

   CCoommppuuttee EEffffiicciieenncciieess ooff MMuullttiissttrraattuumm AAnnaallyyssiiss ooff VVaarriiaannccee

        eff.aovlist(aovlist)

   AArrgguummeennttss::

    aovlist: The result of a call to `aov' with a `Error' term.

   DDeessccrriippttiioonn::

        ~~ A concise (1-5 lines) description of what the func-
        tion does. ~~

   DDeettaaiillss::

        Fixed-effect terms in an analysis of variance model
        with multiple strata may be estimable in more than one
        stratum, in which case there is less than complete
        information in each. The efficiency is the fraction of
        the maximum possible precision (inverse variance)
        obtainable by estimating in just that stratum.

        This is used to pick strata in which to estimate terms
        in `model.tables.aovlist' and elsewhere.

   VVaalluuee::

        A matrix giving for each non-pure-error stratum (row)
        the efficiencies for each fixed-effect term in the
        model.

   AAuutthhoorr((ss))::

        B.D. Ripley

   SSeeee AAllssoo::

        `aov', `model.tables.aovlist', `se.contrast.aovlist'

   EExxaammpplleess::

        ## for balanced designs all efficiencies are zero or one.
        ## so as a statistically meaningless test:
        options(contrasts=c("contr.helmert", "contr.poly"))
        ## 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.aovE <- aov(yield ~  N*P*K + Error(block), npk)
        eff.aovlist(npk.aovE)

