# t2way: A two-way ANOVA for trimmed means, M-estimators, and medians. In WRS2: A Collection of Robust Statistical Methods

 t2way 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. `...` currently ignored.

### Details

`t2way` does not report any degrees of freedom since an adjusted critical value is used. `pbad2way` 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 `dim` design dimensions

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.

`t1way`, `med1way`, `t2way`

### 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"))
``````

WRS2 documentation built on May 29, 2024, 7:37 a.m.