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.
See the vignette for details.
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.