t2way function

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

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.

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.

Returns

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.

See Also

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"))