Improving on Probability Weighting for Household Size

In survey sampling, inverse-probability weights are used to correct for unequal selection probabilities, and poststratification weights are used to correct for known or expected discrepancies between the sample and the population (see, e.g., Kish 1992). In this research note, we consider the effects of these adjustments for household size in telephone polling. In a survey in which households are sampled at random, and then a single individual is sampled from each sampled household, individuals in larger households have a smaller probability of being selected. The probability of an individual being included in the survey is inversely proportional to the size of the household in a simple random sample of households if individuals within a household are selected with equal probability and there is no nonresponse. However, composition of the sample is also affected by nonresponse. One source of nonresponse is nonavailability— no one answers the phone, or no one receives the message on the answering machine. It seems reasonable to suppose that in a larger household it is more likely that someone will be home to receive the phone call. Another source of nonresponse is refusal to participate in the survey.