Calculating Standard Error of Tau - Meta Analysis

by Michael.Brian.Gordon   Last Updated November 08, 2018 23:19 PM

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)
[1] 0.1959592 

Is this the correct method and if not what would the correct method be?



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