Distributional properties and variance-stabilizing transformations for measures of uncontrolled manifold effects

Julius Verrel*

*Corresponding author for this work

Abstract

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.

Original languageEnglish
JournalJournal of Neuroscience Methods
Volume191
Issue number2
Pages (from-to)166-170
Number of pages5
ISSN0165-0270
DOIs
Publication statusPublished - 08.2010

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