• #### Q obtaining statistics from multiple samples

From Cosine@21:1/5 to All on Sun May 23 07:50:44 2021
Hi:

To have enough statistical power, we have to have the size of the sample large enough. What if we have a set of samples of the same type, but the size of each of the samples is not large? Do we have some ways to combine this et of small samples into a
large sample? Or more generally, do we have some ways to obtain the statistics with enough power by some clever ways of using this set of samples?

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• From Rich Ulrich@21:1/5 to All on Sun May 23 13:34:04 2021
On Sun, 23 May 2021 07:50:44 -0700 (PDT), Cosine <asecant@gmail.com>
wrote:

Hi:

To have enough statistical power, we have to have the size of the
sample large enough. What if we have a set of samples of the same
type, but the size of each of the samples is not large? Do we have
some ways to combine this et of small samples into a large sample?
Or more generally, do we have some ways to obtain the statistics
with enough power by some clever ways of using this set of samples?

What comes immediately to my mind -- technically, "multiple
samples" describes the structure of multi-clinic studies (sites,
doctors) and of surveys (individual interviewers).

The analyses eventually want to pool the results. Before pooled
analyses, the clinics or doctors or interviewers are examined to
see if there are notable differences - "notable" meaning, in effect
size, not necessarily by statistical significance. That is a look both
at interesting outcomes and at sample characteristics.

If there are different demographics "between samples" among the
cases or interviewees, that has to be taken into account in the
analyses (if necessary, and if possible) and the write-up (always).

The difficult write-up is where there is "confounding" between
characteristics and location and interesting results. You may
have to make logical arguments about which factors should
be controlled for as statistical factors or covariates, and in which
order; or which results are presented as distinct for distinct groups.
Of course, if the N were large enough, you would be able to
test for interactions - but you are positing subsamples that
are small enough to have small power. So, effect sizes need to
be examined.

--
Rich Ulrich

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• From David Jones@21:1/5 to Rich Ulrich on Sun May 23 17:44:47 2021
Rich Ulrich wrote:

On Sun, 23 May 2021 07:50:44 -0700 (PDT), Cosine <asecant@gmail.com>
wrote:

Hi:

To have enough statistical power, we have to have the size of the
sample large enough. What if we have a set of samples of the same
type, but the size of each of the samples is not large? Do we have
some ways to combine this et of small samples into a large sample?
Or more generally, do we have some ways to obtain the statistics
with enough power by some clever ways of using this set of samples?

What comes immediately to my mind -- technically, "multiple
samples" describes the structure of multi-clinic studies (sites,
doctors) and of surveys (individual interviewers).

The analyses eventually want to pool the results. Before pooled
analyses, the clinics or doctors or interviewers are examined to
see if there are notable differences - "notable" meaning, in effect
size, not necessarily by statistical significance. That is a look both
at interesting outcomes and at sample characteristics.

If there are different demographics "between samples" among the
cases or interviewees, that has to be taken into account in the
analyses (if necessary, and if possible) and the write-up (always).

The difficult write-up is where there is "confounding" between characteristics and location and interesting results. You may
have to make logical arguments about which factors should
be controlled for as statistical factors or covariates, and in which
order; or which results are presented as distinct for distinct groups.
Of course, if the N were large enough, you would be able to
test for interactions - but you are positing subsamples that
are small enough to have small power. So, effect sizes need to
be examined.

A more abstract version of this is where you don't have immediate
access to all the samples but only to results published for each study.
Many of the same concerns apply, so it may be worth looking at
discussions of "meta-analysis" ... for example, see https://en.wikipedia.org/wiki/Meta-analysis .

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