Understanding F-test to compare variances (R's var.test)

Question

I gave run the following codes in R console:

#for built-in matrix ToothGrowth
tooth.1mg <- subset(ToothGrowth, dose==1)
var.test(len~supp,data=tooth.1mg,alternative="two.sided")

I have found the result:

F test to compare two variances
data:  len by supp 

F = 2.4176, num df = 9, denom df = 9, p-value = 0.2046

alternative hypothesis: true ratio of variances is not equal to 1 

95 percent confidence interval:
0.6004952 9.7332038 

sample estimates:
ratio of variances 
2.41759 

But I do not understand what the result expresses. Is that we fail to reject null hypotheses since p-value>sig.level? If so, then I found in most cases by implying the command var.test that we fail to reject null hypotheses since p-value > sig.level. Or, if I focus on confidence interval, it doesn't include hypothesized value which concludes that we reject null hypotheses in favor of alternative hypotheses at 0.05 significance level.

Answer 1

If you read the documentation (type ?var.test or help("var.test") in the console) or look at the output carefully, you will see that it tests whether the ratio between the two variances is 1 (and not whether the difference is 0). The confidence interval therefore does include the hypothesized value (namely 1) and is perfectly coherent with the p value. In both cases, you fail to reject $H_0$ at the specified error level. See also a previous question on this test

Incidentally, the CI is also pretty wide and you have apparently very few observations. I don't know what you are trying to achieve but it might that this test doesn't tell you much about your data.