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Lord's Paradox in a Continuous Setting and a Regression Artifact in Numerical Cognition Research.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Stockholm University. (Mathematics and Applied Mathematics)ORCID-id: 0000-0002-7164-0924
Chalmers University of Technology, Sweden.
2014 (engelsk)Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, nr 4, s. e95949-e95949Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper we review, and elaborate on, the literature on a regression artifact related to Lord's paradox in a continuous setting. Specifically, the question is whether a continuous property of individuals predicts improvement from training between a pretest and a posttest. If the pretest score is included as a covariate, regression to the mean will lead to biased results if two critical conditions are satisfied: (1) the property is correlated with pretest scores and (2) pretest scores include random errors. We discuss how these conditions apply to the analysis in a published experimental study, the authors of which concluded that linearity of children's estimations of numerical magnitudes predicts arithmetic learning from a training program. However, the two critical conditions were clearly met in that study. In a reanalysis we find that the bias in the method can fully account for the effect found in the original study. In other words, data are consistent with the null hypothesis that numerical magnitude estimations are unrelated to arithmetic learning.

sted, utgiver, år, opplag, sider
2014. Vol. 9, nr 4, s. e95949-e95949
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
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URN: urn:nbn:se:mdh:diva-24948DOI: 10.1371/journal.pone.0095949ISI: 000335227400146PubMedID: 24752244Scopus ID: 2-s2.0-84899697810OAI: oai:DiVA.org:mdh-24948DiVA, id: diva2:715221
Tilgjengelig fra: 2014-05-02 Laget: 2014-05-02 Sist oppdatert: 2018-10-16bibliografisk kontrollert

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