True and false agreement relations between 2 qualitative tests

The respective effectiveness of two qualitative tests is usually compared by their results when applied to a same specimen or subject. The results reported in a fourfold table show coincident numbers of double positive and double negative results. That straight concordance is fallacious, including the chance coincidences. Test Kappa measures the true agreement, without the chance coincidences. Kappa value may be compared to a maximum value of agreement depending on the marginal results of the fourfold table. As a matter of fact, the test Kappa is a non parametric correlation function comparable to the non parametric correlation coefficient Phi computed from the value of the chi square test.