[R-meta] meta-analysis of response ratios with low sample sizes

Michael Dewey ||@t@ @end|ng |rom dewey@myzen@co@uk
Fri Jan 18 17:20:40 CET 2019

Dear Ana

Comments in-line

On 18/01/2019 15:24, Ana Benitez wrote:
> Dear Wolfgang (and users of the meta-analysis mailing list),
> I am currently conducting a meta-analisis where I want to assess body size
> shifts in vertebrates living in islands compared to mainland populations
> (a.k.a the island rule). I am using response ratios between the mean size
> of the island population and the mean size of the mainland population. In
> some cases I have measurements for only 2 specimens, and I calculate mean
> and SD for those 2 specimens in order to calculate the sampling variance.
> However, many people would argue that calculating the SD of 2 data points
> is a bit meaningless in most contexts, but in a meta-analytical context I
> would expect that response ratios based on N = 2 for either the treatment
> or control, or both, would be downweighted in the metaanalysis and thus it
> is both informative and interesting to include them in the analyses. I
> would like to know if other people have encountered these situations and
> how they dealt with it. Also, what’s your opinion, Wolfgang?

I think your feeling that (a) you can do it (b) they will be 
downweighted is correct.

> I have a second query, in this same analysis I have cases where only one
> specimen is measured, and thus the SD is zero. To be able to calculate the
> sampling variance I add a small constant (0.5) to both the numerator and
> denominator of the formula. Is this a sensible way to proceed or shall I
> just discard cases where only 1 specimen is measured in either of the two
> populations (or both of them)?

I do not like excluding anything but in this case I think it might be 
better than adding an arbitrary constant. If I was forced to add a 
constant by powerful figures then I would use a range of values to check 
whether the specific value I added was crucial. If it is then I would be 
even more doubtful about the wisdom of adding it.


> Thanks a lot for your time, I am looking forward to your thoughts on these
> two queries.
> Best,
> Ana


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