"Ivan Kelly, James Rotton and Roger Culver (1996) examined over 100 studies on lunar effects and concluded that the studies have failed to show a reliable and significant correlation..."
The only thing the skeptic did was
write a web page on the data, not compiled it in the study. The entire page is written objectively as well; if there was overwhelming evidence that supports full moon phenomenon, then the page would be completely different. One study that shows a slight correlation means nothing compared to 99 others that show none at all.
Why would you think a review of 100+ studies that show no correlation is most likely wrong? Is it because that's not ALL of the studies ever done on the topic were included? I would make a bet that the 100+ studies the researchers used were chosen in a random sampling way, so no matter how many times they've done this same study, they'd get the same exact results: No correlation.
I'd be more skeptical of people's subjective opinions and first hand experiences dealing with paranormal things such as this. I tend to err on the side of science and the evidence out there, rather than several people's first hand experiences.