Daily rainfalls of an inch or more for 100 years at one station have been classified according to the phase of the moon with which they occurred. An apparent significant correlation between two 50-year smoothed sub-series is found to have been induced by the filtering process of taking running sums. When the effects of the ensuing serial dependence are eliminated, the results are not indicative of a significant overall relationship between the series of rainfalls and moon phase. In both sub-series, a persistent trough in frequency count of heavy rainfalls about full moon has been investigated further by examining data from three additional stations in different rainfall regimes. The trough was evident in the data from each of the frequency counts of rainfalls near full moon. However, when each series was viewed in isolation, statistical tests revealed that the observed numbers of rainfall occurrences were not significantly different from the expectations based on the assumption that the series were random. The consistency of the trough rather than its amplitude suggested a weak non-random influence might be present. An additional product of the statistical analysis of the single station data is an indication of the differing filtering effects of the smoothing process as the number of elements in the running sums is increased progressively from one to ten.