Speed-Accuracy Tradeoff

Abstract

The rationale for Fitts’ law is that pointing tasks have the information-theoretic analogy of sending a signal over a noisy channel, thereby matching Shannon’s capacity formula. Yet, the currently received analysis is incomplete and unsatisfactory: There is no explicit communication model for pointing; there is a confusion between central concepts of capacity (a mathematical limit), throughput (an average performance measure), and bandwidth (a physical quantity); and there is also a confusion between source and channel coding so that Shannon’s Theorem 17 can be misinterpreted. We develop an information-theoretic model for pointing tasks where the index of difficulty (ID) is the expression of both a source entropy and a zero-error channel capacity. Then, we extend the model to include misses at rate ε and prove that ID should be adjusted to (1−ε)ID. Finally, we reflect on Shannon’s channel coding theorem and argue that only minimum movement times, not performance averages, should be considered.

Simultaneous control of natural and extra degrees of freedom by isometric force and electromyographic activity in the muscle-to-force null space

“…While Fitts' law validity has been questioned because of its unclear theoretical foundations [51,52], Gori and collaborators [42] derived this law with a simple model of the human performance of an aiming task as a communication process. In this model, the source of the message is the target the individual intends to reach ("aiming is choosing").…”

“…To quantify subjects' performances and to understand how the task could be optimized to match individual control ability, we used a novel index of difficulty (ID), an informationtheoretic metric inspired by Fitts' law. Although Fitts' law general validity has been frequently questioned in the past, Gori and collaborators [42] have proposed an informationtheoretic model of the human motor system for pointing tasks, where the ID is the information about the selection of a target transmitted through a noisy channel. To date, many researches in human motor control have used measured derived from the Fitts' law to evaluate performance in different tasks [43][44][45].…”

Rethinking the Dual Gaussian Distribution Model for Predicting Touch Accuracy in On-screen-start Pointing Tasks

“…For example, the maximum error rate was 56% (Experiment 4), but it is assumed that the error rate should be close to 4% [35,47]. However, as Gori 4% criterion is arbitrary, and error rates can change depending on the target size [18], which is supported by existing empirical data [10,15,49,54]. It is not unusual for the error rate to be quite high, in particular for touch pointing tasks, e.g., an error rate of approximately 20% on average for = 3, 5, and 7-mm diameter circular targets [9] and 64% for 2.4-mm circles [10].…”

A New Approach to Modeling the Prediction of Movement Time

“…In addition to the above studies, fundamental studies were conducted to examine the theory of Fitts' law. For example, Gori et al worked on the rationale of Fitts' law in a pointing task [39], and Muller et al concluded that the control theory complemented Fitts' law [40]. Since the Shannon form was proposed, no studies have investigated the formula for Fitts' paradigm with one-dimensional targets.…”

“…Fitts [15] clearly stated that the analogy to Shannon's Theorem 17 is not proper [56], the ID is not formally derived from information theory [11,15,17,26,42], and the selection between candidates relies on researchers' heuristic considerations. Despite the fact that the analogy of the Canon model to information theory is still controversial in research [16,39,40], the mathematical proofs in these studies suffer the same validation challenge in natural human movement as in the Power model. Human movements might approximate the theoretical argument, but minor deviations could impact the fitness of the formula.…”