summary.aov(object, intercept = F, split = NULL, expand.split = T)
summary.aovlist(object, split = NULL, expand.split = T)

object:

a model object which inherits from the class aov or aovlist.

intercept:

logical flag: if TRUE, the variance attributed to the intercept term is included. This only applies to single strata models.

split:

a list with an element for each model term that is to be subdivided. Each element of split must be named, with a name matching the treatment terms in the model (as used to label the lines of the ANOVA table). Each element of split is also a list, specifying the grouping of contrasts for that term. (Each term has k degrees of freedom. Each of these k degrees of freedom have a corresponding contrast, used in the model fitting.) The grouping is specified by a list of (some of) the integers 1:k. Contrasts corresponding to integers in the same element of the list will be summed.

expand.split:

logical flag: if TRUE, the split is propagated down the hierarchy. If FALSE, the split is restricted to the terms specified in split. This argument is ignored if split is not given.

summary.aovlist returns an object of class "listof" which contains objects of class "anova".

The split argument is particularly useful for testing significance of polynomial terms. For instance, suppose the 4 level ordered factor Sulphur is fitted using the default contrasts contr.poly. Specifying split=list(Sulphur=list(L=1,Q=2,C=3) in the call to summary, will give a summary table with 4 lines summarising the Sulphur main effect: a 3 degree of freedom line for the overall effect of Sulphur, then three 1 degree of freedom lines, one for each of the linear, quadratic and cubic contrasts of sulphur. The sum of squares in the 3 one degree of freedom lines add up to the 3 degree of freedom term. Any higher order terms for which Sulphur is marginal will be similarly split. Alternatively, specifying split=list(Sulphur=list(L=1,rem=2:3) will give a summary table with 3 lines summarising the Sulphur main effect: a 3 degree of freedom line for the overall effects of Sulphur, then a 1 degree of freedom line for the linear effect and a 2 degree of freedom line for the remainder.

# Reference Cochran and Cox, pg 164
# 3x3 factorial split into linear and quadratic components
P <- ordered(rep(1:3, rep(3,3)))
N <- ordered(rep(1:3,3))
Plants <- c(449, 413, 326, 409, 358, 291, 341, 278, 312)

# Convert treatment totals over 12 Replicates to treatment means
Plants <- Plants/12
cox164.df <- data.frame(Plants, P, N)
cox164.aov <- aov(Plants ~ N * P, cox164.df, weight = rep(12,9),
                  qr = T)

summary(cox164.aov)

# Produces the following output:
      Df Sum of Sq  Mean Sq
  N    2  1016.667 508.3333
  P    2   917.389 458.6944
  N:P  4   399.278  99.8194

# Dividing both P and N terms into their linear and quadratic part.
# Both main terms and interaction are split
summary(cox164.aov, split = list(P = list(lin = 1, quad = 2), N =
        list(lin = 1, quad = 2)))

# Produces the following output:
                   Df Sum of Sq  Mean Sq
  N                 2  1016.667  508.333
    N: lin          1  1012.500 1012.500
    N: quad         1     4.167    4.167
  P                 2   917.389  458.694
    P: lin          1   917.347  917.347
    P: quad         1     0.042    0.042
  N:P               4   399.278   99.819
    N:P: lin.lin    1   184.083  184.083
    N:P: quad.lin   1   152.111  152.111
    N:P: lin.quad   1    49.000   49.000
    N:P: quad.quad  1    14.083   14.083

# Dividing only higher order terms, note that protection of the : in
# the list name and that the name 'P:N' will not work
summary(cox164.aov, split = list('N:P' = list(lin.lin = 1,
        quad.terms = 2:4)))

# Produces the following output:
                    Df Sum of Sq  Mean Sq
  N                  2  1016.667 508.3333
  P                  2   917.389 458.6944
  N:P                4   399.278  99.8194
    N:P: lin.lin     1   184.083 184.0833
    N:P: quad.terms  3   215.194  71.7315