Real data often do not approximate the normal distribution. Under nonnormal conditions, psychophysiologists who use parametric statistics may be testing with inadequate power and/or testing a measure of location (i.e., the mean) that does not represent the desired portion of the distribution for statistical comparison. The purpose of this paper is: first, to provide psychophysiologists with a method to investigate group distributional characteristics; second, to evaluate the distributional characteristics of heart period and respiratory sinus arrhythmia in human adults and newborns; third, to demonstrate the increased statistical power that can accompany the selection of an alternative statistical analysis for nonnormal data. Suggestions are provided on how to analyze nonnormal data.