Fit an Analysis of Variance Model
Fit an analysis of variance model by a call to
lm for each stratum.
aov(formula, data = NULL, projections = FALSE, qr = TRUE, contrasts = NULL, ...)
- A formula specifying the model.
- 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.
- Logical flag: should the projections be returned?
- Logical flag: should the QR decomposition be returned?
- A list of contrasts to be used for some of the factors
in the formula. These are not used for any
Errorterm, and supplying contrasts for factors only in the
Errorterm will give a warning.
- Arguments to be passed to
lm, such as
na.action. See Details about
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
summary and so on handle the fit: this is expressed in the
traditional language of the analysis of variance rather than that of
If the formula contains a single
Error term, this is used to
specify error strata, and appropriate models are fitted within each
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
aov is designed for balanced designs, and the results can be
hard to interpret without balance: beware that missing values in the
response(s) will likely lose the balance. If there are two or more
error strata, the methods used are statistically inefficient without
balance, and it may be better to use
Balance can be checked with the
The default contrasts in R are not orthogonal contrasts, and
aov and its helper functions will work better with such
contrasts: see the examples for how to select these.
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.
## 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