discSurv (version 1.1.2)

tauToPearson: Transformation of Tau to Pearson correlation

Description

If the two variables are bivariate normal distributed, this formula maps kendalls tau to bravais pearson correlation coefficient rho.

Usage

tauToPearson(Tau)

Arguments

Tau

Numeric vector in the interval [-1, 1]

Value

• Vector of bravais pearson correlation coefficient rho

Details

This relationship holds only in the case if the two random variables are jointly normal distributed.

References

William H. Kruskal, (1958), Ordinal Measures of Association, Journal of the American Statistical Association, Vol. 53, No. 284, pp. 814-861

See Also

simCompRisk

Examples

# 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