The importance of normalisation in the construction of deprivation indices

Measuring socio-economic deprivation is a major challenge usually addressed through the use of composite indices. This paper aims to clarify the technical details regarding composite index construction. The distribution of some variables, for example unemployment, varies over time, and these variations must be considered when composite indices are periodically re-evaluated. The process of normalisation is examined in detail and particular attention is paid to the importance of symmetry and skewness of the composite variable distributions.

Four different solutions of the Townsend index of socioeconomic deprivation are compared to reveal the effects that differing transformation processes have on the meaning or interpretation of the final index values. Differences in the rank order and the relative separation between values are investigated.

Constituent variables which have been transformed to yield a more symmetric distribution provide indices that behave similarly, irrespective of the actual transformation methods adopted. Normalisation is seen to be of less importance than the removal of variable skewness. Furthermore, the degree of success of the transformation in removing skewness has a major effect in determining the variation between the individual electoral ward scores. Constituent variables undergoing no transformation produce an index that is distorted by the inherent variable skewness, and this index is not consistent between re-evaluations, either temporally or spatially.

Effective transformation of constituent variables should always be undertaken when generating a composite index. The most important aspect is the removal of variable skewness. There is no need for the transformed variables to be normally distributed, only symmetrically distributed, before standardisation. Even where additional parameter weights are to be applied, which significantly alter the final index, appropriate transformation procedures should be adopted for the purpose of consistency over time and between different geographical areas.