# An Instrumental Cognitive Model for Speeded and/or Simple Response Tasks

- Royce Anders,
*Aix-Marseille Université, France*
- F.-Xavier Alario,
*Aix-Marseille Université, France*
- Leendert van Maanen,
*University of Amsterdam, The Netherlands*

## Abstract

Speeded and/or simple response tasks may be cognitively modeled by
a random walk process that accumulates to threshold. In cases of tasks where
mainly one characteristic response is observed, at varying latencies, then random
walks involving only positive drifts that each arrive at a single threshold,
provide a suitable accumulation modeling account of the data; and advantageously,
this accumulation model is exactly described by the shifted Wald (SW) probability
density function. We will demonstrate how the SW distribution is thus a
noteworthy cognitive model for these tasks, which uniquely possesses
simultaneously, high utility as an objective data measurement tool for the
response time (RT) distributions. Per each experiment condition, its three
parameters can decompose the observed mean RT value, quantify the shape and
characteristics of the observed RT distribution, and account for significant
differences between distributions with near-identical mean values; regardless of
whether one accepts the cognitive interpretation of the random-walk accumulation
process. We present the SW model and demonstrate its efficiency and utility on
both simulated and real data.

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