It’s also possible that P(W|”~W”) is way lower than .05, and so the test could be better than that calculation makes it look. This is something you can figure out from basic stats and your experimental design, and I strongly recommend actually running the numbers. Psychology for years has been plagued with studies that are too small to actually provide valuable information, as people in general aren’t good intuitive statisticians.
This is something you can figure out from basic stats and your experimental design, and I strongly recommend actually running the numbers.
As it happens, I learned how to do basic power calculations not that long ago. I didn’t do an explicit calculation for the melatonin trial because I didn’t randomize selection, instead doing an alternating days design and not always following that, so I thought why bother doing one in retrospect?
But if we were to wave that away, the power seems fine. I have something like 141 days of data, of which around 90-100 is usable, giving me maybe <50 pairs? If I fire up R and load in the two means and the standard deviation (which I had left over from calculating the effect size), and then play with the numbers, then to get an 85% chance I could find an effect at p=0.01:
> pwr.t.test(d=(456.4783 - 407.5312) / 131.4656,power=0.85,sig.level=0.01,type="paired",alternative="greater")
Paired t test power calculation
n = 84.3067
d = 0.3723187
sig.level = 0.01
power = 0.85
alternative = greater
NOTE: n is number of *pairs*
If I drop the p=0.01 for 0.05, it looks like I should have had a good shot at detecting the effect:
> pwr.t.test(d=(456.4783 - 407.5312) / 131.4656,power=0.85,sig.level=0.05,type="paired",alternative="greater")
Paired t test power calculation
n = 53.24355
So, it’s not great, but it’s at least not terribly wrong?
EDIT: Just realized that I equivocated over days vs pairs in my existing power analyses; 1 was wrong, but I apparently avoided the error in another, phew.
You’re welcome!
That’s how I did it.
It’s also possible that P(W|”~W”) is way lower than .05, and so the test could be better than that calculation makes it look. This is something you can figure out from basic stats and your experimental design, and I strongly recommend actually running the numbers. Psychology for years has been plagued with studies that are too small to actually provide valuable information, as people in general aren’t good intuitive statisticians.
As it happens, I learned how to do basic power calculations not that long ago. I didn’t do an explicit calculation for the melatonin trial because I didn’t randomize selection, instead doing an alternating days design and not always following that, so I thought why bother doing one in retrospect?
But if we were to wave that away, the power seems fine. I have something like 141 days of data, of which around 90-100 is usable, giving me maybe <50 pairs? If I fire up R and load in the two means and the standard deviation (which I had left over from calculating the effect size), and then play with the numbers, then to get an 85% chance I could find an effect at p=0.01:
If I drop the p=0.01 for 0.05, it looks like I should have had a good shot at detecting the effect:
So, it’s not great, but it’s at least not terribly wrong?
EDIT: Just realized that I equivocated over days vs pairs in my existing power analyses; 1 was wrong, but I apparently avoided the error in another, phew.