场景1：Pearson相关系数与Spearman相关系数之间的转换
Pearson相关系数 $r$
    Spearman相关系数 $r_s$

Pearson相关系数$r$转化Spearman相关系数$r_s$

$$r_s=\frac{6}{\pi}*sin^{-1}(\frac{r}{2})$$

Spearman相关系数$r_s$转化Pearson相关系数$r$

$$r=2*sin(r_s*\frac{\pi}{6})$$
场景2：Pearson相关系数与Kendall相关系数之间的转换
Pearson相关系数 $r$
    Kendall相关系数 $\tau$

Pearson相关系数$r$转化Kendall相关系数$\tau$

$$\tau=\frac{2}{\pi}*sin^{-1}(r)$$

Kendall相关系数$\tau$转化Pearson相关系数$r$

$$r=sin(\tau*\frac{\pi}{2})$$

参考文献:

[1] . Rupinski, M. T., & Dunlap, W. P. (1996). Approximating Pearson Product-Moment Correlations from Kendall’s Tau and Spearman’s Rho. Educational and Psychological Measurement, 56(3), 419–429.
[2]使用该转换公式的文献：Chen, Lihua et al. “The correlation between apparent diffusion coefficient and tumor cellularity in patients: a meta-analysis.” PloS one vol. 8,11 e79008. 11 Nov. 2013, doi:10.1371/journal.pone.0079008