Randomized response
Encyclopedia
Randomized 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 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 abortion
s.
Half the people—or half the questionnaire population—who have not had sex with a prostitute get tails and the other half get heads when they flip the coin. Therefore, half of those who have not had sex with a prostitute will answer "yes" even though they have not done it. So whatever proportion of the group said "no", the true number who did not have sex with a prostitute is double that. For example, if 20% of the population surveyed said "no", then the true fraction that did not have sex with a prostitute is 40%.
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" (½ and ½). 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:
Transformed to yield EP:
The interviewed are asked to secretly throw a die and answer the first question only if they throw a 6, otherwise the second question (
). 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 (
).
Inserted into the formula you get
If all interviewed have answered honestly then their true proportion of consumers is 1/8 (= 12.5 %).
Survey research
Survey research a research method involving the use of questionnaires and/or statistical surveys to gather data about people and their thoughts and behaviours. This method was pioneered in the 1930s and 1940s by sociologist Paul Lazarsfeld. The initial use of the method was to examine the effects...
. It was first proposed by S. L. Warner in 1965 and later modified by B. G. Greenberg 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 abortion
Abortion
Abortion is defined as the termination of pregnancy by the removal or expulsion from the uterus of a fetus or embryo prior to viability. An abortion can occur spontaneously, in which case it is usually called a miscarriage, or it can be purposely induced...
s.
Example
Ask a man whether he had sex with a prostitute this month. Before he answers ask him to flip a coin. Instruct him to answer "yes" if the coin comes up tails, and truthfully, if it comes up heads. Only he knows whether his answer reflects the toss of the coin or his true experience.Half the people—or half the questionnaire population—who have not had sex with a prostitute get tails and the other half get heads when they flip the coin. Therefore, half of those who have not had sex with a prostitute will answer "yes" even though they have not done it. So whatever proportion of the group said "no", the true number who did not have sex with a prostitute is double that. For example, if 20% of the population surveyed said "no", then the true fraction that did not have sex with a prostitute is 40%.
Original version
Warner's original version (1965) is slightly different: The sensitive question is worded in two dichotomousDichotomy
A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts...
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" (½ and ½). 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:
Transformed to yield EP:
Example
- Alternative 1: "I have consumed marijuana."
- Alternative 2: "I have never consumed marijuana."
The interviewed are asked to secretly throw a die and answer the first question only if they throw a 6, otherwise the second question (
). 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 ().Inserted into the formula you get
If all interviewed have answered honestly then their true proportion of consumers is 1/8 (= 12.5 %).