The tides and the phases of the moon are inseparable.
I think that the presence of the word lunacy is evidence enough of an effect. Should we call them astronuts? The Eskimo (Inuit etc)have how many words for snow? 20 or is it 40? because it is central to their existence.
I read an article in News Scientist over 20 years ago that was part of a series on old wives tales. The correlation between full moon and road accidents, murders and riotous behavour shows a correlation. It is above the point where statisticians normally allow for the probablity of randon chance.
More contentious is if you take out the factors like (say) mecahnical failure and natural disasters the effect is beyond that point.
The arguement is even more persuasive if you consider homicides that are not premeditated - harder to quantify but things like the result of domestic violence.
The problem is that it is not a given on any full moon and not a big enough effect to silence doubters. AND it is a statisitcal anomally that does not rule individuals.
Ask workers at psychiatric establishments when they are more vigilant - or police about manning strategies.