Absolute constant values are questionable, but the differences between alternatives are relatively reliable

What it is

KLM constants' absolute seconds are affected by era, device, population, and method, and should not be treated as a precise commitment; but when the same calibration and rules are applied to two alternatives, the relative difference produced by differences in step count, travel distance, and blocking is more robust. This card and "GOMS suits comparing alternatives rather than absolute time prediction" express the same broader principle at different levels: that one says a structural fact about the operation sequence (fewer steps, fewer mode switches) is more robust than the time figure itself; this one goes one layer deeper and specifically asks under what condition the time constants themselves can also hold up under comparison. The answer: as long as the constant error is spread evenly across both alternatives, the difference remains reliable; the moment the error concentrates in one particular operator unit that the two alternatives depend on to different degrees, the difference itself becomes distorted.

Why it happens

Constant error cancels out under comparison only on the condition that it acts on both alternatives simultaneously, in roughly the same direction and magnitude — if both alternatives make heavy use of the "pointing" unit, even a poorly calibrated pointing constant will largely cancel out on subtraction as long as the same inaccurate constant is applied to both sides, leaving a remaining difference that mainly reflects the genuine difference in pointing count or travel distance between the two. But if the two alternatives' operator composition is asymmetric — alternative A relies heavily on a unit whose constant carries particularly large error (a newly emerging gesture input whose constant has not been reliably calibrated yet), while alternative B barely touches that unit — this error no longer acts evenly on both sides. It disproportionately inflates or deflates alternative A's estimate, and the precondition of "cancellation" no longer holds, which drags the computed difference itself down with it. This is also why this card has to come after the two on mental-operator insertion rules and system-response blocking judgment: if either judgment is applied inconsistently between the two alternatives (a looser M insertion rule applied to alternative A, a stricter one to B), the difference is distorted the same way — the source of error is not only miscalibrated constants; inconsistent rule application undermines the precondition for "the difference is reliable" just as much.

Where it stops holding

Two estimates computed under different rules, different device conditions, or different assumed task paths cannot simply be subtracted and compared — such a comparison fails to satisfy even the most basic precondition that "the error runs in roughly the same direction," and the resulting difference means nothing. If the genuine difference between two alternatives happens to lie exactly in a unit whose error is itself large (both relying on some new input method that has not been reliably calibrated), then neither the absolute value nor the difference can be settled from the model's numbers alone — real measurement is needed to fill the gap. When the theoretically computed difference is itself small, consider whether it could be entirely swamped by measurement noise or natural fluctuation in user strategy; a positive or negative sign from the model should not automatically be treated as a settled conclusion.

Applying it

• When reporting a comparison between alternative A and alternative B, list each one's unit sequence, the computed difference, which set of constants was used, which M insertion rule, and which blocking judgment — not just the difference in a single total-seconds figure.
• Strictly ensure the two alternatives being compared use the same set of constants, the same M insertion rule, and the same device condition; note any inconsistency explicitly in the report rather than assuming it can be ignored.
• Run a dedicated sensitivity analysis on whichever unit dominates the current comparison and also carries large error, checking whether the final ranking flips if that unit's constant shifts up or down by some margin.
• How to check: measure both alternatives with a small number of genuinely skilled users and confirm the direction and magnitude of the real difference broadly matches the model's; if the measured result clearly disagrees with the model's difference, first suspect that the error is concentrated in a unit the two alternatives depend on asymmetrically.

Related

• Same group: B4.12.1 Tasks are split into standard units such as keystroke, point, home, draw, mental preparation, and system response · B4.12.2 The placement of the mental preparation unit is governed by heuristic rules and is the main source of estimation error · B4.12.3 System response time counts toward the total only when it blocks the user · B4.12.5 Touch, voice, and gesture lack agreed-upon constants and must be measured before use
• Nearby: B4.04 GOMS · A10 Reaction Time and Movement Time
• Search terms: constant calibration · relative comparison · sensitivity analysis · asymmetric error