We have seen that the NRC perceived qualities of physics PhD programs can be fit to within 9.6% on the average by the simple formula

Qt = a0 + ai Ni + aNobel NNobel 

                                                eq. 5

Here i is summed over five physics sub-specialties with Ni being the number of faculty in that area. Unlike the previously considered linear forms, this formula suggests that there is an optimum balance among the various sub-fields of physics which can be found by differentiating the above formula at fixed total faculty size. The department's perceived quality is then optimized if

Ni/Nj = ai2/aj2

                                                eq. 6

The theoretical quality of a program is given here in terms of six variables and seven free parameters. The question arises whether there are any simpler functions of the research profile of a department which give an equally good or better fit with fewer parameters. The fact that the previous fits show that subatomic physics plays a key role in the high ranked schools and that smaller departments are more likely to be highly ranked if they have a larger fraction of subatomic physics suggests that there should be a simplified fit depending only on these quantities.

We have in fact found the following improved formula

Qt = a0 + asubNsub + aotherNother + aNobelNNobel + ar(Nsub/Ntotal)e

                                                eq. 7
This formula has six free parameters (five coefficients and one exponent) and depends on three quantities: NNobel, the number of Nobel laureates on, or recently on, the faculty, Nsub, the number of nuclear and particle physicists (including mathematical physics, cosmology, cosmic rays etc but excluding plasma) and Nother = Ntotal-Nsub. The fit shown here, with six free parameters has a mean absolute fractional discrepancy from the actual NRC assigned qualities of 0.09178.





a00.92905
asub.24406
aother.24116
aNobel.75297
ar1.5540
e4.17245

Fig. 6



         In spite of the large preferred weighting of the subatomic fraction, the formula still underestimates the NRC assigned quality of Rockefeller University which reported unit particle fraction in the 1990 AIP listings. This formula has the paradoxical implication that, in some cases, a department can improve its quality rating while shrinking in total size. However, the fact that the preferred exponent is so large indicates that the term depending on the ratio is irrelevant to most physics departments. The paucity of examples of departments with ratios near one suggests that this fit might not be a reliable predictor of perceived quality in the vicinity of this configuration.

                  BACK                  NEXT

return to index