stats (version 3.3.3)

aov: Fit an Analysis of Variance Model

Description

Fit an analysis of variance model by a call to lm for each stratum.

Usage

aov(formula, data = NULL, projections = FALSE, qr = TRUE,
    contrasts = NULL, …)

Arguments

formula

A formula specifying the model.

data

A data frame in which the variables specified in the formula will be found. If missing, the variables are searched for in the standard way.

projections

Logical flag: should the projections be returned?

qr

Logical flag: should the QR decomposition be returned?

contrasts

A list of contrasts to be used for some of the factors in the formula. These are not used for any Error term, and supplying contrasts for factors only in the Error term will give a warning.

…

Arguments to be passed to lm, such as subset or na.action. See ‘Details’ about weights.

Value

An object of class c("aov", "lm") or for multiple responses of class c("maov", "aov", "mlm", "lm") or for multiple error strata of class c("aovlist", "listof"). There are print and summary methods available for these.

Details

This provides a wrapper to lm for fitting linear models to balanced or unbalanced experimental designs. The main difference from lm is in the way print, summary and so on handle the fit: this is expressed in the traditional language of the analysis of variance rather than that of linear models. If the formula contains a single Error term, this is used to specify error strata, and appropriate models are fitted within each error stratum. The formula can specify multiple responses. Weights can be specified by a weights argument, but should not be used with an Error term, and are incompletely supported (e.g., not by model.tables).

References

Chambers, J. M., Freeny, A and Heiberger, R. M. (1992) Analysis of variance; designed experiments. Chapter 5 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

See Also

lm, summary.aov, replications, alias, proj, model.tables, TukeyHSD

Examples

## From Venables and Ripley (2002) p.165.

## Set orthogonal contrasts.
op <- options(contrasts = c("contr.helmert", "contr.poly"))
( npk.aov <- aov(yield ~ block + N*P*K, npk) )
summary(npk.aov)
coefficients(npk.aov)

## to show the effects of re-ordering terms contrast the two fits
aov(yield ~ block + N * P + K, npk)
aov(terms(yield ~ block + N * P + K, keep.order = TRUE), npk)


## as a test, not particularly sensible statistically
npk.aovE <- aov(yield ~  N*P*K + Error(block), npk)
npk.aovE
summary(npk.aovE)
options(op)  # reset to previous