Journal of Educational Statistics

An approach for modifying the results of asymptotic theory to improve the performance of statistical procedures in small to moderate sample sizes is described in the context of hypothesis testing. The method is illustrated by a series of examples. Statistical inferences are based in a large part upon prior assumptions about the underlying probability model which generated the data. Although it is not supposed that the assumptions are exactly true, the validity of many statistical procedures relies on the assumptions being close to those satisfied by the data. Stringent assumptions allow the development of exact and often elegant procedures which may have limited usefulness in real prob-lems where these assumptions can be far off. In fact, many classical proce-dures have been found to be quite sensitive to even small deviations from the assumed model (Huber, 1981, chap. 1). On the other hand, with min-imal assumptions one must often rely on approximate procedures based on asymptotic theory whose performance for the small to moderate sampl