Descriptive analysis of student ratings

Let X be a statistical variable representing the student ratings of university teaching. It is natural to assume for X an ordinal scale consisting of k categories (in ascending order of student satisfaction). At first glance, student ratings can be summarized by a location index (such as the mode or the median of X) associated with a convenient measure of dispersion and/or asymmetry. For instance, the median of X may be associated with the opposite of the asymmetry index of Leti, resulting in a synthesis that takes into account the ordinal nature of ratings and also communicates information in an effective way. More generally, there are infinitely many indexes (such as the ordinal counterpart of entropy) that can be properly employed to measure the ordinal dispersion. In addition, on the basis of any measure of ordinal dispersion, it is possible to define the corresponding index of ordinal asymmetry. On the other hand, student ratings are often converted into scores and treated as a quantitative variable. More generally, it is possible to measure student satisfaction by means of a suitable real-valued function, which we denote by S. It turns out that S is naturally defined on the standard simplex, where pi is the relative frequency of the category i (i = 1,2,…,k). Besides, it seems necessary that such a function satisfies some appropriate conditions. For example, the function S is expected to reach its minimum at (1,0,…,0) and its maximum at (0,…,0,1). Finally, it is possible to weigh any measure of student satisfaction by a suitable measure of variability.