# How can I compute the difference in Y-axis values between data sets with similar X-values

I am new to Mathematica, so this might be a very basic question; however, I cannot find a solution to this and it is taking me very long.

For my research I am probing the photoluminescence response of a organic film with and without an external magnetic field, and also take a background measurement with and without the field. This generates large data files, with equal x values (wavelengths) and different y values (intensity) with dimensions {3648, 2}. I would like to ListPlot the difference between the data, but when I do something like this:

Signal = WithMagnet - WithoutMagnet


I end up with a vertical line at x=0.

Can anyone here help me how to plot the difference in y-values while keeping the x-axis the same as in the individual files?

Hope someone can help me with this! Cheers

• Post a link to the data (or a portion of the data here in readable/copy-paste format) and the code you have been using to plot. – Edmund Jul 23 '16 at 12:32

Use Part to subtract intensity and Transpose to align with the wavelength data:

wavelength = Range[350, 750, (400/3647)];

withMagnet = Transpose[{wavelength, RandomReal[1, 3648]}];
withoutMagnet = Transpose[{wavelength, RandomReal[1, 3648]}];

(*The above code just simulates your imported data*)

diff = Transpose[{withoutMagnet[[All, 1]],
withMagnet[[All, 2]] - withoutMagnet[[All, 2]]}];

ListLinePlot[diff, PlotRange -> All, Mesh -> All] • Thanks for the answer. You transpose twice, I do not have to do that right? I now do the following: 'Analyse = Transpose[{without1[[All, 1]], with1[[All, 2]] - without1[[All, 2]]}]; ListPlot[Aanalyse, PlotRange -> All, PlotLabel -> Emission, AxesLabel -> {wavelength, arbitrary units}, LabelStyle -> Directive[Bold, Orange]]' That should give me the correct graph right? As the photoluminescence should be stronger for this film and it has not been showing me good results, I do not really know what to expect from the data, but it looks correct. – Maarten Mennes Jul 25 '16 at 8:33
• Great, thanks! Sorry didn't know how to do that, but did it just now! – Maarten Mennes Jul 26 '16 at 14:13