Related Experiment Video
Updated: Aug 24, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
Forgotten moments: a note on skewness and kurtosis as influential factors in inferences extrapolated from response
1Institute for Child Behavior and Development, University of Illinois, Champaign, Illinois 61820, USA.
Abstract:
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.
Related Concept Videos
Microsoft Excel: Finding Central Tendency, Skew, and Kurtosis
Mean: The arithmetic average of all data points. It is calculated by adding all the values together and dividing by the number of values. The mean is sensitive to extreme values (outliers).
Median: The middle value when the data points are arranged in ascending or descending...
Skewness
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are...
Types of Skewness
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
Outliers and Influential Points
Modified Boxplots
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
Regression Toward the Mean

