# quade.test

##### Quade Test

Performs a Quade test with unreplicated blocked data.

- Keywords
- htest

##### Usage

`quade.test(y, …)`# S3 method for default
quade.test(y, groups, blocks, …)

# S3 method for 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:

the value of Quade's F statistic.

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

the p-value of the test.

the character string `"Quade test"`

.

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

##### Examples

`library(stats)`

```
# NOT RUN {
## 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))
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*