Re: [SIGMETRICS] Open Access: sample size, generalizability and self-selection

From: Stevan Harnad <amsciforum_at_GMAIL.COM>
Date: Sat, 27 Nov 2010 10:03:32 -0500

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On Thu, Nov 25, 2010 at 11:26 PM, Philip Davis <> wrote:

      You seem to have conceded that your small sample size critique does
      not hold.  


I'm not sure why you speak of "concession" since we are talking here about data,
not our respective opinions or preferences.

Your one-year sample was definitely too small and too early to conclude that
there was not going to be an OA citation advantage. However, I agree completely
that a null effect after three years does count as a failure to replicate the
frequently reported OA citation advantage, because many of those reports were
themselves based on samples and time-intervals of comparable size.

What this means is that your three-year outcome would definitely qualify for
inclusion in a meta-analysis of all the tests of the OA citation advantage --
whether their outcomes were positive, negative or null -- with a higher
weighting (for sample size, interval and power) than the one-year study would
have done.

What it certainly does not mean, however, is that your null outcome has now
demonstrated that all the positive outcomes were just a result of a
self-selection artifact (which your randomization has now eliminated)!

The reason -- to remind you again -- is that your study did not replicate the
self-selection bias on its sample population (neither the 1-year sample nor the
3-year sample). Without that, it has definitely not been demonstrated that
randomization eliminates the OA advantage. Your study has just shown (as a few
other studies have already done) that in some samples, no OA citation advantage
is found. 

These null studies have been a small minority, and their sample sizes have been
small -- small not only in terms of the number of articles and journals sampled
but (perhaps even more important) small in terms of the number of fields

All of these variables can be duly taken into account in a meta-analysis, should
someone take up Alma Swan's call to do one: See Gene Glass's comments on this.

      Let's move to your new concern about generalizability:

The concern that tests for the OA citation advantage should be done across all
fields is not a new one; and it continues to be a valid one. One cannot draw
conclusions about all or even most unless the samples are representative of all
or most fields (i.e., not just big enough and long enough, but broad enough).

      While I can't claim negative results across all fields and across
      all times, our randomized controlled trials (RCTs) did involve 36
      journals produced by 7 different publishers in the medical,
      biological, and multi-disciplinary sciences, plus the social
      sciences and humanities.

That's correct. And in any meta-analysis that would duly be taken that into

       The nature of the RCTs means a lot of human intervention goes in to
      set up and run the experiments.  In comparison, retrospective
      observational studies (the studies you cite as comparisons) are
      largely automated and are able to gather a huge amount of data
      quickly with little human intervention.  Yet, if you are basing your
      comparison solely on number of journals and number of articles, then
      you are completely missing the rationale for conducting the RCTs in
      the first place:

The many published comparisons are based on comparing OA and non-OA articles
within the same journal and year. That's the studies that are simply testing
whether there is an OA citation advantage. 

But the comparison you are talking about is the comparison between self-selected
and imposed OA. For that, you need to have a (sufficiently large, long, broad
and representative) sample of self-selected and imposed OA. Then you have to see
which hypothesis the outcome supports: 

According to the self-selection artifact hypothesis, the self-selection sample
should show the usual OA citation advantage whereas the imposed sample should
show no citation advantage (or a significantly smaller one). This would show
whether (and to what degree) the OA citation advantage is the result of a
self-selection bias.

But if the outcome is that the OA citation advantage is the same whether the OA
is self-selected or imposed, then this shows that the self-selection artifact
hypothesis is incorrect.

Your study has shown that in your sample (consisting of OA imposed by
randomization), there is no OA citation advantage (only an OA download
advantage). But it has not shown that there is any OA self-selection advantage
either. Without that, there is only the non-replication of the OA citation

Recall that the few other studies that have failed to replicate the OA citation
advantage were all based on self-selected OA. So it does happen, occasionally,
that a sample fails to find an OA citation advantage. To show that this is
because the randomization has eliminated a self-selection bias requires a lot

And meanwhile, we too have tested whether the OA advantage is an artifact of a
self-selection bias, using mandated OA as the means of imposing the OA, instead
of randomization. This allowed us to test a far bigger, longer, and broader
sample. We replicated the widely reported OA citation advantage for
self-selected OA, and found that OA imposed by mandates results in just as big
an OA citation advantage.

(Yassine Gargouri will soon post the standard error of the mean, based on our
largest sample, for subsamples of the same size as yours; this will give an idea
of the underlying variability as well as the probability of encountering a
subsample with a null outcome. I stress, though, that this is not a substitute
for a meta-analysis.)

      By design, RCTs are better at isolating possible causes, determining
      the direction of causation, and ruling out confounding variables.
       While it is impossible to prove cause and effect, RCTs generally
      provide much stronger evidence than retrospective observational

What you are calling "retrospective observational studies" is self-selected OA
studies. Randomized OA is one way to test the effect of self-selection; but
mandated OA is another. Both can also use multiple regression to control for the
many other variables correlated with citations (and have done so), but mandates
have the advantage of generating a much bigger, longer, and broader sample. (As
mandates grow, it will become easier and easier for others to replicate our
findings with studies of their own, even estimating the time it takes for
mandates to take effect.)

(I expect that the next redoubt of self-selectionists will be to suggest that
there is a "self-selection bias" in mandate adoption, with elite [more
cited/citeable] institutions more likely to adopt an OA mandate. But with a
range that includes Harvard and MIT, to be sure, but also Queensland University
of Technology and University of Minho -- the world's and europe's first
institutions to adopt a university-wide mandate [Southampton's departmental
mandate having been the first of all] it will be easy enough for anyone who is
motivated to test these increasingly far-fetched bias hypotheses to control for
each institution's pre-mandate citation rank: There are now over a hundred
mandates to choose from. No need to wait for RCTs there...)

      Your last concern was about a self-selection control group:

      There were not a lot of cases of self-archiving in our dataset.
       Remember that we were not studying physics and that our studies
      began in 2007.  You will note that I report a positive citation
      effect in my Appendix, but because the act of self-archiving was out
      of our control, we could not distinguish between access and
      self-selection as a definitive cause.  I also report in my
      dissertation that articles selected and promoted by editors were
      more highly-cited, but it appears that editors were simply selecting
      more citable articles (e.g. reviews) to promote.

Yes, there are big problems with gathering the self-selection control data for
randomized OA studies. That's why I recommend using mandated OA instead. And you
can find plenty of it in all fields, not just physics.

Stevan Harnad
Received on Sat Nov 27 2010 - 15:16:38 GMT

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