Decomposing Pearson's χ2 test: A linear regression and its departure from linearity

Zhengyang Zhou, Hung Chih Ku, Guan Xing, Chao Xing

Research output: Contribution to journalArticle

1 Scopus citations

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 χ2-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 χ2-test statistic.

Original languageEnglish (US)
JournalAnnals of Human Genetics
DOIs
StateAccepted/In press - Jan 1 2018

Keywords

  • Linear regression
  • Ordinary least squares
  • Pearson's chi-squared test
  • Trend test

ASJC Scopus subject areas

  • Genetics
  • Genetics(clinical)

Fingerprint Dive into the research topics of 'Decomposing Pearson's χ<sup>2</sup> test: A linear regression and its departure from linearity'. Together they form a unique fingerprint.

  • Cite this