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I have collected papers reporting no. of observed species in two types of habitats, A and A’, and been trying some outcome measures for meta-analysis. I noticed that effect size such as Hedges’ g cannot be calculated for cases where habitat A and A’ both have only one data value (e.g., 23 species in habitat A and 17 species in habitat A’). Unfortunately there are many such studies. Should I omit them from my meta-analysis?

It seems to me that omitting particular type of studies from consideration goes against the spirit of meta-analysis. I mean, if meta-analysis is meant for summing up scattered knowledges in the literature, any collection bias should be minimized. So… does anyone know how to include one-data cases into meta-analysis?

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  • $\begingroup$ It would help to know what your scientific question is. Do you want to be able to say that habitat A has more species than A'? Is there overlap between the species recorded in the two habitats and if so is that important? $\endgroup$ – mdewey Mar 31 '17 at 16:18
  • $\begingroup$ Thank you for your response. As for your first question, yes, I'd like to be able to say that habitat A has more species than A'. And as for the second question, there may or may not be overlap between the species recorded in the two habitats, but that is not so important here. I would greatly appreciate your help! $\endgroup$ – bbKZO Apr 2 '17 at 4:00
  • $\begingroup$ Do all the primary studies report the overlap? So of the 23 and 17 we know there were, say, 9 in common? Are the habitats assumed to be the same size and if not do you have that information for the primary studies? $\endgroup$ – mdewey Apr 2 '17 at 12:47
  • $\begingroup$ Thank you, mdeway. Here are my answers. i) Most studies I collected have reported species lists, from which I can get information on the overlap. Although I haven't checked them carefully, I believe in most studies habitats A and A' actually have some species in common. ii) Habitats are assumed to be the same size. I would appreciate any help, thank you! $\endgroup$ – bbKZO Apr 3 '17 at 11:17
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I would suggest the simplest solution is to treat this as each primary study estimating a single proportion and then meta-analyse them. I would treat the species which appear in both habitats as uninformative as to habitat preference and just use the number of other species. You can then calculate the proportion of species which prefer habitat A which under the null is 0.5. So in your example if 23 were recorded at A and 17 at A' and there were 9 at both the required proportion would be 14/8. Do that for each study. Your software may then let you enter the raw data and compute the proportions and their standard error for you otherwise you need to do it by hand. If the proportions are close to 0 or 1 you may prefer to transform the proportions. If in one study after subtracting the common species there are none left in that habitat you may have trouble computing the standard errors but you software should help you out, usually by adding a small contsant to each habitat (like 0.5).

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  • $\begingroup$ Thank you very much, I really appreciate this. So you are talking about using the log ratio instead of Hedges' g, so that I don't need SDs, right? I'll do it. Another interesting point you made in your comment was omitting the no. of species shared by both habitats A and A'. I haven't thought about it, but maybe that is important. I'll try that too. As for zero-value cases, adding 0.5 to each habitat should work. Thanks again! $\endgroup$ – bbKZO Apr 5 '17 at 3:41
  • $\begingroup$ There are several zillion other things you can meta-analyse apart from Hedges' g. $\endgroup$ – mdewey Apr 5 '17 at 14:12
  • $\begingroup$ OK, I'm slowly learning that there are many outcome measures... anyway, thank you so much for your advice! $\endgroup$ – bbKZO Apr 7 '17 at 8:43

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