A Follow-Up to the Range Disparity Distribution and Its Applications

• Activity Number: 548
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lawrence Marinucci*+ and Paul Lupinacci and Joel Waksman and Tai Xie
• Companies: Acorda Therapeutics, Inc. and Villanova University and Brightech International and Brightech International
• Keywords: probability distribution ; central tendency ; range ; sample distributions ; exceptional values

Abstract

Conventionally, inferential statistics focuses on measures of central tendency, eg, the population mean. Little attention is given to differences in the range of sample distributions, and the range is often associated with exceptional values. Under certain circumstances, effects visible at the edges of a sample distribution may provide more sensitive and even more meaningful measures of differences between populations than the difference in means. In this paper we introduce the Range Disparity Distribution (RDD) to describe the probability that a given number of items in one set fall outside the range of all the items in another set on a given measure. Here we define the RDD, prove that it is a probability distribution, and then proceed to derive the mean and variance. We also provide a statistical test comparing two groups based on the RDD.