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

t2way {WRS2} | R Documentation

## 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

    t2way(formula, data, tr = 0.2)
    pbad2way(formula, data, est = "mom", nboot = 599, pro.dis = FALSE)
    mcp2atm(formula, data, tr = 0.2)
    mcp2a(formula, data, est = "mom", nboot = 599)

### 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 `"onestep"` for one-step M-estimator of location using Huber's Psi, `"mom"` for the modified one-step (MOM) estimator of location based on Huber's Psi, or `"median"`.
`nboot` | number of bootstrap samples.
`pro.dis` | If `FALSE`, Mahalanobis distances are used; if `TRUE` projection distances are computed.

### 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

    ## 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"))

[Package WRS2 version 0.9-2 Index]