Removing an Extraneous Effect in Measuring Correlation Coefficient

Chong-Yau Fu ； Min-Hsun Tsai

《中國統計學報》 45卷4期 (2007/12) Pp. 386-401

https://doi.org/10.29973/JCSA.200712.0004

並列摘要

Pearson correlation coefficient is a measure for the linearity degree between two continuous variables (X, Y). When this measure is spurious from an extraneous variable effect (Z), the partial correlation coefficient is often referred to adjust. However, it is possible to obtain a biased result from only the linear effect removed in the partial correlation coefficient applied.
This study combines the techniques of ”stratification” and ”regression fitting” to replace the deviated value of the formula in the Pearson correlation coefficient. The r(subscript PR), r(subscript GM) and r(subscript GR) are proposed and investigated through simulation technique. And, the results show that r(subscript GR), r(subscript PR) perform very well in simulation Ⅰ, and r(subscript GR) still performs very well in simulation Ⅱ. Meanwhile, in a fetal study, the linear association between femur length and weight is estimated to be about 0.5 (r(subscript PR), r(subscript GR)), instead of 0.91 (uncorrected Pearson correlation coefficient), which is masked from a strong linear association with gestational age.
Therefore, r(subscript GR) is the most reliable estimation and r(subscript PR) provides a possible method for more than one extraneous variable adjusted. Also, noted that the performance of r(subscript PR) varies with two data structure (simulation Ⅰ & Ⅱ).

並列關鍵字

Pearson correlation coefficient ； partial correlation coefficient ； corrected correlation coefficient ； deviated value ； stratification ； regression fitted

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