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I have two lists (first one is data, second one is background) of files that are composed of X and Y coordinates. X coordinates are the same for both lists. I would like to subtract the y coordinates of corresponding files (A1-A2, B1-B2, etc) for whole data set. Is there a quick way to do it? data1 is composed of {a1.txt, a2.txt} and data2 of{b1.txt,b2.txt}

I can only imagine doing a small for loop in which I use following code:

data1[[1]][[All, 2]] - data2[[1]][[All, 2]]

and then I MapThread X and new Y coordinate. data1[[1]]

 X  Y1
0.008362    837448.1111
0.028126    23665.24245
0.048397    2174.605716
0.068667    528.9201242
0.088938    205.8876254
0.109208    98.85484604
0.129477    65.01622775
0.149746    43.40275276
0.170015    35.06444229
0.190282    25.51391261
0.200416    21.10450766

data2[[1]]

X   Y4
0.008362    0.008166246
0.028126    0.02746757
0.048397    0.047264026
0.068667    0.067059506
0.088938    0.086855961
0.109208    0.106651441
0.129477    0.126445943
0.149746    0.146240446
0.170015    0.166034949
0.190282    0.185827498
0.200416    0.195724261

https://www.dropbox.com/sh/gh4ud83lrgfa3jo/AADFIaofouq9X9OUJmeaQ0cna?dl=0

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Your initial thought sounds about right.

A relatively clean way to do this, including very simple error checking, would be something like

diff::badx = "The abscissa values in `1` don't match those in `2`.";
diff[list1_, list2_] :=
  Module[{out = list1},
    If[list1[[All, 1]] != list2[[All, 1]],
      Return[Message[diff::badx, list1, list2], Module]];
    out[[All, 2]] = out[[All, 2]] - list2[[All, 2]];
    out
  ]

In general, your use-case looks like something from spectroscopy. I deal with similar problems frequently, often with quite large datasets. Because of this I find it beneficial to always work with packed arrays, which is much easier if I keep the X and Y values separate.

In this case I would do something like

data = <||> (*initialize an association*)
{data["X"], data["Signal"]} = Transpose[Import["a1.txt"]];
data["Background"] = Last@Transpose[Import["b1.txt"]];
data["Corrected"] = data["Signal"] - data["Background"];

It's very important here to have code that makes sure, that the X values are always the same for all datasets or, otherwise, coerces the datasets to a common set of X values.

Plotting is then trivial like so:

ListPlot[Transpose[{data["X"],data["Corrected"]}]]
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