TABLE OF CONTENTS Randomized response designs are surveys which use a probabilistic device (such as a random number target) to get information about some group of people regarding a sensitive question. Randomized response models are used in situations where the respondent might be uneasy about participating in the survey or might tend to give a false response because of the sensitive nature of the question.
Example 3.3. Suppose that we have a class of 100 college students and we want to estimate the proportion of students attending this college who have cheated on a high school exam. To accomplish this goal, the instructor asks each student in the class to select a number from the random number target in such a way that no one else can see his or her number. The instructor does this to protect confidentiality. The students are then told Raise your hand if either you have cheated on a high school exam or if you selected an odd number from the random number target. A raised hand implies that either the student cheated on a high school exam or got an odd number from the target or both (the two events are not mutually exclusive). So a raised hand does not ensure that the student has cheated. Thus the student is giving the instructor information on a probabilistic basis yet confidentiality is maintained. Suppose that 77 of the 100 students raise their hands. We expect approximately 50 of these got an...
