gwern comments on Value of Information: 8 examples - Less Wrong
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Sleep quality is typically measured by "number of times awakened" or "amount moved" or so on- my experience with melatonin (and I believe gwern's as well, but I didn't check) is that melatonin decreases the number of times I awaken during the night.
But even if you measure that, it's just a proxy. A paralytic drug will reduce the amount I toss and turn at night, but may not improve how I feel the next day. What you would want to do is measure energy level / creativity, but that's even more difficult.
For my melatonin experiment, number of awakenings was 2.86 vs 2.43, but the p-value was only 0.43. The problem is that the standard deviation is 2.25! (On many nights, I awaken zero or one times, but on one particularly bad night, I woke up 7 times.) I suspect more data would show a more reliable effect and maybe a greater effect size than d=0.19.
To expand; if d<=0.19, to detect this effect at p<0.05 with 75% odds, we need ~75 pairs of nights or ~150 nights of data:
Doable, but not trivial.