BDM.test: Brunner-Dette-Munk test

Description

One and two way heteroscedastic rank-based permutation tests. Two way designs are assumed to be factorial, i.e. interactions are tested.

Usage

BDM.test(Y, X)

BDM.2way(Y, X1, X2)

Arguments

Vector of response data. A quantitative vector

A vector of factor levels for a one-way analysis. To be used with BDM.test

A vector of factor levels for the first factor in a two-way factorial design. To be used with BDM.2way.

A vector of factor levels for the second factor in a two-way factorial design. To be used with BDM.2way.

Value

Returns a list with two components
QThe "relative effects" for each group.
TableAn ANOVA type table with hypothesis test results.

Details

A problem with the Kruskal-Wallis test is that, while it does not assume normality for groups, it still assumes homoscedasticity (i.e. the groups have the same distributional shape). As a solution Brunner et al. (1997) proposed a heteroscedastic version of the Kruskal-Wallis test which utilizes the F-distribution. Along with being robust to non-normality and heteroscedasticity, calculations of exact p-values using the Brunner-Dette-Munk method are not made more complex by tied values. This is another obvious advantage over the traditional Kruskal-Wallis approach.

References

Brunner, E., Dette, H., and A. Munk (1997) Box-type approximations in nonparametric factorial designs. Journal of the American Statistical Association. 92: 1494-1502. Wilcox, R. R. (2005) Introduction to Robust Estimation and Hypothesis Testing, Second Edition. Elsevier, Burlington, MA.

Examples

Run this code

rye<-c(50,49.8,52.3,44.5,62.3,74.8,72.5,80.2,47.6,39.5,47.7,50.7)
nutrient<-factor(c(rep(1,4),rep(2,4),rep(3,4)))
BDM.test(Y=rye,X=nutrient)

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