Forgotten moments: a note on skewness and kurtosis as influential factors in inferences extrapolated from response distributions.

It is proposed that reliance on only the mean and standard deviation of a distribution to describe response frequency may lead to erroneous inferences concerning such distributions when skewness and kurtosis are present. After defining the first four moments of a distribution, it is demonstrated analytically that skewness and kurtosis may vary to systematically influence the mean and standard deviation of a set of related distributions. The significance of these relationships for the interpretation of differing response distributions is advanced through examples gleaned from the movement control literature. in addition, it is suggested that the use of bandwidths to select scores from a distribution for subsequent data analysis can further compound the problems of both descriptive and explanatory inference, particularly when skewness and kurtosis are features of such distribution(s). Whether or not inferential statistics are invoked, a veridical perspective of distributions is essential to meaningful data analysis.