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Description of MRPP

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Permutation Methods

Part of the book series: Springer Series in Statistics ((SSS))


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 n1, ...,ng, namely,

$$({y_{11}}, \cdots ,{y_{{n_1}1}}), \cdots ,({y_{1g}}, \cdots ,{y_{{n_g}g}}),$$

from g populations with cumulative distribution functions F1(x), ...,Fg(x), respectively. For simplicity, suppose that population i is normal with mean μi and variance σ2 (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 H0: μ1 = ... =μg versus H1: μi≠μj for some i≠j using the F statistic given by

$$F = \frac{{M{S_{between}}}}{{M{S_{within}}}}$$


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

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© 2001 Springer Science+Business Media New York

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Mielke, P.W., Berry, K.J. (2001). Description of MRPP. In: Permutation Methods. Springer Series in Statistics. Springer, New York, NY.

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3451-5

  • Online ISBN: 978-1-4757-3449-2

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