Calculate percentage difference for two sets of points As the title says, I'd like to calculate the percentage difference for two sets of points. For example, suppose I have $S_{1}=\{(1,x_{1}),(2,x_{2}),(3,x_{3})\}$ and $S_{2}=\{(1,y_{1}),(2,y_{2}),(3,y_{3})\}$. How can I know the difference in percentage between both sets of data. What is the correct way to do that? Is that kind of assessment meaningful to establish to which degree of precision a set of data is preferred over the other?
In my particular case, $S_{1}$ is simply a set of numerical results obtained by DSMC and $S_{2}$ was obtained by a theoretical result. I'd like to quantify how much difference exist between each other in order to establish when it is convenient to use one or the other.
By "difference in percentage" I mean percent difference. Hopefully that clarifies a bit the question.
UPDATE:
Another way to formulate my question would be: How can I arrive to conclusions such as "The results from experiment A are inaccurate by 10% with respect to experiment B", when experiment A and B are a set of values.
 A: It seems to me like you need to formulate a question you want your data to answer. Let me suggest a few (perhaps you can edit your post to reflect what questions make sense for your data):


*

*As the DSMC value increases, does the theoretical result also increase?

*If I know the value of the theoretical result, how accurately can I estimate the value of DSMC?


If the points (1,x1) and (1,y1) refer to the same measurement or the same run of the experiment, or one is an estimate of the other. One natural way to see how related they are related is to plot {(x1,y1),(x2,y2) ...}.
You can read about Pearson correlation and Kendall tau and Spearman rho here:
http://en.wikipedia.org/wiki/Correlation_and_dependence
A: First, let's compare two lists of numbers — are they from the same distribution ?
For example, how close are the lists of 20 numbers, "|" marks,
||||||.||.||...||.....||.|................|.....................................
|||.|...|..|...|.......||...|...|...|.....|..|.................|.....|..........

? To see, visualize, how such lists differ
(whether real, simulated or theoretical),
make a QQ plot:
sort X, sort Y, plot the pairs (Xj, Yj),
see how close that curve is to the line X = Y.
Also, search QQ plot here.
A K-S test
gives a number from 0, X and Y identical,
to 1, way off; you could flip this around to 100 % down to 0 %.
However a QQ plot shows more directly where X and Y differ.
