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quade.test: Quade Test

quade.test

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.

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
(qTst <- quade.test(y))

## Show equivalence of different versions of test :
utils::str(dy <- as.data.frame(as.table(y)))
qT. <- quade.test(Freq ~ Brand|Store, data = dy)
qT.$data.name <- qTst$data.name
stopifnot(all.equal(qTst, qT., tolerance = 1e-15))
dys <- dy[order(dy[,"Freq"]),]
qTs <- quade.test(Freq ~ Brand|Store, data = dys)
qTs$data.name <- qTst$data.name
stopifnot(all.equal(qTst, qTs, tolerance = 1e-15))