The Bipolar Mean Dependece

In this paper an alternative formulation of the mean deviation about the bipolar mean is provided. In addition to this, the concept of bipolar mean-independence is defined in order to evaluate how conditional bipolar means change according to the value of another variable jointly considered. This concept arises from the well-known notion of mean dependence but it exploits the idea DJ the bipolar mean which can be used also for qualitative ordinal variables. A normalized index that measures the strength of the bipolar mean-dependence is also provided. An application presented which highlights the simplicity and interpretability of the proposed methodology.