BDM.test {asbio}

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

Y

Vector of response data. A quantitative vector

X

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

X1

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

X2

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

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.

Value

Returns a list with two components

Q

The "relative effects" for each group.

Table

An ANOVA type table with hypothesis test results.

Note

Code based on Wilcox (2005)

Author(s)

Ken Aho

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.

See Also

kruskal.test, trim.test

Examples

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)