P-value calculation methods for semi-partial correlation coefficients

The p-value calculation methods for the partial and semi-partial correaltion coefficients were proposed by Cohen et al. (2003) and Kim (2015). The method of Cohen et al. (2003) depends on a single and identical statistic for both partial and semi-partial correlations, while Kim (2015)'s method uses two separate statistics for each of partial and semi-partial correlations. In particular, the mathematical expression of the p-value calculation for the semi-partial correlation coefficient differs between Kim (2015) and Cohen et al. (2003). Thus, these two expressions were compared through theoretical aspects and simulations. The results show that the semi-partial correlation coefficients by Kim (2015) is monotonic to the corresponding p-values, while Cohen et al. (2003)'s method does not maintain monotonicity.