How long you'd have to track to actually prove the full moon affects your sleep or mood
Every full moon someone at work swears the moon wrecked their sleep, so at some point I actually ran it against my own logs. About two years of sleep, mood, resting heart rate, the lot.
The correlation between the moon and my sleep quality came out around -0.05. My mood, about +0.08. Both basically noise, and roughly the same near-zero both years. So for me it's just not there. But the part that actually bugged me is that even if there were some small real effect, I couldn't have caught it. I ran the power math and to detect a realistic moon-sized correlation (r around 0.05) you'd need something like 3,000 nights. Call it 8 or 9 years of logging, per metric.
And the full moon only turns up about 12 times a year, so comparing full moon nights against the rest drags it into decades. Between that and the fact that the more metrics you throw at it the more likely one lines up by pure luck, I'm pretty sure the honest answer is "you can't tell, and neither can I". Love the idea, can't afford the sample size.