PairedData (version 1.1.1)

grambsch.Var.test: Grambsch test of scale for paired samples

Description

Robust test of scale for paired samples.

Usage

grambsch.Var.test(x, ...)
# S3 method for default
grambsch.Var.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),...)
# S3 method for paired
grambsch.Var.test(x, ...)

Arguments

x

first sample or an object of class paired.

y

second sample.

alternative

alternative hypothesis.

…

further arguments to be passed to or from methods.

Value

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

statistic

the value of the F-statistic.

p.value

the p-value for the test.

null.value

the specified hypothesized value of the ratio of variances (=1!)

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of test was performed.

data.name

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

Details

Denoting s=x+y and d=x-y, the test proposed by Grambsch (1994, and called by the author 'modified Pitman test') is based on the fact that var(x)-var(y)=cov(x+y,x-y)=cov(s,d). The values z=(s-mean(s))(d-mean(d)) can be tested for null expectation using a classical t test in order to compare the two variances. Note that the p value is computed using the normal distribution.

References

Grambsch,P.M. (1994) Simple robust tests for scale differences in paired data. Biometrika, 81, 359-372.

See Also

Var.test, bonettseier.Var.test

Examples

# NOT RUN {
z<-rnorm(20)
x<-rnorm(20)+z
y<-(rnorm(20)+z)*2
grambsch.Var.test(x,y)

p<-paired(x,y)
grambsch.Var.test(p)
# }