Traditionally, statistical summaries of categorical data often have been visualized using graphical plots of central moments (e.g., mean and standard deviation), or cumulants (e.g., median and quartiles) by box plots. In this work we reexamine the box plot and its relatives and develop a new hybrid summary plot that combines moment, cumulant, and density information. In view of the important role of plots in decision making, our work focuses on incorporating additional descriptive parameters while simultaneously improving the comprehensibility of the summary plots using advanced visual techniques. In many complex situations providing a comprehensive view of the data requires additional summary characteristics, therefore, we submit that these additional parameters, like higher-order central moments can be valuable elements of multi-dimensional summary displays.
@TechReport{ potter:2007:VSS,
author = "Kristin Potter and Joe Kniss and Richard Riesenfeld",
title = "Visual Summary Statistics",
institution = "Univeristy of Utah",
year = "2007",
number = "UUCS-07-004",
}
Lee J. Bain and Max Engelhardt. Introduction to Probability and Mathematical Statistics. Duxbury Press, 1992.
Chandrajit L. Bajaj, Valerio Pascucci, and Daniel R. Schikore. The contour spectrum. In IEEE VIS '97: Proceedings of the 8th conference on Visualization '97, pages 167-173, 1997.
Richard A. Becker and William S. Cleveland. Brushing scatterplots. Technometrics, 29(2):127-142, May 1987.
Yoav Benjamini. Opening the box of a boxplot. The American Statistician, 42(4):257-262, November 1988.
Chamnein Choonpradub and Don McNeil. Can the box plot be improved? Songklanakarin Journal of Science and Technology, 27(3):649-657, 2005.
William S. Cleveland. The Elements of Graphing Data. Hobart Press, 1994.
Sarah E. Geneser, Robert M. Kirby, and Frank B. Sachse. Sensitivity analysis of cardiac electrophysiological models using polynomial chaos. In Proceedings of the 27th Annual IEEE EMBS, 2005.
Kenneth M. Goldberg and Boris Iglewicz. Bivariate extensions of the boxplot. Technometrics, 34(3):307-320, August 1992.
Jerry L. Hintze and Ray D. Nelson. Violin plots: A box plot-density trace synergism. The American Statistician, 52(2):181-184, May 1998.
Robert McGill, John W. Tukey, and Wayne A. Larsen. Variations of box plots. The American Statistician, 32(1):12-16, February 1978.
Peter J. Rousseeuw, Ida Ruts, and John W. Tukey. The bagplot: A bivariate boxplot. The American Statistician, 53(4):382-287, November 1999.
Mary Eleanor Spear. Charting Statistics. McGraw-Hill, 1952.
Phattrawan Tongkumchum. Two-dimensional box plot. Songklanakarin Journal of Science and Technology, 27(4):859-866, 2005.
Edward R. Tufte. The Visual Display of Quantitative Information. Graphics Press, 1983.
John W. Tukey. Exploratory Data Analysis. Addison-Wesley, 1977.
Leland Wilkinson. The Grammar of Graphics. Springer-Verlag New York, Inc., 1999.