Data aggregation and Simpson's paradox gauged by index numbers

Simpson's paradox is a phenomenon occurring in data aggregation in complex systems. It consists in the increase (decrease) of the rate in the data aggregate at the higher level with the simultaneous decrease (increase) of the rate in each subgroup of the lower levels of the hierarchy. Although the nature of this paradox is known, it is difficult to interpret it without gauging the reasons of its occurrence. To capture the causes of the paradox, we elaborated some measures of index analysis. We suggest to apply these measures for estimation of changes due to the partial rates and the structural effects. Using numerical examples from the marketing research field, we show how the elaborated gauges evaluate absolute and relative changes, helping to interpret the incidence cases.