A group's average test score is often used to evaluate different educational approaches, curricula, teachers, and schools. Studies of group test scores over time often try to measure "value-added" by holding constant certain student characteristics such as race, parents' education, or socioeconomic status; however, the important statistical phenomenon of regression to the mean is often ignored. There is a substantial literature on the importance of regression to the mean in a variety of contexts, including individual test scores. Here, we look at regression to the mean in group averages. If this regression is not taken into account, changes in a group's average test score over time may be misinterpreted as changes in the group's average ability rather than natural and expected fluctuations in scores about ability. California Academic Performance Index scores are used to illustrate this argument.