I'm trying to understand the confidence interval returned by the function var.test() in R. More specifically, the confidence interval returned by var.test() is not the one I find when doing the calculation of the F-test by myself. For example :
> s1 <- 10:12 ; s2 <- 13:16 > var(s1)  1 > var(s2)  1.666667 > var.test(s1,s2) F test to compare two variances data: s1 and s2 F = 0.6, num df = 2, denom df = 3, p-value = 0.7926 alternative hypothesis: true ratio of variances is not equal to 1 95 percent confidence interval: 0.03739691 23.49929674 sample estimates: ratio of variances 0.6
The 95% confidence interval here is [0.037,23.499]. I interpret "confidence interval" as "rejection region", i.e. if the test statistic F is inside this interval, the null hypothesis should be accepted, for a given statistical level (95% here). However, when I try to calculate this, I find :
> qf(c(0.025,0.975),length(s1)-1,length(s2)-1)  0.02553268 16.04410643
So I guess I'm wrong when I interpret var.test()'s "confidence interval" as the "rejection region".
So my question is : what does this confidence interval represent?