Discreteness Causes Bias in Percentage-Based Comparisons: A Case Study From Educational Testing.
Discretizing continuous distributions can lead to bias in parameter estimates. We present a case study from educational testing that illustrates dramatic consequences of discreteness when discretizing partitions differ across distributions. The percentage of test takers who score above a certain cut...
| Publicado en: | American Statistician Vol. 69; no. 3; pp. 174 - 182 |
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| Autores principales: | , |
| Formato: | Case Study |
| Publicado: |
Taylor & Francis Ltd
Aug2015
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=109173238&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 109173238 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Aug2015 vid: 69 iid: 3 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 109173238 10.1080/00031305.2015.1031828 ppf: 174 ppct: 8 formats: tig: atl: Discreteness Causes Bias in Percentage-Based Comparisons: A Case Study From Educational Testing. aug: au: Yee, Darrick Ho, Andrew su: Discretization methods Continuous distributions Gaussian distribution Least squares Probability density function sug: subj: Discretization methods Continuous distributions Gaussian distribution Least squares Probability density function keyword: Education Estimation Testing. Education Estimation Testing. ab: Discretizing continuous distributions can lead to bias in parameter estimates. We present a case study from educational testing that illustrates dramatic consequences of discreteness when discretizing partitions differ across distributions. The percentage of test takers who score above a certain cutoff score (percent above cutoff, or “PAC”) often describes overall performance on a test. Year-over-year changes in PAC, or ΔPAC, have gained prominence under recent U.S. education policies, with public schools facing sanctions if they fail to meet PAC targets. In this article, we describe how test score distributions act as continuous distributions that are discretized inconsistently over time. We show that this can propagate considerable bias to PAC trends, where positive ΔPACs appear negative, and vice versa, for a substantial number of actual tests. A simple model shows that this bias applies to any comparison of PAC statistics in which values for one distribution are discretized differently from values for the other. pubtype: Academic Journal doctype: Case Study src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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