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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?

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    $\begingroup$ 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. $\endgroup$
    – mdewey
    May 9 '17 at 16:25
  • $\begingroup$ 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? $\endgroup$
    – Gareth
    Mar 3 at 16:29
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It depends on the type of statistical diffrences you are looking. It also depends upon the data distribution.

enter image description here

A great small table summarizing the statistical test are here with the use cases :

https://cyfar.org/types-statistical-tests

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    $\begingroup$ It would be more help to te OP and to subsequent users if you could summarise which of the tests in the link you think is relevant. Links can go dead which would make your answer useless. $\endgroup$
    – mdewey
    May 9 '17 at 17:39
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    $\begingroup$ This link is not working! $\endgroup$
    – Hefaz
    Apr 9 at 20:11

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