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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?

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  • $\begingroup$ 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. $\endgroup$ – Chris Simokat Jun 12 '11 at 1:39
  • $\begingroup$ Thanks Chris! Yes, that is interesting, and very helpful. $\endgroup$ – Mog Jun 18 '11 at 2:04
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I don't think the Fligner-Killeen test (nor the Brown-Forsythe) test is appropriate since you don't know the median in the published data (if you do have it and simply didn't mention it then never mind).

I wouldn't suggest simulation of the data either unless you're sure the samples follow a specific distribution.

Since you don't have the median and the distribution is uncertain Levene's Test would be appropriate. I've never ran the test in R before, but there is a description of it here. If you're having a lot of trouble getting the R code to work though I'd just compute it by hand given the summary statistics from the literature and your own data. As the wikipedia indicates that statistic is F distributed so you'll need a table if you don't have one.

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  • $\begingroup$ Thanks @Chris! Very helpful response and links. You're right, I don't have the median of the data, nor do I know the distribution. I'm guessing then from your answer, that simple pairwise F-tests on the summary stats (by hand) wouldn't work? $\endgroup$ – Mog Jun 12 '11 at 0:47
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    $\begingroup$ If you had the published study's data there are tests you could run, if you had the median there are tests you can run. I'm having a hard time thinking of a nonparametric procedure that would work with what you have from the published study. Is it not possible to ask the original researcher for a copy of their data set? If I think of something I'll post it. $\endgroup$ – Chris Simokat Jun 12 '11 at 1:33
  • $\begingroup$ Thanks again @Chris. I'll check for the original data set...good idea! $\endgroup$ – Mog Jun 12 '11 at 1:36

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