Information contained in a randomized response The owner of the database could follow the procedure above to introduce randomness in the data before giving the data over to someone else. Someone holds a database with identifiers and answers to a yes/no question.

If everyone were honest, thereвЂ™d be no reason for this exercise in the first place. The calculations above assume that everyone complied with the protocol, which may not be reasonable. So the expected proportion of yes answers is Y = 0.5 p + 0.25, and we can estimate p as 2 Y вЂ“ 0.5. How can the professor estimate p, the proportion of students who cheated? Around half the students will get a head on the first coin and answer truthfully the rest will look at the second coin and answer yes or no with equal probability. Every student has deniability because each вЂњyesвЂќ answer may have come from an innocent student who flipped tails on the first coin and heads on the second. Otherwise the student reports вЂњyesвЂќ if the second coin came up heads and вЂњnoвЂќ it came up tails. If the first coin comes up heads, the student answers the question truthfully, yes or no. Randomized responseД®ach student is asked to flip two coins.

Being a statistician, the professor has a clever way to find out what he wants to know while giving each student deniability. For example, maybe a statistics professor would like to know how many students cheated on a test. Suppose you want to gather data on an incriminating question.

Yes or no coin flip