Amplitude and target diameter in motor programming of discrete, rapid aimed movements: Fitts and Peterson (1964) and Klapp (1975) revisited

Abstract

The reports by Fitts and Peterson [J. Exp. Psychol. 67(2) (1964) 103–113] and Klapp [J. Exp. Psychol. Hum. Percept. Perform. 104(2) (1975) 147–153] concerning the effects of movement amplitude and target diameter on reaction time present conflicting results. Fitts and Peterson reported that reaction time increased when movement amplitude was lengthened. Klapp reported an interaction in which target diameter effect on reaction time was moderated by movement length: for small targets, reaction time decreased with increasing movement length but reaction time remained unchanged (or increased modestly) when target diameter was large. Two experiments were conducted to replicate and examine the inconsistency in the reaction time results. For both experiments movement time results were in agreement with the predictions of Fitts' law. However, the results for reaction time were mixed: support was obtained for Klapp (1975) but not for Fitts and Peterson (1964). Further analysis identified several potential variables that could have influenced reaction time and explained the different effects on reaction time reported by Fitts and Peterson (1964) and Klapp (1975). The potential variables could include: limb posture at the start of a response; number of limb segments required to perform the task; and the effect of pooling reaction time data from targets located right and left of the start point, and from near and far targets.

Introduction

Imagine being in a great hurry and stabbing the elevator button for the 15th floor. Successful performance of this fast, visually guided movement depends on a compromise between speed of the limb (preferred index finger) and accuracy of acquiring the target (elevator button). This compromise between speed and accuracy, typically described as speed–accuracy trade-off, was first reported by Woodworth (1899). Later, Fitts (1954) described this relationship mathematically and formulated the well-known equation “index of difficulty”. The index of difficulty was formed by the ratio between the distance the limb travelled to a target and the width of the target. The index of difficulty is a robust predictor of movement time and the equation describing the relationship is known as Fitts' law (Fitts, 1954; Fitts & Peterson, 1964). Formally, Fitts' law is defined as

$$\text{MT}\text{=a+b}\text{ID}$$

and

$$\text{ID}\text{=}\text{log}{}_2\text{(2A/W),}$$

where MT refers to movement time, ID to the index of difficulty, A to movement amplitude, and W to the width (diameter) of the target. The intercept (a) and slope (b) are empirically defined constants dependent on the nature of the criterion task (Langolf, Chaffin, & Foulke, 1976).

Movement execution and preparation can be viewed as two ends of a continuum describing response production. Thus execution of a visually guided movement cannot occur in isolation. Although it is possible for preparation to occur in the absence of execution, the reverse does not hold. While Fitts' law has a strong association with prediction of movement time, much less attention has been paid to the effects of index of difficulty on reaction time.

For a relatively small pool of studies, reaction time has been reported to increase with increase in index of difficulty (Fitts & Peterson, 1964), and to be unaffected by index of difficulty (Wallace, Newell, & Wade, 1978). When target diameter and movement amplitude were separately manipulated without changing index of difficulty, reaction time varied such that variable movement amplitude resulted in longer reaction time than variable target width (Sheridan, 1981).

With respect to movement amplitude alone, increases have resulted in increased reaction time (Fitts and Peterson, 1964, Semjen and Requin, 1976). Furthermore, Siegel (1977) described a U-shaped relationship between reaction time and movement amplitude, in which reaction time was greatest for the shortest and longest movement amplitude. In contrast, Klapp (1975) reported an interaction between movement amplitude and target diameter in which, for smaller target diameters, reaction time decreased with increase in movement amplitude. This effect was reversed for the larger target diameters. The reported effects of target diameter on reaction time are also inconsistent. Reaction time was unaffected by change in target diameter alone (Fitts and Peterson, 1964, Semjen and Requin, 1976, Wallace et al., 1978). However, it has also been reported that reaction time increased when target diameter was decreased (Goggin and Christina, 1979, Klapp, 1975, Klapp and Greim, 1979, Siegel, 1977).

One explanation for the inconsistency in the literature concerning the effects of movement amplitude and target diameter on reaction time could be in methodological differences between the benchmark studies of Fitts and Peterson (1964) and Klapp (1975). Firstly, Fitts and Peterson reported that the effect on reaction time was due to movement amplitude alone. Later Klapp (1975) argued that the restricted range of movement amplitude (lengths) used by Fitts and Peterson prevented an effect of target diameter on reaction time from being observed. Klapp reasoned that inclusion of smaller amplitudes (movement lengths) would minimise the subjects' ability to utilise visual feedback, and that the whole response needed to be preprogrammed. The increased processing demands of programming would result in lengthened reaction time. According to Fitts' law movement amplitude is defined as the distance from the start point to the centre of the target. Based on this definition, movement amplitude as a separate parameter could not be equal to or less than the radius of the target. Klapp's measure of movement amplitude was the distance from the start point to the leading edge of the target. This inconsistency is potentially confusing because the reported reaction time results are based on a task in which amplitude is not in compliance with Fitts' law. Theoretically, based on the definition of movement length used by Klapp (1975), movement amplitude could be diminished indefinitely and associated with targets of any width. Practically, this is not helpful, as the length of the movement available to meet the speed and accuracy requirements of the response would be influenced by target width. Thus, for short-length movements increase in the diameter of the target would increase movement length.

Secondly, participants in Fitts and Peterson's study were instructed to move fast and accurately, and analysis revealed that their performances were associated with approximately 10% errors. In Klapp's (1975) study the participants were advised to move faster if their error rate was less than 10%, and slower if error rate was greater than 10% during a block of trials. Thus, in Fitts and Peterson's study percentage error was a post hoc dependent measure, and in Klapp's study percentage error was an independent variable that could have influenced subjects' performance differently.

Another issue that could have contributed to the conflicting results about the effects of movement amplitude and target diameter on reaction time is the method of data analysis. Reaction time data from right and left targets (with respect to body midline and/or start point) were pooled together. The assumption that reaction times to targets located left and right of the start are not different can be questioned. Movements that cross the body midline (e.g., to the left in right-handed people) alter the effect on reaction time (Fisk & Goodale, 1985). Fitts and Peterson (1964) reported that reaction time for left and right movements was not different, but the potential right/left effect was not discussed by Klapp (1975). Like Fitts and Peterson, Klapp pooled responses from the left and right targets.

Execution of tasks requiring movement in different directions and for different lengths is likely to be accomplished by recruitment of different limb segments that contribute differently to response production. In these circumstances, it is likely that different preparatory process would be involved. Therefore, a more robust test of the movement amplitude effect on reaction time would require that the number of joints and nature of limb segments involved remain constant.

However, before alternative explanations for differences in effects on reaction time between Fitts and Peterson and Klapp can be proposed, it is necessary that the original studies be replicated within a consistent laboratory setting. In the first experiment (a replication of Fitts & Peterson, 1964) it was hypothesised that reaction time would increase with an increase in movement amplitude and that reaction time would not be affected by the diameter of the target. In the second experiment (a replication of Klapp, 1975) it was hypothesised that reaction time would increase with a decrease in target diameter for short-length movements, and that reaction time would not be affected by the amplitude of the movement. To evaluate the possible effects of pooling data from left and right targets a separate analysis of data from left and right targets was conducted.