Testing for empty sets when misclassifications may be present

A test for empty sets is described. This new test is suitable for testing for mutual exclusivity, sets being nested, and many other configurations. It might be hypothesized that two medical conditions do not both occur in individuals. This can be expressed as an empty intersection of the two sets of people with each condition. An important feature of the test is the incorporation of misclassification rates into the analysis. The test utilizes the potential misclassifications for false designations in the sets that are hypothesized to be empty. The test is quite powerful. When the null hypothesis is rejected, follow-up tests on one or more sets that are included in the null hypothesis can be performed using the same new test. MatLab code is supplied.