Simultaneous Test Envelopes for One- and Two-Sample Graphical Tests

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Graphics*
• Author(s): Fred Webber*+
• Affiliation(s): Raytheon Electronic Systems
• Keywords: Quantile-quantile plot ; Statistical computing ; Monte Carlo ; Robust estimation ; Normal plot ; Randomization test

Abstract

With graphical tests, data and test envelope are simultaneously displayed to assess whether or not the data are well-described by a given probability model. The assumed model is rejected if any data value falls outside the acceptance band defined by the test envelope. Techniques are described for constructing graphical test envelopes appropriate for univariate, two-sample, and linear regression situations. All procedures use computationally intensive techniques to estimate simultaneous test envelopes. The univariate test for a Gaussian model is an exact test approximated using Monte Carlo; the gamma-model univariate test utilizes a bootstrap calculation; the two-sample envelope requires random permutations of the combined data; and regression test envelopes are computed using a bootstrap approach with iteration. The graphical tests use new, very robust, highly efficient data standardization procedures that provide test power approaching that of the best non-robust standardization. These techniques are today best suited only for moderate-sized data sets (say, up to 1000 samples), but the applicable data size will increase with increases in processing speed and memory.