JSM 2005 Online Program

Abstract #304414

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	36
Type:	Contributed
Date/Time:	Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #304414
Title:	A Better Boxplot
Author(s):	Dennis Boos*+ and Jacqueline M. Hughes-Oliver
Companies:	North Carolina State University and North Carolina State University
Address:	, Raleigh, NC, 27695,
Keywords:	Boxplot ; U-statistic ; L-statistic ; efficiency
Abstract:	Conceptually, the boxplot is a great tool for describing and comparing samples based on estimates of the first, second, and third quartiles of a distribution. Boxplots give information about location, scale, skewness, and possible outliers. Operationally, the boxplot does not fair so well in small to moderate samples, say n=10 to n=50. This is due to the use of biased and inefficient estimates of the quartiles and their differences. The typical user is not aware of these problems because individual boxplots, or even groups of boxplots, do not carry information about their operating characteristics. We propose a new modified boxplot that averages over boxplots for samples of size k; k=10 is our main focus. This new boxplot retains all the good conceptual features of the usual boxplot, but has much better bias and efficiency properties. The elements of the new boxplot are U-statistics with kernels of degree k. They are also linear combinations of order statistics (L-statistics), which makes computations and asymptotic analysis easier.

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