A Fitts task requires people to move their hand, or some pointer, along one dimension to reach, as quickly and accurately as possible, a target of width W placed at a distance D [1]. What are the degrees of freedom available in this experimental paradigm? The usual answer is D and W. We suggest that this factorial description of the paradigm is flawed, and will introduce an alternative and (we believe) a more satisfactory description.

The major discovery permitted by Fitts' paradigm is Fitts' law:

MT = k₁ * f(D/W) + k₂

where MT represents movement time (the paradigm's key dependent measure), f is some (linear, logarithmic or power) function, k₁ and k₂ are empirically adjustable coefficients, and f(D/W) is the index of difficulty (ID).

If the ratio D/W substantially influences the dependent measure (Fitts' law says it does), then D and W can no longer be regarded as independent variables, because no separate manipulation of a ratio's numerator or denominator is possible without altering the ratio itself. For example, increasing D at a constant level of W amounts to increasing both the absolute and the relative amplitude of the movement (i.e. both D and D/W), thereby confounding the two effects. The effects of D or W could be evaluated separately only if their inextricable correlate, the ratio D/W (and hence the ID), could be safely ignored - but we know by Fitts' law that this ratio is quite influential.

This confounding factor seems to have been overlooked so far in Fitts' law research, which typically has had recourse to orthogonal D x W experimental designs. We will show that this traditional design has led to measurement errors (e.g. biased estimates of Fitts' law coefficients) and given rise to some conceptual muddles (e.g. the intractable problem of isolating the effect of D).

We will introduce an alternative shape versus size analysis. Suppose we want to measure the effects of the shape and size of a set of rectangles on some dependent measure, e.g. an aesthetic rating. These two effects can be evaluated separately. Not only are a rectangle's aspect ratio and diagonal length orthogonal to each other, but our description is also exhaustive - there is no hidden correlated variable. In contrast, one cannot separate the effects of width and height on the aesthetic rating of rectangles because of the inextricable co-variation of the aspect ratio - a third variable that the width versus height analysis leaves aside. Likewise, we will argue that factorizing Fitts' paradigm in terms of (1) the ratio D/W (task shape) and (2) either D or (D² + W²)^0.5 (task size) allows us to capture all the paradigm's variability, without any confounding effects.

This revised description of Fitts' paradigm, which we will illustrate with some fresh data, sets the stage for confound-free experimental designs that disentangle the effect of the ratio D/W (the determinant of the ID) from that of movement amplitude. Moreover, it opens interesting new avenues for research on human target-directed movement in the new context of multi-scale electronic worlds [2].

References

1. Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381-391.
2. Guiard, Y.; Bourgeois, F.; Mottet, D.; Beaudouin-Lafon, M. (2001). Beyond the 10-bit barrier: Fitts' law in multi-scale electronic worlds. Proceedings of IHM-HCI 2001. Pp. 573-587 in: Blandford, A.; Vanderdonckt, J.; Gray, P. (eds.). People and Computers XV - Interactions without frontiers. London: Springer.

Paper presented at Measuring Behavior 2002 , 4^th International Conference on Methods and Techniques in Behavioral Research, 27-30 August 2002, Amsterdam, The Netherlands

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