TITLE:
Note on Rank-Biserial Correlation when There Are Ties
AUTHORS:
José Moral de la Rubia
KEYWORDS:
Ordinal Variable, Dichotomy, Linear Association, Nonparametric Statistics, Descriptive Statistics
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.5,
October
13,
2022
ABSTRACT: 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 Kendall’s tau-type and
Spearman’s 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-Kruskal’s gamma as compared to Glass’ formula that
matches Somers’ 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-Wallis’ gamma and Somers’ dY|X.