A method is given for estimating, in a subjective sense, the effect of nonresponse in sample surveys. Based on Bayesian techniques, this method produces a subjective probability interval for the statistic that would have been calculated if all nonrespondents had responded. Background information which is recorded for both respondents and nonrespondents plays an important role in sharpening the subjective interval. Real survey data of 660 schools with 188 nonrespondents indicates that the method can be useful in practical problems. The general idea can be applied to any problem with nonrespondents or missing data.