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[R-meta] sample variance estimation of an effect size (reponse ratio) using confidence limits

3 messages · Diego Grados Bedoya, James Pustejovsky

Original
Diego Grados Bedoya
# 
Dear all,

I am trying to estimate the sample error variance of an effect size
(reported as response ratio) based on the confidence intervals (assuming
that it follows a Gaussian distribution). Is it a valid approach to use the
following equation if I do not have the number of comparisons used in the
calculation of the effect size?

*variance = ((mean_ effect_size - lower_limit_confidence_interval) /
1.96)^2*

If I would have the number of comparisons (n), should I go for the
following equation?

*variance = (n^2 * (mean_ effect_size - lower_limit_ confidence_interval))
/ 1.96*

Thanks in advance,

Kind regards,

Diego
James Pustejovsky
# 
Diego,

Is the effect size reported on the log scale (log response ratio, with
range from negative infinity to positive infinity and null value of zero)
or on the ratio scale (range from 0 to infinity, null value of 1)?
Typically, confidence intervals are calculated on the log scale. If the
effect size is reported on the ratio scale, then you can use the formula
you described but you'll first have to convert the response ratio and
confidence limits to the log scale.

James

On Wed, Mar 17, 2021 at 10:09 AM Diego Grados Bedoya <diegogradosb at gmail.com>
wrote:

  
  


  


      

    

    

      
      

        


  

        

      Diego Grados Bedoya
    

    

      
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James,

The effect size was originally reported as a percentage (based on the log
response ratio). I back-transformed it using the equation (exp(RR) - 1) *
100% and I did the same for the confidence intervals. Based on these
back-transformed values I am estimating the variance.

If I use both equations, the values of the variance are
complicity different for each equation.

 Am I missing something?

Thank you,

Diego

        
On Wed, 17 Mar 2021 at 16:12, James Pustejovsky <jepusto at gmail.com> wrote: