La moyenne bipolaire pour l'analyse sensorielle

In a recent work, the bipolar mean was proposed with the aim to summarize the ordinal variables. 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. The measure was derived according to the usual statistical dominance principle that is based on the retro-cumulative frequencies. Later the bipolar mean was extended to the discrete quantitative variables and a new variability measure was introduced, i.e. the mean deviation about the bipolar mean. This measure can be applied also to ordinal variables whose categories are expressed as scores on a numerical scale. Hence, the new way to summarize these variables can be useful in sensory analysis where it is often necessary to compare frequency distributions that represent the evaluations of judges or tasters in relation to some characteristics of different products. The assessment is usually based on simple synthetic measures such as the arithmetic mean or the median, but these indexes can provide contradictory answers. The normalization of the mean deviation about the bipolar mean is proposed in this work. Moreover, some empirical evidences in sensory analysis are given with the purpose of showing how the bipolar mean and the mean deviation about it can sometimes overcome the comparison problems.