Seasonality of rates: testing for seasonal variation when the population at risk is variable

Researchers are interested in seasonality analyses because the results from such analyses can help elucidate the environment's impact on the human condition. We are concerned with seasonal data that generally have small sample size and small amplitude. We present a new frequentist test for seasonal variation of random events coming from a known, possibly variable population at risk. Only one other such procedure appears to be previously available. Easy to apply, and developed within a physico-geometric setting, our test is versatile because it can be used to analyze different kinds of seasonal variation. Also, such setting makes our test both easy to understand and explain to others. A simulation study shows that our test performs better than the other such test. Two examples of real data illustrate our test's application to analyze two different kinds of seasonal patterns. In a third example, we elucidate the effect of the observed-data's variation upon the rates's pattern, thus emphasizing the value of graphics in seasonality analyses.