Kendall Tau - Bayesian/frequentist

dy

Hi,

I would like to conduct Kendall tau's correlational analyses. I am aware that Tau-a does not account for ties, whereas Tau-b and tau-c account for ties. The article by van Doorn and colleagues (van Doorn, J., Ly, A., Marsman, M., & Wagenmakers, E. J. (2018). Bayesian Inference for Kendall’s Rank Correlation Coefficient. American Statistician, 72(4), 303–308. http://doi.org/10.1080/00031305.2016.1264998) uses the formula for Tau-a. However, in JASP, Tau-b is being used. I am confused, and am not sure which is actually being used in the source code. May I know which formula is actually being used in JASP?

Thanks!

Best,

Darren

EJ

Hi Darren,

I'll pass this on to Johnny, but just to be sure: are you asking about the frequentist or the Bayesian implementation?

Cheers,

E.J.

dy

Hi E.J.,

Thanks so much for passing this on to Johnny. I am primarily interested in the Bayesian implementation, but am reporting both p-values and BFs. I believe the basic formula for the statistic used for hypothesis testing should be the same regardless of approach. Besides, in both approaches, the statistic is labelled as tau-b.

Thanks!

Darren

JohnnyB

Hi Darren,

Apologies for the delay in answering. The Bayesian implementation is based on the test statistic (tau) and it's asymptotic distribution. In the article we only speak about the version without ties. However, even with ties present, this method should provide an accurate accounting of the rank correlation. Here is a snippet from the Kendall package in R:

``When ties are present, a normal approximation with continuity correction is used by taking S as normally distributed with mean zero and variance var(S), where var(S) is given by Kendall (1976, eqn 4.4, p.55). Unless ties are very extensive and/or the data is very short, this approximation is adequate. If extensive ties are present then the bootstrap provides an expedient solution (Davison and Hinkley, 1997).''

Kendall, M.G. (1976). Rank Correlation Methods. 4th Ed. Griffin.

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press

The normal approximation mentioned here is also what the Bayesian method builds on, so unless you have very few data points or a very big number of ties, it will be OK.

Kind regards,

Johnny

dy

Hi Johnny,

Thanks so much for the clarification!

Best,

Darren