# How to compare the variance from published summary statistics with own data?

I have compiled a very small set of summary data from the literature, and I wish to compare the variances between aspects of the literature-based data, and to some of my own data. The summary data includes the mean, standard deviation and sample size.

In earlier tests, I compared the variances of one continuous dependent variable among 2 age classes and 2 years. I used the Fligner-Killeen test since I have extreme values in the data and I'm not sure it was normal (can't remember now!). I followed up this broad test with pairwise multiple comparisons using F-tests in R var.test(x~age)

What would be a good way to compare the variances of the literature-sourced data? I've searched through the help files in R, and came up with this method, which I believe generates a random set of numbers with the specified sample size, mean and standard deviation, and then I used those datasets to conduct the F-test:

herring_year1<-rnorm(10,mean=10.5,sd=0.51)
herring_year2<-rnorm(15,mean=10.9,sd=0.43)
var.test(herring_year1,herring_year2)


Would this be a good approach? If not, can you suggest what might be? If so, how can I then compare these variances to my own data set? Should I essentially use the summary data from my own set in the same manner? Or generate the random data for the summary data from the literature and stick it in a file to compare to my raw data?

Also, do I need a broad test initially, or can I go straight to the pairwise comparisons?

• You might find this discussion about broad tests versus pairwise comparisons interesting. I'd be cautious about applying it to this problem since you're lacking the original data and don't have any distribution assumptions to go with, but it is something worth keeping in mind in general. – Chris Simokat Jun 12 '11 at 1:39
• Thanks Chris! Yes, that is interesting, and very helpful. – Mog Jun 18 '11 at 2:04