The use of quasi U-statistics for undergraduate performance assessment

We propose new methodologies to assess Undergraduate performance dissimilarities. Emphasis is given to the sector of High School education from which the College student comes - private or public. Due to the complex structure of Undergraduate courses, the overall performance of a student is not based upon its GPA (Grade Point Average). The sample consists of all undergraduate students entering Unicamp at years 2000-2005 as follows. For each student a vector is formed by his/her grades in each course taken: multiple scores are considered whenever fail/pass grades happen. These vectors are then used in pairwise comparisons of common courses grades between all individuals that entered college in the same year taking into account the entrance rank. These forms a generalized U-statistic based on the classical signed rank kernel. We apply the decomposability of these quasi U-statistics (Pinheiro et al., 2009, 2010) to define average distance measures within and between groups. A test statistic for a homogeneity test among groups can be developed and asymptotic normality under mild conditions can be proved for the test statistic under the null hypothesis.