In the collection of data on environmental health, individuals are frequently reluctant to be entirely candid with surveyors because of concern over the confidentiality of responses. A standard procedure is to inoculate the response with random modification (or error) so that it becomes impossible to identify individual respondents but quite possible to generate unbiased statistical summaries of the entire sample. This paper is directed at generating methods for such random inoculation and abstracting from the inoculated results those conclusions concerning sample response and population estimates. A numerical example of a bivariate randomized procedure is given.