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I have calculated the variance of the Log Effect Size (Ln Response Ratio RR) following the Hegdes et al., 1999 equation:

$$ \frac{(SD_E)^2}{n_E\bar{X}^2_E} + \frac{(SD_C)^2}{n_C\bar{X}^2_C} $$

And also using the function escalc() in metafor package of R (measure = ROM, for Log Response Ratios), and I got the same results of means (yi) and variances (vi) as doing it by hand.

How I should plot these results: a) calculating the se (standard error) of the vi:

se = sq root (vi/(n1i -1)) being n1i = n of treatment

(Is it correctly calculated?)

b) or using directly the vi?

It is a basic question, but I do not know what would be more appropriate.

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The value which escalc returns and which you have hand-calculated is the sampling variance of the estimate which you have. So the standard error is just the square root of the sampling variance. I am not sure what plot you want to achieve so it is hard to say which of the two is relevant. You do presumably know that metafor has a whole range of plots designed for meta-analysis?

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