Rates of phenotypic evolution have changed throughout the history of life, producing variation in levels of morphological, functional, and ecological diversity among groups. Testing for the presence of these rate shifts is a key component of evaluating hypotheses about what causes them. In this paper, general predictions regarding changes in phenotypic diversity as a function of evolutionary history and rates are developed, and tests are derived to evaluate rate changes. Simulations show that these tests are more powerful than existing tests using standardized contrasts. The new approaches are distributed in an application called Brownie and in r8s.