โ Scribed by Eastman, Caroline M.
No coin nor oath required. For personal study only.
The relationship between research productivity and breadth of interest in a group of computer science authors is discussed by Subramanyan (1984). A moderate positive correlation was found between the number of papers published by an author and the number of subareas represented. This correlation is assumed to suggest a positive relationship between research productivity and breadth of interest.
In this question, as in many others, it is important to consider what the data would look like if the variables were independent. Suppose that there is no relationship between research productivity and breadth of interest. It is still to be expected that there would be a positive correlation between the two measurements used, number of papers and number of subareas. This happens because the number of subareas represented in a set of publications is not independent of the size of that set.
This can be illustrated by considering a simple model for breadth of interest. Assume that all authors have exactly the same breath of interest. In particular, all are equally interested in the same m areas. However, not all are equally productive.
If it is assumed that the probability of an author publishing a paper in a subarea is equal for all subareas and that the subareas represented by different papers are independent, then this situation can be modeled as an occupancy problem . Such problems are often framed as urn problems: If k balls are placed in m urns, how many urns are occupied? Here the balls represent papers and the urns represent subareas. The number of occupied urns corresponds to the number of subareas represented in a set of papers.
The expected number of subareas represented in a set of k papers can thus be computed as Suppose that m = 4. (This is the maximum number of subareas represented in Subramanian's sample.) The ex-
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