Book chapter

Nonparametric methods for stratified C-sample designs: a case study

Rosa Arboretti
University of Padua, Italy - ORCID: 0000-0003-1263-0440

Riccardo Ceccato
University of Padua, Italy - ORCID: 0000-0002-8629-8439

Luigi Salmaso
University of Padua, Italy - ORCID: 0000-0001-6501-1585


Several parametric and nonparametric methods have been proposed to deal with stratified C-sample problems where the main interest lies in evaluating the presence of a certain treatment effect, but the strata effects cannot be overlooked. Stratified scenarios can be found in several different fields. In this paper we focus on a particular case study from the field of education, addressing a typical stochastic ordering problem in the presence of stratification. We are interested in assessing how the performance of students from different degree programs at the University of Padova change, in terms of university credits and grades, when compared with their entry test results. To address this problem, we propose an extension of the Non-Parametric Combination (NPC) methodology, a permutation-based technique (see Pesarin and Salmaso, 2010), as a valuable tool to improve the data analytics for monitoring University students’ careers at the School of Engineering of the University of Padova. This new procedure indeed allows us to assess the efficacy of the University of Padova’s entry tests in evaluating and selecting future students.
Read more

Keywords: Nonparametric permutation, Evaluation of Educational Systems



Pages: 17-22

Published by: Firenze University Press

Publication year: 2021

DOI: 10.36253/978-88-5518-304-8.05

Download PDF

© 2021 Author(s)
Content licence CC BY 4.0
Metadata licence CC0 1.0


Publication year: 2021

DOI: 10.36253/978-88-5518-304-8.05

Download XML

© 2021 Author(s)
Content licence CC BY 4.0
Metadata licence CC0 1.0


  1. Basso, D., Pesarin, F., Salmaso, L., Solari, A. (2009). Permutation tests for stochastic ordering and ANOVA: theory and applications with R. Springer Science & Business Media, New York, (NY). 10.1007/978-0-387-85956-9_7
  2. Basso, D., Salmaso, L. (2011). A permutation test for umbrella alternatives. Statistics and Computing, 21(1), pp. 45–54. 10.1007/s11222-009-9145-8
  3. Benjamini, Y., Hochberg, Y. (1995). Controlling the false discovery rate: a practical and pow- erful approach to multiple testing. Journal of the Royal statistical society: series B (Methodological), 57(1), pp. 289–300. 10.1111/j.2517-6161.1995.tb02031.x
  4. Bonnini, S., Prodi, N., Salmaso, L., Visentin, C. (2014). Permutation approaches for stochastic ordering. Communications in Statistics-Theory and Methods, 43(10-12), pp. 2227–2235. 10.1080/03610926.2013.788888
  5. Finos, L., Salmaso, L., Solari, A. (2007). Conditional inference under simultaneous stochastic ordering constraints. Journal of statistical planning and inference, 137(8), pp. 2633–2641. 10.1016/j.jspi.2006.04.014
  6. Finos, L., Pesarin, F., Salmaso, L., Solari, A. (2008). Exact inference for multivariate ordered alternatives. Statistical Methods and Applications, 17(2), pp. 195–208. 10.1007/s10260-007-0052-x
  7. Jonckheere, A. R. (1954). A distribution-free k-sample test against ordered alternatives. Biometrika, 41(1/2), pp. 133–145. 10.1093/biomet/41.1-2.133
  8. Klingenberg, B., Solari, A., Salmaso, L., Pesarin, F. (2009). Testing marginal homogeneity against stochastic order in multivariate ordinal data. Biometrics, 65(2), pp. 452–462. 10.1111/j.1541-0420.2008.01067.x
  9. Mann, H. B., Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), pp. 50–60. 10.1214/aoms/1177730491
  10. Neuhäuser, M., Liu, P.-Y., Hothorn, L. A. (1998). Nonparametric tests for trend: Jonckheere’s test, a modification and a maximum test. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 40(8), pp. 899–909. 10.1002/(sici)1521-4036
  11. Pesarin, F., Salmaso, L. (2010). Permutation tests for complex data: theory, applications and software. John Wiley & Sons, Hoboken, (NJ). 10.1002/9780470689516
  12. R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, (AT).
  13. Shan, G., Young, D., Kang, L. (2014). A New Powerful Nonparametric Rank Test for Ordered Alternative Problem. PloS one, 9(11), pp. 1–10. 10.1371/journal.pone.0112924
  14. Terpstra, T. J. (1952). The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking. Indagationes Mathematicae, 14(3), pp. 327–333. 10.1016/s1385-7258(52)50043-x

Export citation

Selected format

Usage statistics policy

  • 13Chapter Downloads

Cita come:
Arboretti, R.; Ceccato, R.; Salmaso, L.; 2021; Nonparametric methods for stratified C-sample designs: a case study. Firenze, Firenze University Press.


Indici e aggregatori bibliometrici