条件均值的方差分解

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摘要翻译：
我们用两组不同的数据来检验一种明显新的方法来分析一个依赖于定性特征的数值变量的方差。我们建议使用这种方法来补充其他现有的技术，以研究所涉及的变量的相互依赖性。根据我们的方法，方差被表示为正交分量的和，作为条件均值的差，相对于定性特征。方差的结果表达式取决于字符的顺序。我们提出了一种算法，它导致了一个被认为是自然的排序。第一组数据是一组学生在入学考试中取得的分数，基于一个有30个问题的多项选择题测试。在这种情况下，定性特征是并元的，并对应于每个问题的正确或不正确的答案。第二组数据涉及意大利大学毕业生获得学位的延迟。在这种情况下，根据所研究人群的七个具体定性特征（性别、以前的教育程度、工作条件、父母的教育程度、研究领域等）来分析差异
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英文标题：
《Decomposition of variance in terms of conditional means》
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作者：
Alessandro Figa' Talamanca, Angelo Guerriero, Alberto Leone, Gian
  Piero Mignoli, Enrico Rogora
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing techniques to study the interdependence of the variables involved. According to our method the variance is expressed as a sum of orthogonal components, obtained as differences of conditional means, with respect to the qualitative characters. The resulting expression for the variance depends on the ordering in which the characters are considered. We suggest an algorithm which leads to an ordering which is deemed natural. The first set of data concerns the score achieved by a population of students, on an entrance examination, based on a multiple choice test with 30 questions. In this case the qualitative characters are dyadic and correspond to correct or incorrect answer to each question. The second set of data concerns the delay in obtaining the degree for a population of graduates of Italian universities. The variance in this case is analyzed with respect to a set of seven specific qualitative characters of the population studied (gender, previous education, working condition, parent's educational level, field of study, etc.)
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PDF链接：
https://arxiv.org/pdf/710.0849

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关键词：方差分解 条件均值 epidemiology Applications Universities 定性 depends set 意大利 data