Re: Relationship between Pearson rho and Kendall tau

On Jun 30, 2:20 pm, "Schizoid Man" <sc...@xxxxxxxxxxxxxxxx> wrote:
"Ray Koopman" <koop...@xxxxxx> wrote in message news:
On Jun 30, 1:48 pm, "Schizoid Man" <sc...@xxxxxxxxxxxxxxxx> wrote:
Hello,

Does the following relationship always hold, or are there are specific
conditions that they need to be applied under?
tau = 2 * arcsin (rho) / pi

Thanks,
Schiz

In a bivariate normal population in which the Pearson correlation
is rho, the expected value of a sample tau is arcsin(rho)/(pi/2).

Thanks, Ray. Though I'm not sure how (2/pi) arcsin (rho) is different from
arcsin(rho) / (pi/2).

It's not. I write it that way because it comes closer to describing
what's happening: you're dividing an angle, arcsin(rho), by its
maximum possible value, pi/2, to get a value that is in [-1,1].
.

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