SAE Manual Sections 1 to 4_1 (May 06).pdf - National Statistical ...

A Guide to Small Area Estimation - Version 1.1 05/05/2006
1.1 What are Small Area Estimates?
1. Introduction
Most ABS surveys are designed to provide statistically reliable, design based estimates
only at the national and/or state/territory geographic levels. The sheer practical
difficulties and cost of implementing and conducting sample surveys that would provide
reliable estimates at levels finer than state/territory are generally prohibitive, both in
terms of the increased sample size required and the added burden on providers of
survey data (respondents). For purposes of this manual, small area estimation refers
to methods of producing sufficiently reliable estimates for geographic areas that are too
fine to obtain with precision, using direct survey estimation methods. By direct
estimation we mean classical design based survey estimation methods (Saei and
Chambers, 2003) that utilise only the sample units contained in each small area. Small
area estimation methods are used to overcome the problem of small samples sizes to
produce small area estimates that improve upon the quality of direct survey estimates
obtained from the sample in each small area. The more sophisticated of these methods
work by taking advantage of various relationships in the data, and involve, either
implicitly or explicitly, a statistical model 1 to describe these relationships. (See Sections
4.1 & 4.2 for further discussion).
Although conceptually similar, small domain estimates refers to those disaggregated
to fine classificatory levels, such as by socioeconomic status, income, labour force status
or industry. It is important to note that we have not undertaken any empirical study for
small domain estimation methods for this manual, although intuitively we would expect
that most techniques covered in this manual would still apply. The empirical analysis of
this manual is based on knowledge and experience derived from only one empirical
study, this being a study of the incidence of disability in Australia. This study uses data
from the Survey of Disability, Ageing and Carers (SDAC) (see ABS (2003) for more
details).
1 A statistical model is a mathematical representation of the relationship we assume to exist
between the variable we are interested in predicting (known as the response or dependent
variable) and other associated variables (known as the auxiliary, explanatory or independent
variable). A model is then fitted to data that contains observed values for both the
dependent variable and the auxiliary variables for each unit. The fitting process produces
estimates of the model parameters such as intercepts and slopes. The unit here may be a
person, a business or a small area itself, depending upon the level at which we wish to fit the
model. The model also includes one or more error terms to describe the degree of
stochastic or random variation with which predicted values for the response variable deviate
from the observed values.
Australian Bureau of Statistics 5