For the analysis of two-way contingency tables with ordered categories, Yamamoto, Tahata, Suzuki, and Tomizawa (2011) considered a measure to represent the degree of departure from marginal point-symmetry. The maximum value of the measure cannot distinguish two kinds of marginal complete asymmetry with respect to the midpoint. A measure is proposed which can distinguish two kinds of marginal asymmetry with respect to the midpoint. It also gives large-sample confidence interval for the proposed measure.
Iki, T., & Tomizawa, S. (2018). Measure of departure from marginal average point-symmetry for two-way contingency tables. Journal of Modern Applied Statistical Methods, 17(2), eP2667. doi: 10.22237/jmasm/1559569334