Unmatched count

In psychology and social research, unmatched count, or item count, is a technique to improve through anonymity the number of true answers to possibly embarrassing or self-incriminating questions. It is very simple to use but yields only the number of people bearing the property of interest. It was introduced by Raghavarao and Federer in 1979

Method
The participants of the survey are divided into two groups at random. One group (the control group) is asked to answer a few harmless questions, while the other group gets one additional question (hence the name "unmatched count"), the one about the property of interest. The respondents are to reveal only the number of "yes"-answers they have given. Since the interviewer does not know how they arrived at that number, it is safe to answer the awkward question truthfully. Due to the unmatched count of items, the number of people who answered "yes" to the awkward question can be mathematically deduced.

Example
The control group is asked how many of the following statements apply: Let the number of "yes"-answers from this group be 31.
 * I have moved house in the past.
 * I own a pet.
 * I like to go to the theatre.
 * I have never been in a traffic accident.

The second group additionally gets a question concerning the point of interest: Let the number of "yes"-answers from this group be 34.
 * I have cheated on an examination.

Evaluation
The number of "yes"-answers in the control group is called the baseline. It is assumed that the second group would have given the same number, were it not for the critical question. Thus, their additional "yes"-answers (3 in the example) are due to the critical question. Their percentage is used to estimate the percentage of cheaters in the population. Let the number of participants in each group be 50. 3 of them answered "yes" to the critical question, meaning that approximately 6% of the population have cheated on examinations.