Methods for spherical data analysis and visualization

A systematic analysis of the localization of objects in extra-personal space requires a three-dimensional method of documenting location. In auditory localization studies the location of a sound source is often reduced to a directional vector with constant magnitude with respect to the observer, data being plotted on a unit sphere with the observer at the origin. This is an attractive form of data representation as the relevant spherical statistical and graphical methods are well described. In this paper we collect together a set of spherical plotting and statistical procedures to visualize and summarize these data. We describe methods for visualizing auditory localization data without assuming that the principal components of the data are aligned with the coordinate system. As a means of comparing experimental techniques and having a common set of data for the verification of spherical statistics, the software (implemented in MATLAB) and database described in this paper have been placed in the public domain. Although originally intended for the visualization and summarization of auditory psychophysical data, these routines are sufficiently general to be applied in other situations involving spherical data.