This is a methodological critique of research by the Best Practice in Grouping Students (BPGS) project claiming teacher bias in allocating students to first-year secondary school mathematics teaching sets (British Educational Research Journal, 45(4), 873–879). The research assumes that bias could be shown by non-random relationships between ‘misallocations’ to sets and memberships of gender, ethnic and/or socio-economic subgroups. This paper questions the authors’ prescriptions for correct set placements and demonstrates two ways in which non-random relationships between subgroup memberships and (alleged) misplacements could be generated despite all students with similar scores within a school being given the same chance of a set position deemed correct by the researchers. It suggests that the BPGS project results are largely artefacts of their evaluation approach. No claim is made herein that teacher bias plays no part in set allocation, merely that, if it does, the approach by Connolly et al. could not evidence it. A lesson from the critique is that, before drawing inferences from data aggregated from diverse clusters, it is wise for researchers to investigate the way the data are generated at source and patterned by aggregation.

中文翻译：

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SAT、集合和偏见指控：2015 年一些英语学校 11 岁学生分配到数学集合。对 Connolly 等人的回应，2019

这是对学生分组最佳实践 (BPGS) 项目研究的方法论批评，该项目声称教师在将学生分配到一年级中学数学教学集时存在偏见（英国教育研究杂志，45(4), 873–879)。该研究假设偏见可以通过“错误分配”到性别、种族和/或社会经济亚群的集合和成员资格之间的非随机关系来表现出来。本文质疑作者对正确设置位置的规定，并展示了两种方式，尽管学校内所有具有相似分数的学生都获得相同的设置位置机会，但仍可以在子组成员和（所谓的）错位之间产生非随机关系研究人员认为是正确的。这表明 BPGS 项目结果很大程度上是其评估方法的产物。这里没有声称教师偏见在集合分配中没有任何作用，只是说，如果确实如此，Connolly 等人的方法。无法证明。批评的一个教训是，