randomized response

Randomised response is a research method used in structured survey interview. It was first proposed by S. L. Warner in 1965 and later modified by B. G. Greenberg and coauthors in 1969. It allows respondents to respond to sensitive issues (such as criminal behavior or sexuality) while maintaining confidentiality. Chance decides, unknown to the interviewer, whether the question is to be answered truthfully, or "yes", regardless of the truth. For example, social scientists have used it to ask people whether they use drugs, whether they have illegally installed telephones, or whether they have evaded paying taxes. Before abortions were legal, social scientists used the method to ask women whether they had had abortions. The concept is somewhat similar to plausible deniability. Plausible deniability allows the subject to credibly say that they did not make a statement, while the randomized response technique allows the subject to credibly say that they had not been truthful when making a statement.

Randomised response is a research method used in structured survey interview. It was first proposed by S. L. Warner in 1965 and later modified by B. G. Greenberg and coauthors in 1969. It allows respondents to respond to sensitive issues (such as criminal behavior or sexuality) while maintaining confidentiality. Chance decides, unknown to the interviewer, whether the question is to be answered truthfully, or "yes", regardless of the truth. For example, social scientists have used it to ask people whether they use drugs, whether they have illegally installed telephones, or whether they have evaded paying taxes. Before abortions were legal, social scientists used the method to ask women whether they had had abortions. The concept is somewhat similar to plausible deniability. Plausible deniability allows the subject to credibly say that they did not make a statement, while the randomized response technique allows the subject to credibly say that they had not been truthful when making a statement. ==Example== ==Original version== Warner's original version (1965) is slightly different: The sensitive question is worded in two dichotomous alternatives, and chance decides, unknown to the interviewer, which one is to be answered honestly. The interviewer gets a "yes" or "no" without knowing to which of the two questions. For mathematical reasons chance cannot be "fair" ( and ). Let p be the probability to answer the sensitive question and EP the true proportion of those interviewed bearing the embarrassing property, then the proportion of "yes"-answers YA is composed as follows: YA = p\times EP + (1 - p)(1 - EP) Transformed to yield EP: EP = \frac{YA + p - 1}{2p - 1} The interviewed are asked to secretly throw a die and answer the first question only if they throw a 6, otherwise the second question ( p=\tfrac{1}{6} ). The "yes"-answers are now composed of consumers who have thrown a 6 and non-consumers who have thrown a different number. Let the result be 75 "yes"-answers out of 100 interviewed ( YA=\tfrac{3}{4} ). Inserted into the formula you get EP = (\tfrac{3}{4} + \tfrac{1}{6} - 1) / (2\times \tfrac{1}{6} - 1) = \tfrac{1}{8} If all interviewed have answered honestly then their true proportion of consumers is 1/8 (= 12.5%). ==See also== Bogus pipeline Differential privacy Loaded question Unmatched count ==References== ==Further reading==

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