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Searching for a common pooling pattern among several samples

Author

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  • Álvarez-Esteban, P.C.
  • del Barrio, E.
  • Cuesta-Albertos, J.A.
  • Matrán, C.

Abstract

The grades of a Spanish university access exam involving 10 graders are analyzed. The interest focuses on finding the greatest group of graders showing similar grading patterns or, equivalently, on detecting if there are graders whose grades exhibit significant deviations from the pattern determined by the remaining graders. Due to differences in background of the involved students and graders, homogeneity is too strong to be considered as a realistic null model. Instead, the weaker similarity model, which seems to be more appropriate in this setting, is considered. To handle this problem, a statistical procedure designed to search for a hidden main pattern is developed. The procedure is based on the detection and deletion of the graders that are significantly non-similar to (the pooled mixture of) the others. This is performed through the use of a probability metric, a bootstrap approach and a stepwise search algorithm. Moreover, the procedure also allows one to identify which part of the grades of each grader makes her/him different from the others.

Suggested Citation

  • Álvarez-Esteban, P.C. & del Barrio, E. & Cuesta-Albertos, J.A. & Matrán, C., 2013. "Searching for a common pooling pattern among several samples," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 1-14.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:1-14
    DOI: 10.1016/j.csda.2013.04.015
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    References listed on IDEAS

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    1. Zhang, Jin & Wu, Yuehua, 2007. "k-Sample tests based on the likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4682-4691, May.
    2. Martínez-Camblor, Pablo & de Uña-Álvarez, Jacobo, 2009. "Non-parametric k-sample tests: Density functions vs distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3344-3357, July.
    3. Alvarez-Esteban, Pedro Cesar & del Barrio, Eustasio & Cuesta-Albertos, Juan Antonio & Matran, Carlos, 2008. "Trimmed Comparison of Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 697-704, June.
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    Cited by:

    1. Todorov, Diman & Setchi, Rossi, 2014. "Time-efficient estimation of conditional mutual information for variable selection in classification," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 105-127.

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