I now have roughly 2 months of sleep data. The first month (the control phase) I didn't take any sleep supplements, but in the second month (the experiment phase) I took exactly 3mg of melatonin approximately 30 minutes before going to bed each 'night'. During the control phase, I got an average of 406 minutes of sleep per night, with a standard deviation of 136 minutes.
In the experiment phase, I averaged 444 minutes of sleep per night, with a standard deviation of 98 minutes.
Therefore, on melatonin, I average an extra 38 minutes of sleep per night and experienced significantly less variation in the total length of sleep.
For the control phase of the trial, I averaged 115 minutes in REM sleep, with a standard deviation of 43 minutes.
During the experiment phase, I averaged about 125 minutes of REM sleep, also with a standard deviation of 41 minutes.
Therefore, while on melatonin, I was getting about 10 extra minutes of REM sleep per night with about same amount of variance.
For the control portion of the trial, I got about 37 minutes of deep sleep on average, with a standard deviation of approximately 23 minutes.
In the experiment phase, I got an average of 34 minutes of deep sleep, with a standard deviation of 12 minutes.
While taking melatonin, I average 3 minutes less deep sleep, but with quite a bit less variance as well.
During the control phase, I woke up about 3 times per night, with a standard deviation of 2 times.
In the experiment portion, I also awoke about 3 times a night with a standard deviation of 2 times.
Being on melatonin didn't seem to make any difference in the number of times I woke up during the night.
According to the preliminary data, while on melatonin, I seemed to get more total sleep, more REM sleep, less deep sleep, and wake up about the same number of times each night. Because this isn't enough data to be very confident in the results, I plan on continuing this experiment for at least another 4 months (2 on and 2 off of melatonin) and will analyze the results for the significance and magnitude of the effects (if there really are any) while throwing out the outliers (since my sleep schedule is so erratic).