# [R-meta] Overlapping CIs with significant difference among subgroups

Gerta Ruecker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Thu Jun 4 19:27:18 CEST 2020

```Dear Rafael,

To avoid any confusion:

Yes, the standard error is the square root of the *sampling variance*,
which is the variance of a statistic (for example, a mean, or an
estimated proportion, or an estimated relative risk, there are many
other examples of estimates).

Particularly, for a mean the sampling variance is the (estimated)
population variance, divided by n. The standard error is the square root
of the sampling variance.

Both the sampling variance and the standard error describe how precise
an estimate is, which is reflected by their (inverse) dependence on the
sample size.

By contrast, the population variance and its square root (the standard
deviation) describe the variability of a measure in a population - which
is a very different thing.

These are general definitions, there is nothing special with meta-analysis.

Best,

Gerta

Am 04.06.2020 um 16:48 schrieb Rafael Rios:
> Dear Dr. Gerta and Dr. Wolfgang,
>
> I want to highlight that the standard error in a meta-analytical approach
> is equivalent to the standard deviation of statistics. For statistics, the
> standard error is the standard deviation divided by the square root of the
> number of samples, which is used to calculate confidence intervals. In a
> meta-analysis, the standard error is the square root of the variance. I
> know this information is clear to you but may not be clear to other
> significance, since readers generally interpret the information by
> analyzing graphs. However, I agree that confidence intervals provide
> important information. I started this discussion because I was asked by a
> Referee in a high-impact journal. Thank you for the clarification. It was
>
> Best wishes,
> _______________________________________________________
>
> *Prof. Dr. Rafael Rios Moura*
> Coordenador de Pesquisa e do NEPEE/CNPq
> Laboratório de Ecologia e Zoologia (LEZ)
>
> ORCID: http://orcid.org/0000-0002-7911-4734
> Currículo Lattes: http://lattes.cnpq.br/4264357546465157
> <http://orcid.org/0000-0002-7911-4734>
> <http://lattes.cnpq.br/4264357546465157>
> <http://lattes.cnpq.br/4264357546465157>Research Gate:
> https://www.researchgate.net/profile/Rafael_Rios_Moura2
> <http://orcid.org/0000-0002-7911-4734>
> <http://orcid.org/0000-0002-7911-4734>
>
>
> Em qui., 4 de jun. de 2020 às 10:33, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> escreveu:
>
>> I was going to ask the same thing. I don't see how SEs would be more
>> informative than CIs.
>>
>> But -- if two (independent) estimates have the same precision (i.e.,
>> standard error), then one can show that their 83.4% CIs will just touch
>> when the (two-sided) p-value for a Wald-type test of the difference is
>> equal to .05. So, in that case, 83.4% CIs will directly tell you whether
>> the difference is significant or not.
>>
>> Unfortunately, this doesn't work when the standard errors of the estimates
>> are not the same. The larger the difference in SEs, the wider one needs to
>> make the CI to have equivalence between 'non-overlap = significant
>> difference'.
>>
>> Best,
>> Wolfgang
>>
>>> -----Original Message-----
>>> From: R-sig-meta-analysis [mailto:
>> r-sig-meta-analysis-bounces using r-project.org]
>>> On Behalf Of Gerta Ruecker
>>> Sent: Thursday, 04 June, 2020 11:32
>>> To: r-sig-meta-analysis using r-project.org
>>> Subject: Re: [R-meta] Overlapping CIs with significant difference among
>>> subgroups
>>>
>>> Dear Rafael,
>>>
>>> First of all, the information content of standard errors and confidence
>>> intervals is identical, they can be transformed into each other.
>>> Secondly, to present standard errors in a graph, one would probably show
>>> x ± SE(x) instead of x ± 1.96*SE(x). But what would be the advantage?
>>> The interpretation of this intercval would mean that the true value is
>>> covered by 68% of all such intervals (=1-2*(1-pnorm(1))). I don't think
>>> that this is of more interest than a confidence interval.
>>>
>>> The main aim of a forest plot is interval estimation, not statistically
>>> comparing different studies.
>>>
>>> Best,
>>>
>>> Gerta
>>>
>>> Am 04.06.2020 um 08:26 schrieb Rafael Rios:
>>>> Dear Dr. Wolfgang,
>>>>
>>>> Thank you for the feedback. I was wondering why meta-analysts did not
>>>> exhibit standard errors instead of confidence intervals in graphs. I can
>>>> understand the importance of showing that CIs did not include zero, but
>>>> standard errors can be more informative when comparing subgroups of a
>>>> moderator. This is just a curiosity.
>>>>
>>>> Best wishes,
>>>>
>>>> Rafael.
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>>
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--

Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.uniklinik-freiburg.de/imbi.html

```