# Proof That Theory Matters

October 15, 2012
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(This article was originally published at Normal Deviate, and syndicated at StatsBlogs.)

Proof That Theory Matters

The title of this post is a slight exaggeration but I do want to discuss an interesting paper by Steve Stigler that provides empirical support for the fact that:

… there is a tendency for influence to flow from theory to applications to a much greater extent than in the reverse direction.

Steve is a professor in the department of statistics at the University of Chicago and is known, among many other things, for his scholarly work on the history of statistics. His father was the Nobel prize winning economist George Stigler.

1. The Paper

The paper is “Citation patterns in the journals of statistics and probability,” which appeared in Statistical Science in 1994 (p 94-108). I think you can get it from the following link.

The article examines citation data between various journals. Obviously the data are now out of date. And there are many practical problems with citation data which Stigler discusses at length in the article.

The part of the paper I want to focus on is where Stigler adopts an economic point if view and treats citations as a form of trade. Citations are viewed as imports and exports. Restricting to eight major journals, Stigler assigns an export score ${S}$ to each journal. The difference of these scores measures the exporting power of one journal to another. Specifically, he defines

$\displaystyle {\rm logodds} (A\ {\rm exports\ to\ B}| {\rm A\ and\ B\ trade})= S_A - S_B.$

There are eight journals but only seven free parameters (since the relevant quantities are differences). So, without loss of generality, he takes The Annals of Statistics to be the baseline journal with score ${S=0}$. This results in the following export scores:

 Journal Score Annals 0.00 Biometrics -1.19 Biometrika -0.35 Communications -3.27 JASA -0.81 JRSS B -0.06 JRSS C -1.30 Technometrics -0.98

To quote from the paper: “The larger the export score, the greater the propensity to export intellectual influence.” In particular, we see that The Annals is the largest exporter.

Later, he puts the journals into three groups: theory (Annals, Biometrika, JRSS B), applied (Biometrics, Technometrics, JRSS C) and mixed (JASA). The result is:

 Theory 0 Mixed -0.66 Applied -0.99

Again we see a flow from theory to applied. The importance of this finding should not be underestimated. Quoting again from the paper:

Thus, we have striking evidence supporting a fundamental role for basic theory that runs strongly counter to the sometimes voiced claim that basic theory is not relevant to applicable methodology.

Another interesting finding in the paper is that there is very little intellectual trade between statistics journals and probability journals.

2. Conclusion

I am fascinated by this paper. The role of theory versus applied work is sometimes controversial and I believe this is one of the few quantitative studies about this issue. The data on which the study was based are now out of date. It would be great if someone would do an updated analysis. And of course we have many new sources of information such as Google Scholar.

3. Reference

Stigler, S.M. (1994). Citation patterns in the journals of statistics and probability. Statistical Science, 94-108.

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