| aov {stats} | R Documentation |
Fit an analysis of variance model by a call to lm for each stratum.
aov(formula, data = NULL, projections = FALSE, qr = TRUE,
contrasts = NULL, ...)
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. |
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).
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 "aovlist". There are
print and summary methods available for these.
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 lme.
Balance can be checked with the replications function.
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.
The design was inspired by the S function of the same name described in Chambers et al. (1992).
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.
lm, summary.aov,
replications, alias,
proj, model.tables, TukeyHSD
## From Venables and Ripley (2002) p.165.
N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
K=factor(K), yield=yield)
## 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