Permutation Methods pp 9-65 | Cite as

# Description of MRPP

Chapter

## Abstract

Multiresponse permutation procedures (MRPP) are a class of permutation methods of one or more dimensions for distinguishing possible differences among two or more groups. To motivate MRPP, initially consider samples of independent and identically distributed univariate random variables of sizes n
from
where

_{1}, ...,n_{g}, namely,$$({y_{11}}, \cdots ,{y_{{n_1}1}}), \cdots ,({y_{1g}}, \cdots ,{y_{{n_g}g}}),$$

*g*populations with cumulative distribution functions F^{1}(x), ...,F_{g}(x), respectively. For simplicity, suppose that population i is normal with mean μ_{i}and variance σ^{2}(i = 1, ...,g). This is the standard one-way classification model with*g*groups. In the classical test of a null hypothesis of no group differences, one tests H^{0}: μ^{1}= ... =μ^{g}versus H^{1}: μ^{i}≠μ^{j}for some i≠j using the*F*statistic given by$$F = \frac{{M{S_{between}}}}{{M{S_{within}}}}$$

$$M{S_{between}} = M{S_{treatment}} = \frac{1}{{g - 1}}S{S_{between,}}$$

$$S{S_{between}} = \sum\limits_{i = 1}^g {{n_i}} {({\bar y_i} - \bar y)^2},$$

## Keywords

Location Shift Unequal Sample Size Power Comparison Pearson Type MRPP Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 2001