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

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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

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## 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"))

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