ESTIMATING PUBLIC OPINION WITH THE RANDOMIZED RESPONSE MODEL

The problem of obtaining truthful responses in sample surveys to questions that are of a sensitive or embarrassing nature has been of concern to researchers. For example, Wiseman recently found that socially undesirable responses were more likely to appear in a mail questionnaire than in a personal interview survey.' Since, in many situations, personal interviews are desirable because of the nature of the survey, the problem of reducing response bias becomes one of developing an interviewing technique for which the reasons respondents are not being completely candid are substantially reduced. Warner proposed such a method in 1965 and his technique, the randomized response model, has received a considerable amount of attention in the literature.2 The model is designed to reduce the likelihood of respondents giving an untruthful answer to a question of a sensitive nature. This is done by allowing the respondent to select a question, by chance, from two questions without revealing to the interviewer the particular question that has been selected. For example, suppose we are interested in estimating the proportion of women in a population that have had an illegitimate child. Utilizing the model, the respondent selects one of the following two statements with known probabilities, P and (1P), respectively: Statement 1: I have had an illegitimate child. Statement 2: I have not had an illegitimate child. The answer is either "yes" or "no" regardless of the statement that is selected. The reply has no meaning for the interviewer, who does not know which statement has been selected. After the interviewing procedure is