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A nonparametric approach to assess undergraduate performance

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  • Hildete P. Pinheiro
  • Pranab K. Sen
  • Aluísio Pinheiro
  • Samara F. Kiihl

Abstract

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.

Suggested Citation

  • Hildete P. Pinheiro & Pranab K. Sen & Aluísio Pinheiro & Samara F. Kiihl, 2020. "A nonparametric approach to assess undergraduate performance," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 538-558, November.
    • Handle: RePEc:bla:stanee:v:74:y:2020:i:4:p:538-558
    DOI: 10.1111/stan.12217
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    References listed on IDEAS

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    1. Aluísio Pinheiro & Pranab Sen & Hildete Pinheiro, 2011. "A class of asymptotically normal degenerate quasi U-statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1165-1182, December.
    2. Elisa Rose Birch & Paul W. Miller, 2006. "Student Outcomes At University In Australia: A Quantile Regression Approach," Australian Economic Papers, Wiley Blackwell, vol. 45(1), pages 1-17, March.
    3. Rafael Pimentel Maia & Hildete Prisco Pinheiro & Aluísio Pinheiro, 2016. "Academic performance of students from entrance to graduation via quasi U-statistics: a study at a Brazilian research university," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(1), pages 72-86, January.
    4. Smith, Jeremy & Naylor, Robin, 2005. "Schooling effects on subsequent university performance: evidence for the UK university population," Economics of Education Review, Elsevier, vol. 24(5), pages 549-562, October.
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