%0 Journal Article
%T Note on Rank-Biserial Correlation when There Are Ties
%A Jos¨Ś Moral de la Rubia
%J Open Journal of Statistics
%P 597-622
%@ 2161-7198
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojs.2022.125036
%X The objective of this
article is to demonstrate with examples that the two-sided tie correction does not work
well. This correction was developed by Cureton so that KendallĄŻs tau-type and
SpearmanĄŻs rho-type formulas for rank-biserial correlation yield the same
result when ties are present. However, a correction based on the bracket ties achieves the desired
goal, which is demonstrated algebraically
and checked with three examples. On the one hand, the 10-element random sample
given by Cureton, in which the two-sided tie correction performs well, is taken up. On the other
hand, two other examples are given, one with a 7-element random sample and the
other with a clinical random sample of 31 participants, in which the two-sided tie correction does not work,
but the new correction does. It is concluded that the new corrected formulas
coincide with Goodman-KruskalĄŻs gamma as compared to GlassĄŻ formula that
matches SomersĄŻ dY|X or asymmetric measure of association of Y ranking with respect to X dichotomy.
The use of this underreported coefficient is suggested, which is very easy to
calculate from its equivalence with Kruskal-WallisĄŻ gamma and SomersĄŻ dY|X.
%K Ordinal Variable
%K Dichotomy
%K Linear Association
%K Nonparametric Statistics
%K Descriptive Statistics
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=120366