Fuzzy and Randomized Confidence Intervals and P-values

University of Minnesota, Twin Cities     School of Statistics

Papers

There are three papers on this subject:

Fuzzy and Randomized Confidence Intervals and P-values
by Charles J. Geyer and Glen D. Meeden
To appear (with discussion) in Statistical Science

and

Fuzzy P-values in Latent Variable Problems
by Elizabeth A. Thompson and Charles J. Geyer

and

Fuzzy P-values and Ties in Nonparametric Tests
by Charles J. Geyer

Computing

R Packages

The computing for Geyer and Meeden (2005) was done with a somewhat primitive R package ump. Now (at version 0.5) it only does UMPU tests and confidence intervals, fuzzy and randomized, for the binomial distribution.

The source tarball ump_0.5-1.tar.gz is available here, but the package is better installed from CRAN under contributed extension packages.

The computing for Geyer (submitted) was done with an R package fuzzyRankTests. Now (at version 0.3) it only does fuzzy-exact tests and confidence intervals, that are the competitors of the classical sign test, Wilcoxon signed rank test, Mann-Whitney-Wilcoxon rank sum tests, and their associated confidence intervals.

The source tarball fuzzyRankTests_0.3.tar.gz is available here, but the package is better installed from CRAN under contributed extension packages.

Rweb

The R package can be tried out on line using Rweb.

Morgan

The computing for Thompson and Geyer (2005) was done in the computer package MORGAN (in an experimental, not yet released version, that will eventually be released).

Talks

Overheads for talk given at University of Minnesota and at the JSM in San Francisco as PostScript or as PDF.

Overheads for talk given at the Fred Hutchinson Cancer Research Center in Seattle as PDF

Overheads for talk given June 23, 2005 at WNAR in Fairbanks as PDF

Teaching

Fuzzy confidence intervals and P-values, computed using the R package fuzzyRankTests are being taught in Stat 5601 (master's level service course on nonparametrics also taken by undergrads). See web pages on fuzzy P-values and confidence intervals, the sign test and associated procedures, the Wilcoxon signed rank test and associated procedures, the Mann-Whitney-Wilcoxon rank sum test and associated procedures.

Fuzzy confidence intervals and P-values, computed using the R package ump are being taught in Stat 5021 (master's level service course on basic statistics). See the handout A fuzzy binomal confidence interval.

Fuzzy Error Bars

An example of fuzzy confidence intervals used as error bars that didn't fit in Geyer and Meeden (2005). This example was done in Sweave. The Rnw (R noweb) source is available.

More Fuzzy Confidence Intervals

The discussants for the paper by Geyer and Meeden (2005) proposed (or perhaps found in old literature) two fuzzy confidence intervals for the binomial distribution that are different from the UMPU intervals proposed by Geyer and Meeden (2005).

An example of these three fuzzy confidence intervals compared clarifies the agreement and disagreement between Geyer and Meeden (2005) and their discussants (who are cited therein).