Test whether there is a significant difference between two groups I have some trouble with the last test I need to perform for my bachelor thesis. I have two variables and I need to test whether there is a significant difference. The first variable has all the returns of stocks on specific days. The second variable has these returns as well, however some days have been deleted. I want to test whether there is a significant difference between 'before' and 'after' the filtering. Is it OK if I perform a Paired Sample T-test, or should I use another test? 
Every help is very appreciated! 
 A: You would instead compare the values in your group (i.e. for which the condition exists) with the values not in your group (i.e. have two sets with no days in common), but you can't ignore the time structure and pretend you have independence.
Returns may tend to be relatively uncorrelated (mostly, more or less), but even if that's the case you can't ignore the heteroskedasticity (the time-structure that people use ARCH and GARCH for).
One approach might be to fit some model to the data that describes such anticipated features of the data and which includes a mean-level predictor which is 1 or 0 to indicate that grouping relating to what you want to check for I mentioned in the first paragraph - everything in the condition vs not in the condition) and make your comparison that way (by testing whether the coefficient for that dummy was different from 0).
A: A paired test does not make sense, what will you pair the full data values whose values have been deleted from the other set with?
If the goal is to see if the filtering changes the mean significantly (as opposed to any change in the mean being explained by chance) then I would suggest a permutation/randomization test where you look at how much the mean changes when you delete/filter.  Then do a bunch of times where you delete/filter the same number of observations at random and see how much the mean changes from the original dataset and see how the mean changes.  You then compare your original change to these random changes to see if the original filtering stands out as different.  You should probably consult with a statistician to make sure that you do this correctly and give the correct interpretation (does your university have a stats department? a consulting service?) 
