wilcoxtestClust {htestClust}

Rank Sum and Signed Rank Tests for Clustered Data

Description

Performs a one-sample or paired cluster-weighted signed rank test, or a cluster- or group-weighted rank sum test. These tests are appropriate for clustered data with potentially informative cluster size.

Usage

wilcoxtestClust(x, ...)

## Default S3 method:
wilcoxtestClust(
  x,
  y = NULL,
  idx,
  idy = NULL,
  alternative = c("two.sided", "less", "greater"),
  mu = 0,
  paired = FALSE,
  method = c("cluster", "group"),
  ...
)

## S3 method for class 'formula'
wilcoxtestClust(formula, id, data, subset, na.action, ...)

Arguments

x, y

numeric vectors of data values.

...

further arguments to be passed to or from methods.

idx

vector or factor object denoting cluster membership for x observations (or cluster membership for paired observations when paired is TRUE). Length must be equal to length of x.

idy

vector or factor object denoting cluster membership for y observations. Length must be equal to length of y

alternative

indicates the alternative hypothesis and must be one of "two.sided", "greater", or "less".You can specify just the initial letter.

mu

a number specifying an optional parameter used to form the null hypothesis. Ignored when performing a rank-sum test. See 'Details'.

paired

a logical indicating whether x and y are paired. When TRUE, the cluster-weighted signed rank test is performed.

method

a character string specifying the method of rank sum test to be performed. See 'Details'.

formula

a formula of the form lhs ~ rhs, where lhs is a numeric variable giving the data values and rhs a numeric or factor with two levels giving the corresponding groups.

id

a vector or factor object denoting cluster membership.

data

an optional matrix or data frame containing variables in the formula formula and id. 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 data contain NAs. Defaults to getOption("na.action").

Details

The formula interface is only applicable for the 2-sample rank-sum tests.

If only x and idx are given, a cluster-weighted signed rank test of the null that the distribution of x is symmetric about mu is performed.

If x and y are given and paired is TRUE, only idx is necessary (idy is ignored). In this case, a cluster-weighted signed-rank test of the null that the distribution of x - y is symmetric about mu is performed.

When method is cluster, the cluster-weighted rank sum test of Datta and Satten (2005) is performed. The data must have complete intra-cluster group distribution (i.e., all clusters must contain observations belonging to both groups) for this test to be performed.

When method is group, the group-weighted rank-sum test of Dutta and Datta (2015) is performed. This test is appropriate for clustered data with potentially informative intra-cluster group size. Incomplete intra-cluster group distribution is permitted.

For the rank sum tests, the null is that the two groups follow the same marginal distribution. mu is ignored when performing these tests.

The tests performed by this function involve computation of reweighted empirical CDFs. This is computationally intensive and can result in lengthy execution time for large data sets.

Value

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

statistic

the value of the test statistic.

p.value

the p-value of the test.

null.value

the location parameter mu. Always 0 for rank sum test.

data.name

a character string giving the name(s) of the data and the total number of clusters.

method

a character string indicating the test performed and method of construction.

alternative

a character string describing the alternative hypothesis.

M

the number of clusters.

References

Datta, S., Satten, G. (2005) Rank-sum tests for clustered data. J. Am. Stat. Assoc., 100, 908–915.

Datta, S., Satten, G. (2008) A signed-rank test for clustered data. Biometrics, 64, 501–507.

Dutta, S., Datta, S. (2015) A rank-sum test for clustered data when the number of subjects in a group within a cluster is informative. Biometrics, 72, 432–440.

Examples

  data(screen8)
  ## One-sample signed rank test
  wilcoxtestClust(x=screen8$math, idx=screen8$sch.id, mu=70)

  ## Paired signed rank test
  wilcoxtestClust(x=screen8$math, y=screen8$read, idx=screen8$sch.id, paired=TRUE, mu=10)

  ## Cluster-weighted rank sum test
  wilcoxtestClust(math~gender, id=sch.id, data=screen8)


  ## Group-weighted rank sum test
  boys <- subset(screen8, gender=='M')
  girls <- subset(screen8, gender=='F')
  wilcoxtestClust(x=boys$math, y=girls$math, idx=boys$sch.id, idy=girls$sch.id, method="group")

  ## Group-weighted rank sum test using formula method
  wilcoxtestClust(math~gender, id=sch.id, data=screen8, method="group")