Distributional properties and variance-stabilizing transformations for measures of uncontrolled manifold effects.
In the uncontrolled manifold (UCM) approach, variability in elemental variables (such as joint angles or muscle modes) is decomposed into goal-equivalent and non-goal-equivalent variability components (GEV, NGEV) with regard to a specified task variable. A UCM effect is present, when GEV exceeds NGEV, and different indices have been proposed to quantify the strength of UCM effects. We propose variance-stabilizing transformations for each of these measures. Our results indicate that the variability components should be log-transformed prior to statistical analysis, to reduce non-normality and inhomogeneity of variances. Moreover, it is formally shown that the UCM indices are identical after appropriate variance-stabilizing transformations. The theoretical analysis is illustrated by empirical and simulated data from a study on manual pointing.
Verrel
Julius
J
Max Planck Institute for Human Development, Lentzeallee 94, D-14195 Berlin, Germany. verrel@mpib-berlin.mpg.de
D000328:Adult; D000465:Algorithms; D000704:Analysis of Variance; D001696:Biomechanical Phenomena / Q000502:physiology; D003198:Computer Simulation / Q000592:standards*; D005121:Extremities / Q000033:anatomy & histology / Q000502:physiology; D006801:Humans; D007596:Joints / Q000033:anatomy & histology / Q000502:physiology; D009068:Movement / Q000502:physiology*; D009119:Muscle Contraction / Q000502:physiology; D018482:Muscle, Skeletal / Q000033:anatomy & histology / Q000502:physiology; D016059:Range of Motion, Articular / Q000502:physiology; D013647:Task Performance and Analysis; D055815:Young Adult