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41 – Advances in Sampling Techniques and Tools

Dealing with Inaccurate Measures of Size in Two-Stage Probability Proportional to Size Sample Designs: Applications in African Household Surveys

at U.S. Centers for Disease Control and Prevention

Two-stage sample designs are used for household surveys in many countries. At the first stage, primary sampling units (PSUs) are sampled with probabilities proportional to their estimated sizes (PPES). A list of households is compiled in the selected PSUs, and households are selected with equal probability from each PSU. With this design, an overall equal probability sample design would yield a constant number of households from each sampled PSU if the measure of size used in the PPES selection were directly proportional to the number of households listed. However, there are often sizable differences between the measures of size used in the PPES selection and the listed sizes. Two common methods for dealing with these differences are: (1) to retain the equal probability sample design, allowing the sample size to vary across the sampled PSUs; and (2) to retain the fixed sample size in each PSU and to compensate for the unequal selection probabilities by weighting. This paper discusses the theoretical and practical advantages and disadvantages of these two methods. The discussion is illustrated with data from the Population-based HIV Impact Assessment (PHIA) surveys that have been conducted in several African countries. In all of these countries the PSUs were the enumeration areas (EAs) used in the most recent population census, and they were sampled with probabilities proportional to the EAs' population sizes at the time of the census.