9 - Adjustment of Data

Abstract

Survey data can be used to estimate the joint distribution of several polytomous variables in a population. If the survey data are supplemented by some information from population censuses concerning the distribution of these variables, then the joint distribution can be estimated with increased precision. The method of adjustment developed by Deming and Stephan applies if a table providing the joint distribution of two or more polytomous variables has been obtained from a population sample and if some tables of marginal distributions of these variables have been obtained from a population census. The joint population distribution of the variables is obtained through an iterative proportional fitting algorithm. The Deming–Stephan algorithm produces consistent estimates of joint population probabilities if the sample is a simple random sample. In this case, relatively simple formulas are also available for estimation of asymptotic standard deviations of the probability estimates. The Census does provide a cross-classification of educations of husbands and wives. The adjustment methods described in the chapter have been used extensively to describe relationships between discrete variables. The Newton–Raphson algorithm or the Deming–Stephan algorithm can be used to test the hypothesis of the adjustment of data.