Laws calibrated under separate conditions double-count preparation and response when added

What it is

Interaction laws are fitted under their own controlled conditions, and their intercepts often already include stimulus encoding, motor preparation, response execution, or device delay. Directly adding model predictions can count the same preparation or response time twice and inflate total task-time estimates.

Why it happens

Experimental models absorb stable costs unexplained by their main variable into an intercept. Models focused on search, choice, or pointing may each include common stages from trial onset to response; in real tasks such stages can overlap too. Adding equations is not adding processes unless their non-overlapping coverage is established.

Studying it

Draw a task timeline and define each stage boundary, then use process tracing, gaze, trajectories, or separated experiments to estimate non-overlapping components. Compare direct addition with end-to-end measurement and inspect duplicated intercepts. When composition is needed, prefer a unified regression or hierarchical process model over stitching absolute numbers from studies.

Where it stops holding

When parameters are derived from segmented phases of the same task, boundaries are explicit, and phases are genuinely serial, appropriate composition can help. The point is not that models can never be added, but that addition needs evidence. Even non-overlapping phases retain individual variation and parallel processing.

Related

• Same group: B1.17.2 Parallel operations cannot be estimated by adding time · B1.17.3 Adding group-average predictions amplifies rather than cancels error · 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: model composition · intercept · task-time prediction