Skip to main content

Description of MRPP

  • Chapter
Permutation Methods

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

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 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

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

where

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Mielke, P.W., Berry, K.J. (2001). Description of MRPP. In: Permutation Methods. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3449-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3449-2_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-3451-5

  • Online ISBN: 978-1-4757-3449-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics