"An integrity test is a test which is administered for the purpose of learning more about someone's honesty and adherence to ethical principles. Such tests are used as pre-employment screenings to help companies identify applicants with high levels of integrity, and they may also be used as followups for people who are already employed to confirm that they are adhering to the company's code of conduct. The law surrounding integrity tests is variable, and they may not be legal in all areas.

Sometimes a company will hire a mystery shopping company to perform an integrity shop. It may entail going to a specific bar or store at a specific time and targeting an employee. "
http://www.wisegeek.com/what-is-an-integrity-test.htm