There's the argument that people tend to be more crazy and/or active during a full Moon compared to nights when the Moon isn't full. First of all, the Moon can be out during the day, although it is true a full Moon doesn't rise until the evening hours. Does a full Moon have anything to do with people's behavior on Earth? The answer is a clear no. There have been several studies (a few cited below) that a full Moon has no influence whatsoever on the behavior of people.
Lunacy and the Full Moon
Moonstruck! Does The Full Moon Influence Behavior? - This website links to many, many studies. Some do show a positive correlation, but most do not and some show a negative correlation.
Does a full moon make people mad?
It appears clear from the multiple studies that the Moon plays no role at all in the behavior of people. So why then do so many people think a full Moon causes people to act out? It's a memory bias. There's a preconceived notion that people act out during a full Moon, so when it does happen, people remember that act. However, when the Moon is not full and people act out, no one links it to the Moon because they aren't thinking about it. When the actual data is looked at over several months and many people, there's no correlation between acting out and a full Moon.