Abstract
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.
Highlights
Fitts’ law and the Difficulty of Simple Aimed MovementFitts’ law is a well-known rule of thumb of experimental psychology discovered by Fitts [1] half a century ago
Human Performance Constraints far we have considered the range of difficulty that is geometrically available in the Fitts paradigm
One important fact that seems to have been overlooked so far is that the y-intercept of a linear regression—i.e., the value taken by y at the abscissa x = 0, estimated through leftward extrapolation from a necessarily finite test range—is interpretable only to the extent that x = 0 marks an identified physical limit
Summary
Fitts’ law is a well-known rule of thumb of experimental psychology discovered by Fitts [1] half a century ago. In what we will call the Fitts paradigm, experimenters measure movement time, a random dependent variable, while systematically varying the target layout by manipulating target distance D and target tolerance W. The meaning of the movement’s endpoint spread is interpretable more safely in the discrete case, that variability being generated just by the execution of the movement, whereas in the reciprocal case the spread reflects, to some unknown extent, the variability of the start point [4,5] It is the discrete protocol, more suitable for basic research investigations, that will be considered by default. The subject of the present paper is the measurement of the difficulty of aimed movement within the framework of the Fitts paradigm This is a theoretical subject in the sense that it requires the discussion of abstract concepts. The constraints that affect D/W qua a number and D/W qua a physical variable are quite different, justifying the numerical/physical distinction crucial to the section
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