Acute condition contrasts under shared temporal drift: polynomial cancellation, precision, and timing

Abstract

To determine when three neutral attempts improve estimation of an acute A–B motor-performance difference during a seven-attempt session. The schedules were R–A–B–R–B–A–R and R–B–A–R–A–B–R, where R is the same movement under a neutral instruction. The contrast subtracts one sixth of the signed reference second difference from the mirrored A–B comparison. Polynomial cancellation, measurement variance, carryover bias, and weights for unequal onset times were derived analytically. Ten drift and error conditions each used 20,000 simulated studies of 40 independently generated individuals. The timing analysis used 50,000 grids at each of five jitter levels. No participants were recruited. The fixed contrast removed shared polynomial drift through degree three and equalled the minimum-variance linear unbiased regression contrast under equal independent error variances. With condition and reference error standard deviations of 1 cm, quadratic-drift root mean squared error decreased from 1.449 to 1.080 cm; with flat drift it increased from 1.000 to 1.080 cm. A fatigue step increased error from 0.999 to 1.269 cm, and reference error of 3 cm reversed the benefit under quadratic drift. Differential carryover remained biased, with corrected population-mean interval coverage of 29.40%. Timestamp-aware weights restored polynomial cancellation on irregular grids but increased measurement variance. For shared cubic drift and independent errors, correction reduces individual mean squared error when the absolute drift bias exceeds the reference-error standard deviation divided by \(\sqrt 6\). Equal task definitions, qualified recovery intervals, recorded onset times, and complete cycles are required. Differential carryover and changing condition effects remain outside the constant-offset model.