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首页> 外文期刊>Annals of Human Genetics >Decomposing Pearson's χ 2 2 test: A linear regression and its departure from linearity
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Decomposing Pearson's χ 2 2 test: A linear regression and its departure from linearity

机译：分解Pearson的χ2 2测试：线性回归及其偏离线性

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Abstract In case–control genetic association studies, a standard practice is to perform the Cochran‐Armitage (CA) trend test under the assumption of the additive model because of its robustness. We could even identify situations in which it outperformed the analysis model consistent with the underlying inheritance mode. In this article, we analytically reveal the statistical basis that leads to the phenomenon. By elucidating the origin of the CA trend test as a linear regression model, we decompose Pearson's χ 2 ‐test statistic into two components—one is the CA trend test statistic that measures the goodness of fit of the linear regression model, and the other measures the discrepancy between data and the linear regression model. Under this framework, we show that the additive coding scheme, as well as the multiplicative coding scheme, increases the coefficient of determination of the regression model by increasing the spread of data points. We also obtain the conditions under which the CA trend test statistic equals the MAX statistic and Pearson's χ 2 ‐test statistic.
机译：摘要在病例控制遗传协会研究中，标准做法是由于其鲁棒性，在添加剂模型的假设下执行Cochran-armitage（CA）趋势测试。我们甚至可以识别它表现出与底层遗传模式一致的分析模型的情况。在本文中，我们分析了揭示了导致现象的统计基础。通过阐明CA趋势试验的起源作为线性回归模型，我们将Pearson的χ2 - 最统计分为两个组件 - 一个是CA趋势测试统计，测量线性回归模型的良好性，以及其他措施数据与线性回归模型之间的差异。在该框架下，我们表明添加剂编码方案以及乘法编码方案，通过增加数据点的扩展来增加回归模型的确定系数。我们还获得了CA趋势试验统计数据的条件等于MAX统计和Pearson的χ2 - 最统计。

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