EDIT: Let’s cool it with the downvotes, dudes. We’re not out to cut funding to your black hole detection chamber or revoke the degrees of chiropractors just because a couple of us don’t believe in it, okay? Chill out, participate with the prompt and continue with having a nice day. I’m sure almost everybody has something to add.
The only difference between a full moon and a new moon is how much light it reflects towards the earth. The moon is still there. If there were some sort of magnetic or gravitational effect on you while you slept, the effect would be the same whether the sun was shining on the side you can see or not.
The reason there is a difference in how much light is reflected, is because the moon is in a different position. During a new moon, it’s on the day side of the earth (so in between the sun and the earth) while during a full moon, it’s on the night side.
So there could theoretically be a gravitational effect, although I don’t think it would impact anyone’s sleep.
If anyone is noticing a difference in sleep quality, it’s most likely indeed to do with the amount of light.