Use of Percentage Change in Small Area Statistics

Abstract

This paper presents a method for predicting the postcensal estimates for small area statistics. The method regressed the percentage changes in the dependent variable on the percentage changes in the symptomatic (independent) variables for a sample of some areas over two censuses to estimate the postcensal values for all the areas. The method can use raw and transformed data and has been used to estimate population values for 83 enumeration areas of Colchester District in 1981. 1 Introduction and review In this paper we present a technique called 'percentage change' method for estimation of small area statistics. It is a variation on previously published 'sample-regression' techniques in which we replace as the variables in the regression the ratio of values at successive time points, as for example used by Schmitt & Crosetti (1954), by the percentage change in these values. We evaluate this technique by applying it to data relating to 83 Census Enumeration areas in the Colchester area from the 1971 and 1981 Censuses. We also evaluate its performance when the data is first subject to various transformations. The methods of small area statistics are concerned with estimation for areas for which the usual techniques of sample surveys are inadequate. We may for example have a survey of the number of diseased elm trees in the British Isles found by sampling a number of kilometre squares spread across the British Isles. This will be perfectly adequate for estimating the overall number of such trees but if we were to try to use the same survey for estimating the number of such trees in a particular County our sample would probably prove too small. Alternatively, a national survey of voting intentions would probably provide too little information to give an accurate estimate of the voting intentions of a particular ethnic minority. Sample surveys can of course be designed so as to permit estimation for subpopulations, so called 'planned do- mains', but many subpopulations are unplanned particularly when it comes to secon- dary analysis of data. Thus a small area may be described in geographical terms, and may be as small as a Census enumeration district in the UK or as large as a County in the USA, or small areas may 'cross-cut' geographical areas and defined in terms of 'social class', ethnic origin, etc. Small area techniques are used when the subpopulation in which we are interested is anything from one tenth to one ten thousandth of the original population though obviously special techniques are more necessary the smaller the proportion. Small area methods are characterised by the use of sources of data other than sample surveys. Particular use is made of Census data and Administrative registers such as the Electoral Roll, Registers of Births, Marriages and Deaths, etc. The different methods are best classified by the type of data used and indeed the type of data available usually determines the method to be used.