"Rank Biserial Correlation" in jamovi
Posted: Tue Dec 07, 2021 2:22 pm
Cureton (1956) wrote:
"A formula is developed for the correlation between a ranking (possibly including ties and a dichotomy, with limits which are always ± 1. This formula is shown to be equivalent both to Kendall's tau and Spearman's ρ."
[ Cureton, E. E. (1956). Rank-biserial correlation. Psychometrika, 3, 287–290. https://doi.org/10.1007/BF02289138 ]
But this appears not to be the case! Jamovi reports the effect-size for the Mann-Whitney U test as a "Rank Biserial Correlation." However, the result seems incorrect to me. I've used the Spearman's rho routine, and alternately have rank-transformed the data and then computed Pearson's r. They confirm, for example, that the rank biserial correlation between y = {3, 9, 6, 5, 7, 2} and x = {0, 1, 0, 1, 1, 0} is 0.683. Not 0.778, which is the value reported as the rank biserial correlation accompanying the Mann-Whitney U. See the attached jamovi file (Version 2.2.2).
Glass (1965) on the other hand seems to write that the rank biserial correlation is merely an estimate of what the Spearman rho would be if the dichotomous variable (in the rank biserial correlation) were the result of the forced dichotomization of a rank variable.
This seems to be a bit of a mess, doesn't it?
"A formula is developed for the correlation between a ranking (possibly including ties and a dichotomy, with limits which are always ± 1. This formula is shown to be equivalent both to Kendall's tau and Spearman's ρ."
[ Cureton, E. E. (1956). Rank-biserial correlation. Psychometrika, 3, 287–290. https://doi.org/10.1007/BF02289138 ]
But this appears not to be the case! Jamovi reports the effect-size for the Mann-Whitney U test as a "Rank Biserial Correlation." However, the result seems incorrect to me. I've used the Spearman's rho routine, and alternately have rank-transformed the data and then computed Pearson's r. They confirm, for example, that the rank biserial correlation between y = {3, 9, 6, 5, 7, 2} and x = {0, 1, 0, 1, 1, 0} is 0.683. Not 0.778, which is the value reported as the rank biserial correlation accompanying the Mann-Whitney U. See the attached jamovi file (Version 2.2.2).
Glass (1965) on the other hand seems to write that the rank biserial correlation is merely an estimate of what the Spearman rho would be if the dichotomous variable (in the rank biserial correlation) were the result of the forced dichotomization of a rank variable.
This seems to be a bit of a mess, doesn't it?