Title: Director, Biostatistics and Stat Programming
Institution: Purdue Pharma LP
Street: 201 College Road East
City: Princeton NJ
Phone: (609) 919-3425
Fax: (609) 452-7211
Authors: David R. Bristol and Nicole Stouffer
Title: A Stepwise Maximum Modulus Test With Unequal Variances
Abstract: The maximum modulus test for comparing the means of normal distributions, discussed by Tukey (1953)and others, is usually examined with the assumption of equal variances. A competing procedure, discussed by Chakraborti (1991),for use when the unknown variances are not assumed to be equal is presented and examined in further detail. Results of simulations are presented to examine various aspects of these procedures, such as comparisons of overall Type I error rate and power when the variances are, and are not, equal. Probabilities associated with the competing procedure are easier to obtain and this procedurew also exhibits properties which allow it to be easily adapted to sequential sampling (i.e. one treatment at a time). Some aspects of the sequential testing, such as total sample size, are presented. The sequential sampling scheme often results in a smaller total number of observations than simultaneously sampling from all treatments. However, this advantage ! is achieved at the expense of a possible increase in the total duration.
References: Tukey, JW (1953). The Problems of Multiple Comparisons. Unpublished Manuscript. Chakraborti, S (1991). Graphical Comparison of Means With a Standard in the One-Way Layout, Journal of Applied Statistics 18(3), 319-329.