The comparative evaluation of excellence for student awards

A recurring problem in the award of academic honors is the comparison of the highest grade achieved by students from different groups with different traditions, practices, and evaluation scales. Group averages are not useful because it is the position of the top student that is of interest, not the average; also, the normal distribution cannot be assumed for the upper tail of the distribution, which must be obtained from the data. We find that the upper grades of each group can be modeled very well, permitting the statistical theory of extremes to be used. From the model which we fit to each group separately, we obtain the probability for a top grade at least as high as the one observed, and from this, we obtain the return period which is the expected interval before the return of a similarly high grade. This return period is a common measure which enables top grades from several disparate groups to be compared on the basis of how rare or exceptional they are as members of their own group. The precision of the return period is estimated from the correlation coefficient of the regression model and used to indicate the effectiveness of the decision in a particular case. The method is applied to data from different disciplines at the University of Waterloo, including comparisons among Engineering Departments.