Quantiative comparison of two distributions

[ebutler]

I'm an experimental physicist and I have an experiment where I measure the deflection of atoms in a magnetic field. The atoms travel through the field and I have a position sensitive detector, so I get a list of positions, which I usually look at by binning them. The distributions don't follow any nice functional form, or anything like that.

To first order, what I'm looking for is any effect of the magnetic field on the final distribution. So, I have two data sets - one with the deflecting magnet on, the other with it off. I'm looking for a good way of expressing the level to which there is (or isn't) a difference in the two distributions.

I don't have a lot of experience with statistics like this, but I had a first try - For each bin, I calculated the the difference in the number of counts, divided by the expected deviation. I assume that the uncertainty is Poissonian in nature, so this is (N1-N2)/(sqrt( N1 + N2)). Then I looked at the distribution of these values and see if it's compatible with a normal distribution (I figured that if only random fluctuations are present, this might be okay).

Is there a better way to do this? It feels like there must be something worked out from related disciplines (comparing spectra or something), but a trawl of the internet hasn't turned up anything.

Thanks in advance!

[Profjgmiller]

See if the test on the attached file helps.

If this is not what you're looking for, let me know.

Also, let me know if you need clarification on what I did.