On the Measurement of Movement Difficulty in the Standard Approach to Fitts' Law

Fitts' law is an empirical rule of thumb which predicts the time it takes people, under time pressure, to reach with some pointer a target of width W located at a distance D. It has been traditionally assumed that the predictor of movement time must be some mathematical transform of the quotient of D/W, called the index of difficulty (ID) of the movement task. We ask about the scale of measurement involved in this independent variable. We show that because there is no such thing as a zero-difficulty movement, the IDs of the literature run on non-ratio scales of measurement. One notable consequence is that, contrary to a widespread belief, the value of the y-intercept of Fitts' law is uninterpretable. To improve the traditional Fitts paradigm, we suggest grounding difficulty on relative target tolerance W/D, which has a physical zero, unlike relative target distance D/W. If no one can explain what is meant by a zero-difficulty movement task, everyone can understand what is meant by a target layout whose relative tolerance W/D is zero, and hence whose relative intolerance 1-W/D is 1 or 100%. We use the data of Fitts' famous tapping experiment to illustrate these points. Beyond the scale of measurement issue, there is reason to doubt that task difficulty is the right object to try to measure in basic research on Fitts' law, target layout manipulations having never provided users of the traditional Fitts paradigm with satisfactory control over the variations of the speed and accuracy of movements. We advocate the trade-off paradigm, a recently proposed alternative, which is immune to this criticism.