ENTROPY OF SPEED AND ACCURACY TRADE-OFF IN SPACE-TIME

Open Access
Author:
Hsieh, Tsung-yu
Graduate Program:
Kinesiology
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 17, 2015
Committee Members:
  • Karl Maxim Newell, Dissertation Advisor
  • Karl Maxim Newell, Committee Chair
  • John Henry Challis, Committee Member
  • Kristina A Neely, Committee Member
  • Runze Li, Committee Member
Keywords:
  • Speed-accuracy trade-off
  • movement entropy
  • space-time constraints
  • force-time constraints
  • isometric force task
Abstract:
The relation between movement speed and accuracy is one of the most robust phenomena in human movement performance. The essence of the speed-accuracy relation is that with an increase in movement speed there is concomitant decrease in movement accuracy. Different descriptions and explanations of the speed-accuracy relation have been proposed for characterizing time matching and time minimization movement tasks. Nevertheless, these accounts have emphasized the spatial dimension of the phenomenon providing a limited assessment given that human movement takes place in both space and time. It follows that there is a potential for both spatial error and temporal error in motor task. Hancock and Newell (1985) proposed a space-time framework of the movement speed-accuracy relation that is based on the space-time principle that the spatial component of movement is always measured with respect to time and that the temporal component of movement is always measured with respect to space (Minkowski, 1908). However, although the spatial and temporal error was considered as complementary features, they were still considered separately, as function of other features. This dissertation investigated this problem considering the joint entropy as a way to examine the movement variability of different tasks while also integrating the space-time properties of the movement. Three experiments were conducted to investigate two hypotheses: that when space and time are integrated in one measure – the joint entropy – the phenomenon will be characterized by a U-shape function – revealing an optimal region of time/space variability; and that when space and time are integrated, different descriptions of speed-accuracy trade-off phenomenon are not necessary given that the constraints are the same. Experiment 1 was set-up to investigate the space-time entropy of movement outcome as a function of a range of spatial (10, 20 and 30 cm) and temporal (250 to 2,500 ms) criteria in a discrete aiming task. The joint space-time entropy was lowest when the relative contribution of spatial and temporal task criteria was comparable (i.e., mid-range of space-time constraints), and it increased with a greater trade-off between spatial or temporal task demands, revealing a U-shaped function across space-time task criteria. In Experiment 2, two sub-experiments in an isometric single finger force task investigated the joint force-time entropy with: a) fixed time to peak force and different percentages of force level; and b) fixed percentage of force level and different times to peak force. This was done to test whether the U-shape would be generalizable across different tasks. The findings show that force error and timing error are dependent but complementary when considered in the same framework with the joint force-time entropy at a minimum in the middle parameter range of discrete impulse. In Experiment 3, time matching and time minimization movement tasks were used to test whether these different task descriptions of speed and accuracy were due to different temporal and spatial task constraints. The results showed that the joint space-time entropy of outcome did not change across tasks and conditions – revealing a common level of space-time entropy between these two categories of aiming tasks. Overall, these results showed that the joint information entropy analysis revealed the structure of movement accuracy masked by the distributional analysis of movement data when either the spatial or temporal dimensions of movement error considered alone and independently. The main contribution of this study was the cohesion of the methodological approach developed in terms of joint information entropy that provides an alternative perspective and a more complete account from which to describe and explain the speed and accuracy trade-off phenomenon.