Adding group-average predictions amplifies rather than cancels error

What it is

Interaction laws generally predict group-average performance under particular conditions, carrying parameter uncertainty, individual variation, and measurement error. Adding predicted times across steps does not magically cancel error; uncertainty propagates across components, so a total-time interval can be much wider than any one estimate.

Why it happens

Step errors arise from model mismatch, device conditions, user strategy, and random variation. If errors correlate—one user is generally slower or one device delayed—they shift together. Even independent errors retain accumulated variance; adding point estimates as exact constants creates false decimal precision.

Studying it

Report confidence intervals for model parameters and predictions, then calculate a combined range through resampling, Bayesian posterior draws, or error propagation. Measure end-to-end tasks and inspect residuals for systematic bias. Stratify by user, device, and condition rather than comparing only a grand mean.

Where it stops holding

Uncertainty-aware addition can still aid coarse capacity planning or selection among clearly separated alternatives. The problem is treating a combined value as a precise promise for one person or one operation. More data can reduce parameter uncertainty but cannot eliminate structural and strategic variation.

Related

• Same group: B1.17.1 Laws calibrated under separate conditions double-count preparation and response when added · B1.17.2 Parallel operations cannot be estimated by adding time · B1.17.4 A predicted difference smaller than individual variation is not design evidence · B1.17.5 A law's ordering of alternatives is more credible than its absolute value
• Nearby: B1.01 Fitts's law · B1.04 Hick-Hyman law
• Search terms: prediction uncertainty · error propagation · confidence interval