quade.test               package:ctest               R Documentation

Quade Test

Description:

     Performs a Quade test with unreplicated blocked data.

Usage:

     quade.test(y, groups, blocks, ...)
     quade.test(formula, data, subset, na.action, ...)

Arguments:

       y: either a numeric vector of data values, or a data matrix.

  groups: a vector giving the group for the corresponding elements of
          `y' if this is a vector;  ignored if `y' is a matrix. If not
          a factor object, it is coerced to one.

  blocks: a vector giving the block for the corresponding elements of
          `y' if this is a vector;  ignored if `y' is a matrix. If not
          a factor object, it is coerced to one.

 formula: a formula of the form `a ~ b | c', where `a', `b' and `c'
          give the data values and corresponding groups and blocks,
          respectively.

    data: an optional data frame containing the variables in the model
          formula.

  subset: an optional vector specifying a subset of observations to be
          used.

na.action: a function which indicates what should happen when the data
          contain `NA's.  Defaults to `getOption("na.action")'.

     ...: further arguments to be passed to or from methods.

Details:

     `quade.test' can be used for analyzing unreplicated complete block
     designs (i.e., there is exactly one observation in `y' for each
     combination of levels of `groups' and `blocks') where the
     normality assumption may be violated.

     The null hypothesis is that apart from an effect of `blocks', the
     location parameter of `y' is the same in each of the `groups'.

     If `y' is a matrix, `groups' and `blocks' are obtained from the
     column and row indices, respectively.  `NA''s are not allowed in
     `groups' or `blocks';  if `y' contains `NA''s, corresponding
     blocks are removed.

Value:

     A list with class `"htest"' containing the following components: 

statistic: the value of Quade's F statistic.

parameter: a vector with the numerator and denominator degrees  of
          freedom of the approximate F distribution of the test
          statistic.

 p.value: the p-value of the test.

  method: the character string `"Quade test"'.

data.name: a character string giving the names of the data.

References:

     D. Quade (1979), Using weighted rankings in the analysis of
     complete blocks with additive block effects. Journal of the
     American Statistical Association, 74, 680-683.

     W. J. Conover (1999), Practical nonparametric statistics. New
     York: John Wiley & Sons. Pages 373-380.

See Also:

     `friedman.test'.

Examples:

     ## Conover (1999, p. 375f):
     ## Numbers of five brands of a new hand lotion sold in seven stores
     ## during one week.
     y <- matrix(c( 5,  4,  7, 10, 12,
                    1,  3,  1,  0,  2,
                   16, 12, 22, 22, 35,
                    5,  4,  3,  5,  4,
                   10,  9,  7, 13, 10,
                   19, 18, 28, 37, 58,
                   10,  7,  6,  8,  7),
                 nr = 7, byrow = TRUE,
                 dimnames =
                 list(Store = as.character(1:7),
                      Brand = LETTERS[1:5]))
     y
     quade.test(y)

