Information theory, entropy, and movement variability

This thesis examines the variability of discrete aiming movements in terms of information theory and entropy. Four experiments were conducted to examine the information theory approach of entropy to the distributional statistics of movement variability. The trajectory variability and outcome variability were investigated by means of both information entropy and distributional measures, particularly standard deviation and coefficient of variation. This approach to measuring information entropy and mutual information in human movements was theoretically and practically developed. In Experiment 1, the analysis of information entropy revealed that the data distributions of movement trajectory were not normal and the analysis provided a new concept to interpret the variability in discrete aiming movements. In Experiment 2, the outcome variability inferred from the coefficient of variation revealed the robustness of spatial and temporal logistic variability functions of the aiming tasks, verifying the real speed-accuracy relation in a space-time model of variability. In Experiment 3, mutual information showed that there is modulation of movement trajectory, a feature that is difficult to observe through the traditional analysis of movement kinematic parameters. Based on the probability method used in the information entropy analysis, Experiment 4 developed an unified spatio-temporal variable and used it to examine how movement strategies and task goals change the variability of discrete aiming movements. Overall, these results showed that the probability-based information entropy analysis revealed the structure of movement variability masked by the distributional standard deviation estimates of movement data. The chief contribution of this study was the demonstration of information entropy as a viable measure of variability in an aiming movement task.