quade.test               package:stats               R Documentation

Quade Test

Description:

     Performs a Quade test with unreplicated blocked data.

Usage:

     quade.test(y, ...)

     ## Default S3 method:
     quade.test(y, groups, blocks, ...)

     ## S3 method for class 'formula':
     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 matrix or data frame (or similar: see
          'model.frame') containing the variables in the formula
          'formula'.  By default the variables are taken from
          'environment(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.

     William 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),
                 nrow = 7, byrow = TRUE,
                 dimnames =
                 list(Store = as.character(1:7),
                      Brand = LETTERS[1:5]))
     y
     quade.test(y)

