[Feature Request]: improved CI calculation for Spearman and Kendall correlation

[TarandeepKang]

Description

z-transformation may not be optimal

Purpose

No response

Use-case

In keeping with current best practice (and the insistence of a reviewer of one of my papers) consider implementing a few corrections

Is your feature request related to a problem?

No response

Is your feature request related to a JASP module?

Regression

Describe the solution you would like

No response

Describe alternatives that you have considered

No response

Additional context

I raised this issue a few years ago #752 and the team decided the current z-transform option was best. I think it might be time to discuss again whether to consider implementing corrections for improved CIs

Bishara, A. J., Hittner, J. B. (2017). Confidence intervals for correlations when data are not normal. Behavior Research Methods, 49, 294–309 . https://doi.org/10.3758/s13428-016-0702-8

Bonett, D. G., & Wright, T. A. (2000). Sample size requirements for estimating pearson, kendall and spearman correlations. Psychometrika, 65(1), 23–28. https://doi.org/10.1007/BF02294183

Fieller, E. C., Hartley, H. O., & Pearson, E. S. (1957). Tests for Rank Correlation Coefficients. I. Biometrika, 44(3/4), 470–481. https://doi.org/10.2307/2332878

Code available

https://rpubs.com/seriousstats/616206

From this blog

https://seriousstats.wordpress.com/2020/05/18/cis-for-spearmans-rho-and-kendalls-tau/

Now also implemented in this package:

https://easystats.github.io/correlation/reference/correlation.html

[EJWagenmakers]

Let me get this straight. So we are in the situation where the parametric assumptions are violated; we choose a rank-based method (Spearman or Kendall) and then you propose to compute the 95% CI on these in a different way than we do now, is that correct? (we do offer the bootstrap as a generic solution, and I find it hard to believe that it would not perform well unless under extreme circumstances that would prompt caution regardless).

[TarandeepKang]

Hi EJ, Yes, that's right, I'm not suggesting we do away with the bootstrap, just consider whether the Fieller/ Bonnet &wright correction could be an alternative? The B&H paper seems to be making exactly the point that under at least three different conditions the the z based interval (which unless I'm wrong is what is currently implemented) is not ideal.

PS, I'm willing to accept I might be completely wrong and if I am, I will happily go hide in the nearest corner, and give your opinion to my reviewer. If I am wrong, I can only apologise..

[EJWagenmakers]

I added Johnny and Don, who may know more. [Of course the best solution is to simply report the Bayesian posterior and the issues do not arise, as the Bayesian formalism allows only a single estimate, namely the entire posterior distribution]

[TarandeepKang]

Thanks, I appreciate the consideration! Believe it or not, I am going increasingly Bayesian (thanks in very great part to last year's workshop). But as a concession to my supervisor who literally hasn't "taken a stats class since 1989", I'm including both approaches for now. And anyway, the laggards who don't want to go Bayesian yet, we might as well give them the best possible frequentist results?

[Kucharssim]

Just as a side note, Kendall's CI is based on the work of Hollander, M., Wolfe, D. A., & Chicken, E. reported in their book Nonparametric statistical methods (3rd edition). It's not based on Fisher's Z transform. Spearman CI is currently indeed based on the standard procedure involving the Z transform.

[TarandeepKang]

Oops, lets not change the Kendall method, then. I'm sure my reviewer will be more than happy when I tell them the current method methods are from the "Bible" of nonparametric statistics! But, unless I'm completely mistaken, I think my point re Spearman stands.

[TarandeepKang]

Hi All, I just want to check if there's been any update on this. As a side note, it's good to know that the confidence interval for the candle correlation is based on Hollander et al., but I wonder if it would be worthwhile adding a note to that effect in the documentation. I know this is made clear in the documentation for the function in the stats package?

I would certainly be glad to hear what you think of the supposedly improved method suggested for Spearman CIs?

[TarandeepKang]

Hi @EJWagenmakers, sincerest apologies for the annoyance, and for reopening this issue, but I wonder if you and your team have had any chance to give this any further thought?