Description of MRPP

  • Paul W. MielkeJr.
  • Kenneth J. Berry
Part of the Springer Series in Statistics book series (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
$$F = \frac{{M{S_{between}}}}{{M{S_{within}}}}$$
$$M{S_{between}} = M{S_{treatment}} = \frac{1}{{g - 1}}S{S_{between,}}$$
$$S{S_{between}} = \sum\limits_{i = 1}^g {{n_i}} {({\bar y_i} - \bar y)^2},$$


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

Authors and Affiliations

  • Paul W. MielkeJr.
    • 1
  • Kenneth J. Berry
    • 2
  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.Department of SociologyColorado State UniversityFort CollinsUSA

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