wle.var.test {wle}R Documentation

Weighted F Test to Compare Two Variances

Description

Performs an Weighted F test to compare the variances of two samples from normal populations. The WF-test is based on weighted likelihood.

Usage

wle.var.test(x, y, ratio = 1, alternative = c("two.sided", "less", "greater"),
         conf.level = 0.95, x.root=1, y.root=1)

Arguments

x, y fitted linear model objects (inheriting from class "wle.lm") or fitted normal model objects (inheriting from class "wle.normal").
ratio the hypothesized ratio of the population variances of x and y.
alternative the alternative hypothesis; must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
conf.level confidence level for the returned confidence interval.
x.root the 'x' root used.
y.root the 'y' root used.

Details

The null hypothesis is that the ratio of the variances in the data to which the normal model (wle.normal) or linear models (wle.lm) x and y were fitted, is equal to ratio.

Value

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

statistic the value of the WF test statistic.
parameter the degrees of the freedom of the WF distribtion of the test statistic.
p.value the p-value of the test.
conf.int a confidence interval for the ratio of the population variances.
estimate the ratio of the sample variances from x and y.
null.value the ratio of population variances under the null.
alternative a character string describing the alternative hypothesis.
method the string "WF test to compare two variances".
data.name a character string giving the names of the data.

References

Agostinelli, C., (1998). Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D Thesis, Department of Statistics, University of Padova (in italian).

Agostinelli, C., (1998). Un approccio robusto alla verifica d'ipotesi basato sulla funzione di verosimiglianza pesata - Robust Testing Hypotheses via Weighted Likelihood function, submitted to {it Statistica}, revised february 2000 (in italian).

Agostinelli, C., Markatou, M. (2001) Test of hypotheses based on the Weighted Likelihood Methodology, in print {it Statistica Sinica} probably vol. 11, n. 2, Aprile 2001.

Examples


set.seed(1234)

x <- rnorm(30,0,1)
y <- rnorm(30,10,1)

res.x <- wle.normal(x,group=5)
res.y <- wle.normal(y,group=5)

wle.var.test(res.x, res.y) # Do x and y have the same variance?

set.seed(1234)

x <- c(rnorm(30,0,1),rnorm(10,10,1))
y <- c(rnorm(30,10,1),rnorm(10,0,5))

res.x <- wle.normal(x,group=5,num.sol=2)
res.y <- wle.normal(y,group=5)

res.x
wle.var.test(res.x, res.y, x.root=1)
if (res.x$tot.sol>1) wle.var.test(res.x, res.y, x.root=2)