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gwern comments on Value of Information: 8 examples - Less Wrong Discussion

48 Post author: gwern 18 May 2012 11:45PM

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Comment author: gwern 26 May 2012 07:57:14PM 1 point [-]

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.

Comment author: gwern 27 May 2012 02:48:26PM 0 points [-]

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:

pwr.t.test(d=(456.4783 - (456.4783 - 17.32))/131.4656,power=0.5,sig.level=0.05,type="paired",alternative="greater")
n = 75.44403
d = 0.1911111

Doable, but not trivial.

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