# Calculate pairwise multiple comparisons between mean rank sums

### Description

The Kruskal and Wallis one-way analysis of variance by ranks or van der Waerden's normal score test can be employed, if the data do not meet the assumptions for one-way ANOVA. Provided that significant differences were detected by the omnibus test, one may be interested in applying post-hoc tests for pairwise multiple comparisons (such as Nemenyi's test, Dunn's test, Conover's test, van der Waerden's test). Similarly, one-way ANOVA with repeated measures that is also referred to as ANOVA with unreplicated block design can also be conducted via the Friedman-Test or the Quade-test. The consequent post-hoc pairwise multiple comparison tests according to Nemenyi, Conover and Quade are also provided in this package. Finally Durbin's test for a two-way balanced incomplete block design (BIBD) is also given in this package.

### Details

Package: | PMCMR |

Type: | Package |

Version: | 4.1 |

Date: | 2016-01-06 |

License: | >= GPL-3 |

See the vignette for details.

### Author(s)

Thorsten Pohlert

Maintainer: <thorsten.pohlert@gmx.de>

### References

W. J. Conover and R. L. Iman (1979), *On multiple-comparisons
procedures*, Tech. Rep. LA-7677-MS, Los Alamos Scientific Laboratory.

W. J. Conover (1999), *Practical nonparametric Statistics*, 3rd. Edition, Wiley.

Janez Demsar (2006), Statistical comparisons of classifiers over multiple data sets, *Journal of Machine Learning Research*, 7, 1-30.

O.J. Dunn (1964). Multiple comparisons using rank sums. *Technometrics*, 6, 241-252.

S. A. Glantz (2012), *Primer of Biostatistics*, 7th edition. New
York: McGraw Hill.

N. A. Heckert and J. J. Filliben (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions. National Institute of Standards and Technology Handbook Series, June 2003.

A. R. Jonckheere (1954). A distribution-free k-sample test against
ordered alternatives. *Biometrica*, 41, 133-145.

P. Nemenyi (1963) *Distribution-free Multiple Comparisons*. Ph.D. thesis, Princeton University.

D. Quade (1979), Using weighted rankings in the analysis of complete blocks with additive block effects. *Journal of the American Statistical Association*, 74, 680-683.

Lothar Sachs (1997), *Angewandte Statistik*. Berlin:
Springer. Pages: 668-675.

### See Also

`posthoc.kruskal.nemenyi.test`

,
`posthoc.kruskal.dunn.test`

,
`posthoc.kruskal.conover.test`

,
`posthoc.friedman.nemenyi.test`

,
`posthoc.friedman.conover.test`

,
`posthoc.quade.test`

,
`dunn.test.control`

,
`jonckheere.test`

,
`durbin.test`

,
`posthoc.durbin.test`

,
`kruskal.test`

,
`friedman.test`

,
`Tukey`

,
`TDist`

,
`Chisquare`

,
`Normal`

,
`p.adjust`

,
`print.PMCMR`

,
`summary.PMCMR`

,
`get.pvalues`

,
`multcompLetters`