# [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
Thu Mar 18 09:47:25 CET 2021

```James,

Thank you for the example (I followed those steps). However, it is not
clear to me yet if including the number of comparisons (n) of the effect
size (if it is available) will result in a different estimate of the
variance (based on *variance = (n^2 * (mean_ effect_size - lower_limit_
confidence_interval)) / 1.96)*. For instance, if n would have been provided

Diego

On Wed, 17 Mar 2021 at 16:42, James Pustejovsky <jepusto using gmail.com> wrote:

> The variances will be quite different. Only the one based on the log scale
> is correct. Here's an example:
> Percentage change = +24.6%, 95% CI [18.5%, 31.0%]
>
> Back-transform to log response ratio using LRR = log[(% change) / 100 + 1]:
> LRR = 0.22, 95% CI [0.17, 0.27]
>
> Calculate SE of log response ratio using SE_LRR = [U - L] / (2 *
> z_critical)
> SE_LRR = [0.27 - 0.17] / (2 * 1.96) = 0.025
>
> On Wed, Mar 17, 2021 at 10:30 AM Diego Grados Bedoya <
>
>> 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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```