quadeAllPairsTest {PMCMRplus}

All-Pairs Comparisons for Unreplicated Blocked Data (Quade's All-Pairs Test)

Description

Performs Quade multiple-comparison test for unreplicated blocked data.

Usage

quadeAllPairsTest(y, ...)

## Default S3 method:
quadeAllPairsTest(
  y,
  groups,
  blocks,
  dist = c("TDist", "Normal"),
  p.adjust.method = p.adjust.methods,
  ...
)

Arguments

y

a numeric vector of data values, or a list of numeric data vectors.

groups

a vector or factor object giving the group for the corresponding elements of "x". Ignored with a warning if "x" is a list.

blocks

a vector or factor object giving the block for the corresponding elements of "x". Ignored with a warning if "x" is a list.

dist

the test distribution. Defaults to "TDist".

p.adjust.method

method for adjusting p values (see p.adjust).

...

further arguments to be passed to or from methods.

Details

For all-pairs comparisons of unreplicated blocked data Quade's test can be applied. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: \theta_i = \theta_j is tested in the two-tailed test against the alternative A_{ij}: \theta_i \ne \theta_j, ~~ i \ne j.

The function has included two methods for approximate p-value estimation:

TDist

p-values are computed from the t distribution

Normal

p-values are computed from the standard normal distribution

If no p-value adjustment is performed (p.adjust.method = "none"), than a simple protected test is recommended, i.e. all-pairs comparisons should only be applied after a significant quade.test. However, any method as implemented in p.adjust.methods can be selected by the user.

Value

A list with class "PMCMR" containing the following components:

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

statistic

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

References

W. J. Conover (1999), Practical nonparametric Statistics, 3rd. Edition, Wiley.

N. A. Heckert and J. J. Filliben (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions. National Institute of Standards and Technology Handbook Series, June 2003.

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.

See Also

quade.test, friedmanTest

Examples

## Sachs, 1997, p. 675
## Six persons (block) received six different diuretics
## (A to F, treatment).
## The responses are the Na-concentration (mval)
## in the urine measured 2 hours after each treatment.
##
y <- matrix(c(
3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
26.65),nrow=6, ncol=6,
dimnames=list(1:6, LETTERS[1:6]))
print(y)

## Global test
quade.test(y)

## All-pairs comparisons
quadeAllPairsTest(y, dist="TDist", p.adjust.method="holm")