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I'd like to conduct a three-level meta-analysis using R. I see that several papers recommend calculating the level 1 sampling variance using Cheung's 2014 formula 14. However, I'm wondering if it is possible to calculate the sampling variance if I don't have access to all of the standard errors associated with my effect sizes?

Thanks so much.

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  • $\begingroup$ It is not clear to me how you are going to do a multi-level m-a without standard errors for the effect sizes. $\endgroup$
    – mdewey
    May 18, 2022 at 12:45
  • $\begingroup$ I'm wondering if there is a way that this is possible — I'm not able to access all of the standard errors, so I'm wondering if there is a formula to estimate them based on sample size and correlations? Thank you! $\endgroup$
    – Abe
    May 18, 2022 at 18:37

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Basically if you do not have standard errors then there are a number of options.

1 it may be possible to back-calculate them from significance tests (or $p$-values) and the sample sizes.

2 it may be possible to impute them from similar studies which used the same measure under similar circumstances. In this case it would be wise to do a sensitivity analysis using a variety of imputed values. Mark the imputed values in some way if you provide a main forest plot.

3 authors of the primary studies may be contactable and may be willing to supply the missing values if you explain why you need them. If they do be sure to acknowledge their help in your paper and flag the results they supplied.

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  • $\begingroup$ I am wondering if this is the correct formula: SE = sqrt ((1-r^2)/(n-2))... or if the r’s are converted to Fisher’s z-values first then: SE = 1 / sqrt (N-3)... these do not seem to rely on the p-value. Does this look correct? I referenced the following posts: [1] stats.stackexchange.com/questions/226380/… [2] stats.stackexchange.com/questions/360718/… $\endgroup$
    – Abe
    May 20, 2022 at 11:53
  • $\begingroup$ Use the z-transformation, always. $\endgroup$
    – mdewey
    May 20, 2022 at 13:24

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