Interactive · from Volume 1
Measurement error and attenuation
Two measures with a real association of 0.70. Lower the reliability of either one and the observed correlation falls, even though the true relationship has not changed at all.
Each measure has a fixed true score, and the slider sets that measure's reliability: the share of its observed variance that is true score rather than noise. The page adds an independent random draw to each patient, mean zero, with a standard deviation of √(1/reliability − 1) in units of the true score. So at 1.00 nothing is added at all; at 0.80 the noise has half the spread of the true scores; at 0.50 it has exactly the same spread.
The random draw is fixed, so moving a slider rescales the same jitter rather than reshuffling the picture. That is why points slide rather than jump.
The third figure is the textbook prediction, true r multiplied by √(reliability A × reliability B). Watch it track the observed value as you move either slider.
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