

   FFiitt aann AAnnaallyyssiiss ooff VVaarriiaannccee MMooddeell

        aov(formula, data=sys.parent(), projections=FALSE, contrasts=NULL, ...)

   AArrgguummeennttss::

    formula: A formula specifying the model.

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

   projections: Not implemented: for compatibility with S.

   contrasts: A list of contrasts to be used for some of the
             factors in the formula. This is not supported by
             the current version of `model.matrix.default' and
             so has no effect.

        ...: Arguments to be passed to `lm', such as `subset'
             or `na.action'.

   DDeessccrriippttiioonn::

        This provides a wrapper to `lm' for fitting linear mod-
        els to balanced or unbalanced experimental designs. The
        call to `lm' sets `singular.ok' to `TRUE' to allow for
        aliased effects.

        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 of linear models.

   VVaalluuee::

        An object of class `"lm"' with the additional class
        `"aov"'.

   WWAARRNNIINNGG::

        This implementation is much more basic than that in S;
        in particular `Error' is not allowed in the formula and
        there is no support for multistratum models such as
        split-plot designs.

   AAuutthhoorr((ss))::

        B.D. Ripley

   SSeeee AAllssoo::

        `lm',`alias'

   EExxaammpplleess::

        ## From Venables and Ripley (1997) p.210.
        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)
        npk.aov <- aov(yield ~ block + N*P*K, npk)
        npk.aov
        summary(npk.aov)
        coefficients(npk.aov)

