Randomized Response Techniques

1

• Randomized Response Techniques
• Basic ideas
•   To reduce refusals and distorted responses to
  a sensitive question in a survey, a statistical
  method has been developed.

2

• This method is designed to estimate the
  proportion of sensitive attribute, while
  protecting the privacy of individual
  respondents. In other words, we can assess group
  attributes without disclosing individual
  behavior. It is a truly a public health
  oriented research technique.

3

• In this method, the sensitive question is
  paired with an insensitive question, and the
  respondents are asked to choose one of the
  questions using a random mechanism. The
  interviewer will record yes or no without
  knowing which question is answered.

4

• Model
•   Using the questions and notations in Section
  14.8 (page 448), p (the proportion of yes
  responses obtained in the survey) would be the
  sum of two probabilities (1) probability of
  yes responses on the sensitive (Se) question
  and (2) probability of yes responses on the
  insensitive (In) question.

5

• The two probabilities of intersection in the
  right hand side of equation can be expressed in
  terms of conditional probabilities
• Let and
  . Note that is unknown quantity
  to be estimated and that is known quantity
  based on the insensitive question.

6

• Based on the probability in the random
  mechanism, let , and
  .
• Then the above equation becomes
• Solving for

, we get
7

• Sampling variance of the estimate is given by
• Note that sampling variance would be smaller
  if we choose a random mechanism that would make
  more respondents answer the sensitive question.
  If it gets closer to one, the respondents
  suspicion would increase, defeating the purpose
  the randomized response technique.

8

• Illustrative example
•   Using the data giving in the text, the
  estimate proportion of respondents who have ever
  used cocaine for recreational purposes is 36.7.
• Assuming the sample size of this survey is
  100, standard error of the estimate is

, or 6.5
9

• References
•   For further information about the two-question
  model shown above, see Reference 27 cited in the
  text.
•  
• The original idea of this technique was due to
  Warner (see Reference 26), an economist, without
  using the unrelated, insensitive question.