Almost all results in software testing, and almost all software testing tools, assume that each test in a test suite will produce the same result regardless of the order in which the tests are executed. We have shown that this "test independence" assumption does not hold by identifying test suites in publicly available source where executing the tests in "isolation" (i.e., in a clean virtual machine) produces a different results from executing them one after another. We are formalizing the notion of test dependence, identifying additional examples of test dependence (including in manually- and automatically-produced test suites), and defining efficient algorithms to approximate the (NP-complete) problem of identifying whether there are dependencies in a test suite.