A nonparametric approach to assess undergraduate performance

• Published in: Statistica Neerlandica 2020-11, Vol.74 (4), p.538-558
• Main Authors: Pinheiro, Hildete P., Sen, Pranab K., Pinheiro, Aluísio, Kiihl, Samara F.
• Format: Article
• Language: English
• Subjects: bootstrap; diversity measures; Entrance examinations; Entrances; Maximum power; nonparametric methods; Nonparametric statistics; Normal distribution; quasi U statistics; Resampling; Research facilities; Statistical tests; Students; union intersection principle
• ISSN: 0039-0402; 1467-9574
• DOI: 10.1111/stan.12217

Nonparametric methodologies are proposed to assess college students' performance. Emphasis is given to gender and sector of high school. The application concerns the University of Campinas, a research university in Southeast Brazil. In Brazil college studies are based on a somewhat rigid set of subjects for each major. For this reason a simple GPA comparison may hide true performance. Therefore, we define individual vectors of course grades. These vectors are used in pairwise comparisons of common subject grades for individuals who entered college in the same year. The relative college performances of any two students are compared with their relative performances on the entrance exam score. A procedure based on generalized U‐statistics is developed to test if there is selection bias in the entrance exam by some predefined groups, which is equipped with asymptotically normal distribution under both null and alternative hypotheses. Maximum power is attained by employing the union intersection principle, and resampling techniques such as nonparametric bootstrap are employed to generate the empirical distribution of the test statistics and get p‐values.