Comparison of two tests for seasonal variation

Statistical analyses of seasonal variation are important in the medical and social sciences because the results from such analyses can help elucidate the environment's impact on human activity, behavior, and health. Generally, we are concerned with a data set of just 12 frequencies over a one-year period, and both the sample size and the variation's amplitude are small, features that complicate the analysis; to assist in these situations, statisticians have created specialized tests for such data. One of those tests is an optimal-power likelihood-ratio test, whose application can fail because of computational complications. We are interested in the practical application of the said likelihood-ratio test, and so we present previously unknown information about the following: (1) When is the likelihood-ratio test likely to fail, and what are the chances for such failure to happen? (2) If the likelihood-ratio test does fail, what other test should the researcher use? Also, we provide new insights as to when and why the likelihood-ratio test would fail. Thus, in this study, we round out and complete important information about the performance of the optimal-power likelihood-ratio test for seasonality. Our results are useful to researchers who plan to do an analysis of seasonal variation.