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June, 1966 An Asymptotically Distribution-free Multiple Comparison Procedure- Treatments vs. Control
Myles Hollander
Ann. Math. Statist. 37(3): 735-738 (June, 1966). DOI: 10.1214/aoms/1177699472

Abstract

Let $X_{i0}$ and $X_{ij} (i = 1, \cdots, n; j = 1, \cdots, k)$ be the independent measurements on the control and $j$th treatment in the $i$th block, with $P(X_{ij} \leqq x) = F_j(x - b_i)$ Here $b_i$ is the block $i$ nuisance parameter and the $F_j; j = 0, \cdots, k$, are assumed continuous. Nemenyi [5] suggests treatment-control comparisons based on the statistic $T = \max_j T_{0j}$ where $T_{0j}$ is defined by (2.1). It is shown here that, under the null hypothesis \begin{equation*}\tag{1.1}H_0:F_j = F \text{(unknown)},\quad j = 0, \cdots, k,\end{equation*} $T$ is neither distribution-free for finite $n$, nor asymptotically distribution-free. We also modify Nemenyi's procedure so that it is asymptotically distribution-free.

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Myles Hollander. "An Asymptotically Distribution-free Multiple Comparison Procedure- Treatments vs. Control." Ann. Math. Statist. 37 (3) 735 - 738, June, 1966. https://doi.org/10.1214/aoms/1177699472

Information

Published: June, 1966
First available in Project Euclid: 27 April 2007

zbMATH: 0147.19004
MathSciNet: MR192612
Digital Object Identifier: 10.1214/aoms/1177699472

Rights: Copyright © 1966 Institute of Mathematical Statistics

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Vol.37 • No. 3 • June, 1966
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