vartest: Calibrated variance test between two or more independent samples

Description

Tests the equality of variance for continuous independent samples using Welch's ANOVA on the square of the centered variables.

Usage

vartest(x, y, ...)

Value

Returns the result of the test with its corresponding p-value and the value of the test statistic. In the two sample case, the function also returns the confidence interval for the difference of the two variances.

Arguments

x, y: the two continuous variables for the two samples variance test.
...: other parameters such as alternative which indicates the alternative hypothesis as one of "two.sided", "greater" or "less", or data and formula to include a dataset with a formula from the command vartest(x~y,data=dataset) with dataset the name of the data.

Details

For the two sample variance test, the null hypothesis is: H0 var(X)=var(Y) where var represents the variance. The alternative is specified by the alternative argument. The test uses Welch's ANOVA procedure on the variables \((x_i-mean(x))^2\), \((y_i-mean(y))^2\) and is asymptotically well calibrated in the sense that the rejection probability under the null hypothesis is asymptotically equal to the level of the test. The test can be applied to more than two groups in which case it tests if all groups have the same variance.

Examples

Run this code

#Application on the Evans dataset
data(Evans)
#Description of this dataset is available in the lbreg package
with(Evans,var.test(CHL[CDH==0],CHL[CDH==1]))
with(Evans,vartest(CHL[CDH==0],CHL[CDH==1]))
vartest(CHL~CDH,data=Evans) #using formulas

#Similar pvalues between var.test and vartest

# \donttest{
#Simulated data
n=60 #sample size
M=10000 #number of replications
testone=function(n){
X=rnorm(n,0,1)
Y=rchisq(2*n,df=2)/2
list(test1=vartest(X,Y)$p.value,test2=var.test(X,Y)$p.value) #var.test is the standard Fisher test
}
res1=res2=rep(NA,M)
# Replications to check if the corrected Fisher test and the standard test are well calibrated
for (i in 1:M)
{
result=testone(n)
res1[i]=result$test1
res2[i]=result$test2
}
mean(res1<0.05)  #0.0515
mean(res2<0.05)  #0.1509# }