fac.aov(formula=<<see below>>, data=<<see below>>,
          response=<<see below>>, ...)

formula:

a formula describing the model. If a formula is given and data (see below) is omitted, the current search list is used to find the terms in this formula; usually a data frame will have been attached.

data:

a data frame, typically of class "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.

response:

response variable. The default selects the first non factor in 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).

...:

arguments to be passed to aov.

feffects:

estimated factorial effects of each term in the model. Factorial effects for two level factor are, by convention, the mean change in response between the two levels of the factor. The intercept is not included, nor any with nonestimable coefficients, hence the length of feffects is the number of estimable terms in the model, excluding the intercept.

fcoefficients:

estimated coefficients of each term in the model. The length of fcoefficients is the number of estimable terms in the model, including the intercept.

seffects:

If 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:

if the residual degrees of freedom is greater than 0, 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:

the estimated pseudo standard error of the effects. See pse.

tse:

the estimated 60% trimmed standard error of the effects. See tse.

ase:

the estimated adaptive standard error of the effects. See ase.

sse:

if the residual degrees of freedom is greater than 0, sse is the sum of squares of errors. Otherwise, sse is set to NA.

adj.coef:

scale factor applied to each coefficient, so 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:

the name of the design, which is taken as the design.name attribute of data, if it exists.

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.

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))