# Accession Number:

## ADA109283

# Title:

## On a Locally Optimal Procedure Based on Ranks for Comparison of Treatments with a Control

# Descriptive Note:

## Mimeograph series

# Corporate Author:

## PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1981-07-01

# Pagination or Media Count:

## 10.0

# Abstract:

Let Phi sub 1,...,Phi sub k be independent populations representing k experimental treatments and let Phi sub O be the control treatment. Let fx, Theta sub i denote the density of Phi sub i, iO,1,...,k, satisfying certain regularity conditions. Any population Phi sub i is said to be superior to the control if Theta sub i Theta sub O, and inferior otherwise. We assume that the value of Theta sub O is unknown but a good upper bound Theta sub O is known. We are interested in selecting a subset possibly empty of the k experimental treatments consisting of the ones that are superior to the control. Though the functional form of fx,Theta is assumed to be known, we derive a procedure based on ranks in view of the usual considerations of robustness against possible deviations from the model. In deriving the rule, we control the error probabilities and maximize the ability to detect a superior population in a certain local sense. The rule is based on the ranks of the obvservations in a pooled sample of k1n n from each population observations. In the special case of logistic density, this rule is expressed in terms of the rank-sum statistics. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability