Academic performance of students from entrance to graduation via quasi U-statistics: a study at a Brazilian research university

Abstract

We present novel methodology to assess undergraduate students' performance. Emphasis is given to potential dissimilar behaviors due to high school background and gender. The proposed method is based on measures of diversity and on the decomposability of quasi U-statistics to define average distances between and within groups. One advantage of the new method over the classical analysis of variance is its robustness to distributional deviation from the normality. Moreover, compared with other nonparametric methods, it also includes tests for interaction effects which are not rank transform procedures. The variance of the test statistic is estimated by jackknife and p-values are computed using its asymptotic distribution. A college education performance data is analyzed. The data set is formed by students who entered in the University of Campinas, Brazil, between 1997 and 2000. Their academic performance has been recorded until graduation or drop-out. The classical ANOVA points to significant effects of gender, type of high school and working status. However, the residual analysis indicates a highly significant deviation from normality. The quasi U-statistics nonparametric tests proposed here present significant effect of interaction between type of high school and gender but did not present a significant effect of working status. The proposed nonparametric method also results in smaller error variances, illustrating its robustness against model misspecification.

Keywords:

• asymptotic theory
• diversity measures
• jackknife
• nonparametric methods
• interaction effect

Acknowledgments

We thank the referees for their valuable comments and the following people for their direct support regarding databases used for this study: Renato L. Pedrosa, Associate Coordinator of the Center for Advanced Studies at Unicamp, Mauricio Kleink, Coordinator of the Admissions Committee (Comvest) at Unicamp, Antonio Faggiani, Coordinator of the Academic Records Division (DAC) at Unicamp, Renato Hirata, database specialist at Comvest, Gleyson R. do Nascimento and Flavio Ferraresi, trainees at Comvest and Silvio de Souza, database specialist at DAC.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed at 10.1080/02664763.2015.1077939.

Notes

1. Pardo is commonly used in Brazil to refer to individuals with varied racial ancestries.

Additional information

Funding

R. P. Maia was supported by CAPES-Brazil, H.P. Pinheiro's research was partially supported by CNPq-Brazil [305988/2012-3] and FAPESP [2011/15047-7], A. Pinheiro's research was supported by FAPESP [13/00506-1] and CNPq [308439/2014-7 and 401478/2012-2].