BDM.test {asbio} | R Documentation |

## 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 |

`X1` |
A vector of factor levels for the first factor in a two-way factorial design. To be used with |

`X2` |
A vector of factor levels for the second factor in a two-way factorial design. To be used with |

### 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

### 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)
```

*asbio*version 1.9-7 Index]