Movement Speed and Accuracy in Space and Time: The Complementarity of Error Distributions

ABSTRACT

Movement speed-accuracy trade-off is a function of the space-time constraints of the task. We investigated the space-time account of Hancock and Newell (1985) and the hypothesis of complementarity between the four moments of the error distribution in space and time. Twelve participants performed 15 conditions in a line drawing task composed of different spatial (10, 20, and 30 cm) and temporal (250 to 2,500 ms) criteria. The results showed that all moments of distributions changed systematically between conditions but there were some departures from the Hancock and Newell predictions. In contrast, individual analysis revealed the complementarity of the spatial and temporal error including a trade-off between the four moments of error. These findings support a complementary space-time account of movement speed and accuracy.

KEYWORDS:

• movement variability
• speed-accuracy trade-off
• space-time constraints

Notes

1. An average of 1.97 trials were taken per subject per condition. This was not influenced by condition (all conditions showed similar number of outliers).

2. Hancock and Newell (1985) based many of their assumptions on the maximum average velocity for a given movement amplitude. Note, however, that the maximum average velocity is highly dependent on the task constraints. In the follow-through paradigm the maximum average velocity arises from the shortest time an individual can move their arm through a given movement amplitude. In the discrete matching – aiming paradigm (as it is here) the maximum average velocity depends on the tolerance ratio of the target criteria that the experimenter accepts for a given amplitude.

3. The negative values of R² are related to the constraints we imposed on the model. We are constraining the model to have specific properties. If the data do not follow the model, it is possible for the variance not explained by the model (the summed distance of the model to the data) to be larger than the variance itself. This causes the R² ([Total variance – Variance not explained by the model]/Total variance) to be negative.

4. Indeed, when an unconstrained polynomial was fitted, the simplest version was a linear trend with negative intercept and positive slope for all amplitudes (R² = 0.95).

5. “I presume that the term complementarity is used to mean that the spatial and temporal errors are viewed as the parts that sum to the whole, which is presumably space-time error. If that is all that is meant, then I do not have serious objection. Even so, given this definition, I wonder what it means to say that data showed "high" or a "tight" complementarity between two kinds of error. But the authors also say that the spatial error and temporal error functions have the "same form." The authors seem to be saying that the effect of (a) movement amplitude and (b) movement time manipulations on accuracy are the same when the measurement aspects of the space-time perspective are taken into account. I assume that this is what is meant by "high complementarity" between the two types of error measurement.” (Schmidt, 1994; pp. 24–25)

Additional information

Funding

Matheus M. Pacheco was funded by CNPq, Brazil (211487/2013-9).