I am conducting a meta analysis using the
metafor package in R and am trying to calculate the Standard Error (if possible) of the Tau statistic.
The S.E of the tau-squared is obviously available easily from output of the
metafor::rma function for example:
Random-Effects Model (k = 6; tau^2 estimator: REML) tau^2 (estimated amount of total heterogeneity): 0.0331 (SE = 0.0384) tau (square root of estimated tau^2 value): 0.1820 I^2 (total heterogeneity / total variability): 56.53% H^2 (total variability / sampling variability): 2.30 Test for Heterogeneity: Q(df = 5) = 12.8056, p-val = 0.0253 Model Results: estimate se zval pval ci.lb ci.ub 0.3463 0.1012 3.4239 0.0006 0.1481 0.5446 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I know from this this answer that creating CI's for Tau is is straight forward (simply square root the upper and lower bounds) can the same be applied to the standard error? So in the above case the standard error would be:
> sqrt(0.0384)  0.1959592
Is this the correct method and if not what would the correct method be?