The formalization of the intuitive idea of statistical indexes


  • Tommaso Gastaldi



After a brief analysis of the concept of statistical index the author explains the general requirements which a statistical index has to satisfy. The main requirement is for the characteristics actually measured by the index to coincide with the characteristic to be quantified of which one usually has an intuitive idea. Formally this means that the total preordination which the index induces on the set D of the possible distributions must not contradict the preordination which can be defined in D on the sole basis of intuitive evidence. Another important requirement is for the value which the index takes in relation to any distribution not to be blatantly disproportionate with the intensity assumed by the characteristic under examination in that distribution. The author points out that disregarding this requirement means not to recognize interpretative meaning in the quantification produced by the index. To ignore it would be to consider the statistical index as a mere tool for comparing distributions in relation to the characteristic under examination. The opportunity of utilizing the increasing transformations of the indices that in practice have been shown to be right for quantifying a certain characteristic as indices of the same characteristic is also discussed. On the basis of this a "conservation principle for the descriptive capacity" of the index is attained. Through this the "advantages" and "disadvantages" acquired in any increasing transformation can find a global form of compensation. In conclusion it is observed that the quantification produced by the index limited though it may be due to certain instances of an intuitive nature distinguishes such an index from any other and gives it a certain peculiar "interpretation of reality". In the light of this indices may be considered as "bridges" throw down by our rational abilities between those points of solid ground where logic is backed up by the intuitive notion we have of the measured characteristic. They also represent real "artificial senses" capable of selecting only those aspects of reality through which we have rendered them perceptible this forming a "filtered" image by means of their functional structure. Each individual index contributes to the building up of an image of reality or rather of the distribution we are interested in studying in the same way that each of our ordinary senses contributes to the erection of an image of external reality.

How to Cite

Gastaldi, T. (1988). The formalization of the intuitive idea of statistical indexes. Statistica, 48(3/4), 243–258.