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?