fac.aov
that contains the analysis
of variance of the specified fractional factorial design.
fac.aov(formula=<<see below>>, data=<<see below>>, response=<<see below>>, ...)
"fac.design"
, in which the variables named
in formula are to be found. If data is omitted, the current
search list is used to find the objects in formula;
frequently, a data frame will have been attached.
data
,
if supplied. This argument is used to specify the response when
the first argument is a
fac.design
(See Details for this calling option).
aov
.
"fac.aov"
which inherits from
"aov"
.
It contains all the components returned by
aov
. In addition,
the following components are returned:
coefficients
, hence the length
of feffects is the number of estimable terms in the model, excluding
the intercept.
fcoefficients
is the number of estimable terms in the model,
including the intercept.
df.residual
==0, this is identical to
feffects
. If not, it is
c(feffects, effects[-seq(feffects)]/2)
. Thus
seffects
is always
the vector of effects from a saturated model. This is useful in
calculating scale estimates such as the psuedo standard error (see
below).
mse
is
an estimate of the standard error of the effects calculated as
(rms error) * sqrt(4/n)
where
n
is the number of
observations. If there are no residual degrees of freedom,
mse
is set to
NA
.
pse
.
tse
.
ase
.
sse
is
the sum of squares of errors. Otherwise,
sse
is set
to
NA
.
feffects
have standard error
equal to
sqrt(4/n)*sigma^2
, the standard error of a factorial effect;
that is,
feffects
=
fcoefficients*adj.coef
.
design.name
attribute of
data
, if it exists.
See help for the
fac.aov
object.
This function allows a simpler calling sequence than the
S-PLUS convention of
formula, data
. If the first argument is of
class
fac.design
, this is treated as the
data
argument. The
formula is inferred as
formula(data)
. The response can be specified
by the
response
argument - by default it is the first non-factor in
data
. Since fractional
factorial designs are typically saturated, this alternative call provides a
simpler syntax, and by default a saturated model is supplied by
formula.fac.aov
.
Standard errors are estimated using pseudo, trimmed and adaptive
standard error estimates. Each of these methods use the distribution
of the one degree of freedom
seffects
. In the case of the saturated
model, these are identical to the
feffects
of the model. In the case
of the unsaturated model, the
feffects
are supplemented with the
scaled one
degree of freedom
effects
from the completion of the Q matrix in the
QR decomposition. This makes
pse
,
tse
and
ase
valid estimates of
the error even when the model is not saturated. However, when there is
replication in the model
mse
is always to be preferred as the
standard error estimate.
Berk, K. N. and R. R. Picard (1991), Significance tests for
saturated orthogonal arrays,
Journal of Quality Technology,
23, 79-89.
Box, G. E. P., W. G. Hunter, J. S. Hunter (1978),
Statistics for Experimenters,
New York: Wiley.
Haaland, P. D. (1989),
Experimental Design in Biotechnology,
New York: Marcel Dekker.
Haaland, P. D. and M. A. O'Connell (1994), Inference for effect
saturated fractional factorials, to appear in Technometrics.
# the following four calls to fac.aov are equivalent: attach(buffer.df) buffer.fac1 <-fac.aov(rate~pH*chelex*azide*gent*thimer) detach() buffer.fac2 <- fac.aov(buffer.df) buffer.fac3 <- fac.aov(rate~pH*chelex*azide*gent*thimer, buffer.df) buffer.fac4 <- fac.aov(buffer.df, response = rate) # the following two calls to fac.aov are equivalent buffer.fac5 <- fac.aov(sqrt(rate)~pH*thimer*gent*azide, buffer.df) buffer.fac6 <- fac.aov(buffer.df,response=sqrt(rate))