regression 30%
interpretation 30% of the extreme score is due to luck; 70% is real.
Batting average
First half.340, league μ=.260, r≈.50 predicted true.300
Marathon time
Elite 210 min, μ=270, σ=30, r=.65 predicted 249 min
Twin study (heritability)
Height: r≈.80, extreme 2σ 80% real, 20% luck
Exam retake
Score 145, μ=100, σ=15, r=.75 predicted 133.8
Frequently asked
What does reliability (r) mean?
Correlation between pre‑ and post‑measurement (or true‑score proportion). r=0 means pure luck, r=1 means no regression.
How is predicted true score calculated?
Kelley’s formula: r·X + (1‑r)·μ. It shrinks the observed score toward the mean.
Why does regression happen?
Extreme scores contain more measurement error; upon retest, scores tend to move toward the population mean.