Resource Allocation by Measures of Relative Social Need in Geographical Areas: The Relevance of the Signed χ 2,the Percentage,and the Raw Count

Abstract

The construction of social indices to compare local areas from census and other data has an important influence on the allocation of public resources. There has been debate in past years on the choice of variables for such indices and on the means used to combine percentages measured for more than one variable. More recently the percentage and its z-score have given way to the signed χ² statistic as a more appropriate means of identifying concentrations of need. In this paper the relative merits of the signed χ² statistic, the percentage, and the raw count are discussed in relation to two separate objectives in resource allocation: identification of concentrations of need (geographic targeting) and calculation of local budgets (resource distribution). The signed χ² statistic is shown to overcome disadvantages of the percentage when identifying high concentrations of need but entails its own disadvantages. It is arbitrary in its construction, its ranking of areas is dependent on the choice of a reference area, and it is misleading for areas of low concentration of need. These conclusions apply both to comparison of large local areas such as local authority districts and to comparison of small areas within a locality. Alternatives are discussed.

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