On an Extension of Woodruff's Method for Calculating Sampling Variability for Medians

• Activity Number: 364
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Claude Girard*+
• Companies: Statistics Canada
• Keywords: Woodruff ; median ; variance

Abstract

Woodruff developed a method that constructs confidence intervals for the median having approximately sought level. Also known, but not well documented, is the sigma-extension: the possibility to draw from Woodruff's method a point estimate of sampling variability for an estimate of the median. Unfortunately, the sigma-extension yields sampling variability estimates dependent upon the confidence level first used to construct the confidence interval they are derived from. Furthermore, these sampling variability estimates are rather unstable. These problems may deter practitioners from using the sigma-extension. Both the dependence and instability arise from the way Woodruff's method is usually implemented. We propose a modification to Woodruff's method implementation that gives rise to a sigma-extension free of the dependence on confidence levels and yields more stable sampling variability estimates. The approach is quite possibly novel from a practitioner point-of-view, while from a theoretical perspective it uses ideas already known in the literature but presented in a way not easily seen to be of immediate use to the practicing statistician.