Source
r/AskStatistics•
hover2pie

Combining standard error of the mean for a ratio?

Hi everyone - thought I would give this a shot. I'm writing a paper (neuroscience) and trying to figure out how to combine the SEM for a ratio. I've spent some time on the internet searching, but haven't found exactly what I need.

I have two measurements, say x and y, and I need the ratio x/y with the corresponding standard error of the mean. I found http://www.talkstats.com/showthread.php/16499-Standard-deviation-of-the-Ratio-of-two-means, so I have a formula for the variance, but I don't know how to incorporate the number of measurements (there are 9 measurements for x and 10 for y) to get from standard deviation to standard error.

If anyone has thoughts, that would be awesome.

Posted Jul 1, 2014, 1:28 AM UTC

12
TheRealBeakerboy•

In engineering school we were taught, if z=x/y and Sx = error of x

(Sz/z)^2 =(Sx/x)^2 + (Sy/y)^2

1
StatNoodle•

If y is unlikely to get near zero, it would probably suffice to just compute the z's for the sample and take the average and standard error for that. A better approach would be to just bootstrap it.

If y is likely to get near zero, you probably should reconsider whether taking a ratio makes sense for your problem in the first place. Of course, bootstrapping would still work.

It isn't just the y=0 case...the covariance between x and y enter into it, as well.

1