Calculation of the individual standard error of the mean for meta analysis bias estimation I am trying to run the egger's test to check my meta analysis for publication bias.
My data consists of a correlation effect size and a sample size from each study.
I understand that the egger's regression is based on the individual standard error of the mean for each observation. 
I need help to calculate that based on the effect size and sample size which are the only variables I have.
Thanks
 A: If these are standard correlation coefficients which you meta-analysed using Fisher's hyperbolic arctangent transformation (also known as z) then you can calculate the standard error for z using the sample size. Then you have what you want. Otherwise you can use a version of Egger's method but not using standard error. See

@article{moreno09,
   author = {Moreno, S G and Sutton, A J and Ades, A E and Stanley, T D
      and Abrams, K R and Peters, J L and Cooper, N J},
   title = {Assessment of regression--based methods to adjust for
      publication bias through a comprehensive simulation study},
   journal = {BMC Medical Research Methodology},
   year = {2009},
   volume = {9},
   number = {2},
   keywords = {meta-analysis, publication bias, meta-regression}
}

for various options or
@article{peters06,
   author = {Peters, J L and Sutton, A J and Jones, D R and Abrams, K R and
      Rushton, L},
   title = {Comparison of two methods to detect publication bias in
      meta--analysis},
   journal = {Journal of the American Medical Association},
   year = {2006},
   volume = {295},
   pages = {676--680},
   keywords = {meta-analysis, publication bias, meta-regression}
}

A: I do not favor the term 'publication bias', as the broader concept of small study effects is more appropriate and meaningfulfor most meta-analyses or meta-epidemiologic studies. See for instance this work by Rucker et al, authors of 'Meta-Analysis with R':
http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000151/abstract
In any case, there are several tests appraising small study effects, and, for instance, as also suggested by mdewey, the Peters test is suitable for your case (being based on point estimate and inverse of sample size): 
http://jama.jamanetwork.com/article.aspx?articleid=202337
In this article, Peters et al clearly spell out that they '...recommend a simple weighted linear regression with lnOR as the dependent variable and the inverse of the total sample size as the independent variable. This is a minor modification of Macaskill's test, with the inverse of the total sample size as the independent variable rather than total sample size.' They go on elaborating that the 'use of sample size reduces the correlation between the lnOR and its SE'.
