# A two-way ANOVA for trimmed means, M-estimators, and medians.

### Description

The `t2way`

function computes a two-way ANOVA for trimmed means with interactions effects. Corresponding post hoc tests are in `mcp2atm`

. `pbad2way`

performs a two-way ANOVA using M-estimators for location with `mcp2a`

for post hoc tests.

### Usage

1 2 3 4 |

### Arguments

`formula` |
an object of class formula. |

`data` |
an optional data frame for the input data. |

`tr` |
trim level for the mean. |

`est` |
Estimate to be used for the group comparisons: either |

`nboot` |
number of bootstrap samples. |

`pro.dis` |
If |

### Details

The `pbad2way`

function returns p-values only. If it happens that the variance-covariance matrix in the Mahalanobis distance computation
is singular, it is suggested to use the projection distances by setting `pro.dis = TRUE`

.

### Value

The functions `t2way`

and `pbad2way`

return an object of class `t2way`

containing:

`Qa` |
first main effect |

`A.p.value` |
p-value first main effect |

`Qb` |
second main effect |

`B.p.value` |
p-value second main effect |

`Qab` |
interaction effect |

`AB.p.value` |
p-value interaction effect |

`call` |
function call |

`varnames` |
variable names |

The functions `mcp2atm`

and `mcp2a`

return an object of class `mcp`

containing:

`effects` |
list with post hoc comparisons for all effects |

`contrasts` |
design matrix |

### References

Wilcox, R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Elsevier.

### See Also

`t1way`

, `med1way`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
## 2-way ANOVA on trimmed means
t2way(attractiveness ~ gender*alcohol, data = goggles)
## post hoc tests
mcp2atm(attractiveness ~ gender*alcohol, data = goggles)
## 2-way ANOVA on MOM estimator
pbad2way(attractiveness ~ gender*alcohol, data = goggles)
## post hoc tests
mcp2a(attractiveness ~ gender*alcohol, data = goggles)
## 2-way ANOVA on medians
pbad2way(attractiveness ~ gender*alcohol, data = goggles, est = "median")
## post hoc tests
mcp2a(attractiveness ~ gender*alcohol, data = goggles, est = "median")
## extract design matrix
model.matrix(mcp2a(attractiveness ~ gender*alcohol, data = goggles, est = "median"))
``` |