Multivariate nonparametric methods in two-way balanced designs: performances and limitations in small samples

Fabrizio Ronchi, Solomon W. Harrar, Luigi Salmaso

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Investigations of multivariate population are pretty common in applied researches, and the two-way crossed factorial design is a common design used at the exploratory phase in industrial applications. When assumptions such as multivariate normality and covariance homogeneity are violated, the conventional wisdom is to resort to nonparametric tests for hypotheses testing. In this paper we compare the performances, and in particular the power, of some nonparametric and semi-parametric methods that have been developed in recent years. Specifically, we examined resampling methods and robust versions of classical multivariate analysis of variance (MANOVA) tests. In a simulation study, we generate data sets with different configurations of factor's effect, number of replicates, number of response variables under null hypothesis, and number of response variables under alternative hypothesis. The objective is to elicit practical advice and guides to practitioners regarding the sensitivity of the tests in the various configurations, the tradeoff between power and type I error, the strategic impact of increasing number of response variables, and the favourable performance of one test when the alternative is sparse. A real case study from an industrial engineering experiment in thermoformed packaging production is used to compare and illustrate the application of the various methods.

Original languageEnglish
Pages (from-to)1714-1741
Number of pages28
JournalJournal of Applied Statistics
Issue number7
StatePublished - 2022

Bibliographical note

Funding Information:
Authors would like to thank the Editor and Referees for useful comments and suggestions which helped improving the manuscript.

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.


  • Factorial design
  • multivariate analysis
  • nonparametric combination
  • permutation
  • power

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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