# Testing whether two data sets are statistically different

I would appreciate if someone could answer my question simply, without the use of any complex terms and high-end detail.

I have two data sets. These correspond to measurements on the same thing being studied. Each of the two data sets has N number of points. Each point in each data set has an associated error, which can be assumed to be Gaussian standard deviation.

So an example might look something like this with N=5:

First data set:
data points = 12.5, 13.5, 14.2, 12.7, 13.8
error on data points = 0.5, 0.4, 0.7, 0.6, 0.51

Second data set:
data points = 12.1, 12.5, 13.8, 14.1, 14.9
error on data points =  0.6, 0.4, 0.5, 0.9, 0.7


What I want to know is the following: how do I test to see if the two data sets are statistically different? That is, are they statistically consistent with each other within the errors, or are they statistically different?

• When you say "on the same object" do you mean you have 2N measurements on one object, N measurements on each of two objects, 2 measurements on each of N objects, one measurement on each of 2N objects, or something else? What do you mean by a unique error? What feature of the two data sets do you wish to compare? If you edit these details into your question then someone may be able to help you. May 9 '17 at 16:25
• Wouldnt you take the differences between each data point and its counterpart and then calculate a standard deviation measure of the differences as a starting point, where the a significantly small enough STDEV would indicate correlation between the two sets? Mar 3 at 16:29