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

[Viechtbauer, Wolfgang (SP)]

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.