On Sun, 30 Aug 2015 08:36:07 -0700, Christopher Green wrote:
The results of the "reproducibility project" have been getting a lot
of
attention this week. However, it makes the same mistake of relying
uncritically on the "critical value" dichotomy as do many psychological
studies. Re-interpreting the results using a Bayesian approach adds
some much-needed nuance to the findings. And here it is:
http://alexanderetz.com/
[snip]
NOTE: This is a blog by Alexander Etz and the page has entries
from various dates.The entry referred to above is dated August 30, 2015.
Etz argues, like Geoff Cummings and other anti-NHST populizers
(I don't know if Etz makes the argument that Cummings does that
NHST "rots your brain" or leads to the corruption of the mind and
to confusion and error or, as a Bayesian, is more "nuanced" about
such claims) that NHST is bad, m'kay, and a Bayesian approach is
more informative and "nuanced". YMMV.
Etz takes the results from the Nosek Gang (i.e., Reproducibility
Project that authored the Science article that everyone is grumbling
about; I note without comment that Nosek Tweeted a "nice post-pub
peer review" that appears on Etz's Twitter feed on his blog page) and
computes something called a Bayes Factor (BF) which is supposed
to provide a measure of the strength of failure or success of
replication
Etz goes over what a BF and provides a link to a website for BF
where one can become converted.
Long story short: if a replication result has a BF greater than 3,
then this counts as a moderate or better success. So, what
does the additional Bayesian analysis tell us? I quote from
Etz's blog post:
|To summarize the graphic and the results discussed above,
|this method identifies roughly as many replications with
|moderate success or better (BF>3) as the counting
|significance method (32 vs 35).
To be clear: Using the Bayes Factor method identifies 32
successful replications (of varying degrees) compared to the
Nosek Gang's 35 based on whether the results were significant
or not.
I think this is the kind of nuance that non-Bayesians expect
from a Bayesian approach. ;-) <-- NOTE.
I believe that if one gets religion and starts to think like a
Bayesian, then what Etz and other Bayesians do makes
some/moderate/lots (note the nuance) of sense. But
if you don't think like a Bayesian (neither Fisher nor
Jerzy Neyman and a lot of other statisticians didn't) then
it is not always clear what a Bayesian approach buys one
though there may situations when it is the method of choice.
For a more "catholic" view of statistical analysis as well as
arguing against overzealousness in promoting Bayesian
methods, see good old Gerd Gigerenzer's commentary
on Bayesian analysis in a special issue of the "Journal of
Management" on Bayesian analysis in organizational science;
see:
http://jom.sagepub.com/content/41/2/421.abstract
And let's not forget what the famous Bayesian LJ Savage
had to say about NHST, particularly Fisher's approach; see:
Savage, L. J. (1976). On rereading RA Fisher. The Annals
of Statistics, 441-500.
A copy of this article is available at:
http://projecteuclid.org/download/pdf_1/euclid.aos/1176343456
One wonders if BF is no BFD. ;-)
-Mike Palij
New York University
m...@nyu.edu
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