An extended difference of coherence test for comparing and combining several independent coherence estimates: theory and application to the study of motor units and physiological tremor

Abstract

Recently there has been an increase in the use of spectral methods for the analysis of experimental data. These analytical methods allow the study of interactions between simultaneously recorded signals and are particularly suited to the study of systems displaying rhythmic behaviour. A useful parameter in this context is the coherence function which provides a bounded measure of linear association between two signals. In this report we introduce two new techniques for dealing with an arbitrary number of independent coherence estimates. The first technique provides a test to compare the coherence estimates for statistically significant differences. The second allows the original coherence estimates to be combined, or 'pooled' into a single representative estimate. These two measures, taken together, provide a powerful tool for characterising and summarising the correlations within data sets. Applications of the techniques are illustrated by analysing the interactions between single motor unit discharges and finger tremor, and between pairs of motor unit discharges in human subjects.