THE BIPOLAR MEAN IN SENSORY ANALYSIS

The bipolar mean has recently been put forward with the aim of summarizing ordinal variables [1]. It is a synthetic distribution where the total size n is concentrated on one of the k categories of the variable or, at most, on two consecutive categories. This measure is derived according to the usual statistical dominance criterion that is based on retro-cumulative frequencies. Further improvements to the bipolar mean include extensions to discrete quantitative variables and a new variability measure, i.e. the "mean deviation about the bipolar mean". The bipolar mean can also be applied to ordinal variables whose categories are expressed as scores on a numerical scale. Hence, this new way of summarizing such variables can be useful in sensory analysis, where it is often necessary to compare frequency distributions representing the evaluation of certain characteristics made by judges or tasters about different products. The assessment is usually based on simple synthetic measures such as the arithmetic mean or the median. These indexes however, can result in contradictory answers. In this work, we present the normalization of the mean deviation of the bipolar mean. Moreover, some empirical evidence in sensory analysis is given with the purpose of showing how the bipolar mean and the relative mean deviation can sometimes overcome these problems of comparison.