Hypocrisy results when one part of a value system is demonstrably at odds with another and the person or group of people holding those values fails to account for the discrepancy. Hypocrisy is considered to be the opposite of integrity.
A value is an assumption upon which implementation or other values can be extrapolated. A value system is a set of consistent values and measures. A system with perfect integrity yields a singular extrapolation, which can be tested via the Scientific Method.
Integrity of a value system is tested scientifically by using the values, methods and measures of the system to create a hypothesis of an expected cause and effect relationship. When the cause creates the expected effect consistently amongst multiple unbiased testers, the value system is said to have integrity.
For example, Newtonian Physics, General Relativity and Quantum Mechanics are three value systems at odds with each other that all produce accurate scientific results within their respective domains. As such, the Scientific Method is not useful for identifying absolute truth, but for testing the integrity of a value system and thereby its usefulness for extrapolation within its specified domain.
The pretension of such tests to detect fake answers plays a crucial role in this respect, because the naive really believe such outright lies and behave accordingly, reporting their past deviance because they fear that otherwise their answers will reveal it. The more Pollyannaish the answers, the higher the integrity score.
The philosophy of mathematics bases integrity on consistency of mathematical proof, which one can test weakly or strongly, as part of the process of differentiating it from folk mathematics. Mathematical integrity becomes strengthened through definition as the result of a tautology and where it demonstrably forms a part of a larger and consistent body of mathematics.
There is personal integrity, professional integrity, artistic integrity, and intellectual integrity.