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

Diego Grados Bedoya d|egogr@do@b @end|ng |rom gm@||@com
Wed Mar 17 16:30:01 CET 2021

```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 using gmail.com> wrote:

> 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 <
>
>> 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*
>>
>>
>> Kind regards,
>>
>> Diego
>>
>>         [[alternative HTML version deleted]]
>>
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>>
>

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```