When survival data can be divided into natural groups, such as in a clinical trial with patients from a number of different institutions, the question arises whether effects are different for the different groups. For situations where one is concerned with a random pattern of variation over groups, this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups. These tests are closely related to the locally most powerful tests of Liang for testing for variation across a large number of strata. The tests are applied to data from a lung cancer trial conducted by the Eastern Cooperative Oncology Group.