Polar and Cartesian Structure in the Data of Fitts’s (1954) Classic Experiments—with a Criterion for Distinguishing a Strong and a Weak Version of Fitts’ Law

Abstract

The time T needed to reach a target of width W located at distance D varies as a logarithmic or power function of the quotient of D/W. The received, strong version of Fitts’ law requires isochrony—the invariance of T across different D/W conditions with the same quotient—but there is room for a weaker, yet nontrivial version of Fitts’ law where scale influences T without interacting with the crucial quotient. The data of Fitts’s historic experiments are submitted to Cartesian/polar analysis. While tapping beautifully illustrates the strong, isochronous version of Fitts’ law, contrary to a widespread belief Fitts’s other two experiments were not just half-failed corroborations: The disc-transfer data eloquently illustrate the weak version of Fitts’ law, and the pin-transfer data flatly violate the law. Surprisingly, however, the pin-transfer data are remarkably simple in the alternative Cartesian description system, factors D and W exerting separate, additive effects on T. PUBLIC SIGNIFICANCE STATEMENT. Sixty years ago Fitts published the first experimental demonstration of the quantitative rule famously known today as Fitts’ law. This paper reports a complete reanalysis of the numerical data that Fitts tabulated in detail in his article, revealing patterns of remarkable coherence that had been so far unsuspected due to undetected ambiguities concerning the dimensions of Fitts’ law. One particular intriguing discovery is that there exist two different versions of Fitts’ law, both eloquently illustrated by Fitts’s own data.