Transformation of Tau to Pearson correlation
If the two variables are bivariate normal distributed, this formula maps kendalls tau to bravais pearson correlation coefficient rho.
tauToPearson(Tau)
Tau |
Numeric vector in the interval [-1, 1] |
This relationship holds only in the case if the two random variables are jointly normal distributed.
Vector of bravais pearson correlation coefficient rho
Thomas Welchowski welchow@imbie.meb.uni-bonn.de
William H. Kruskal, (1958), Ordinal Measures of Association, Journal of the American Statistical Association, Vol. 53, No. 284, pp. 814-861
# Plot of relation between kendalls tau and pearson correlation MaxDisc1 <- nlminb(start=0.5, objective=function (x) -abs(tauToPearson (x)-x)) MaxDisc2 <- nlminb(start=-0.5, objective=function (x) -abs(tauToPearson (x)-x)) plot(x=seq(-1,1,length.out=500), y=tauToPearson(seq(-1,1,length.out=500)), xlab=expression(tau), ylab=expression(rho), type="l", las=1, main="Relationship between tau and pearson correlation (bivariate normal)", lwd=2) lines(x=seq(-1,1,length.out=500), y=seq(-1,1,length.out=500), lty=2) segments(x0=0, y0=-1.25, x1=0, y1=0, lty=2) segments(x0=-1.25, y0=0, x1=0, y1=0, lty=2) segments(x0=MaxDisc1$par, y0=-1.25, x1=MaxDisc1$par, y1=tauToPearson (MaxDisc1$par), lty=2) segments(x0=MaxDisc2$par, y0=-1.25, x1=MaxDisc2$par, y1=tauToPearson (MaxDisc2$par), lty=2) # The maximum discrepancy between pearson and spearman is at # a kendalls tau value about 0.56 and -0.56
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.