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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!

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  • $\begingroup$ Sample 1 is complete data, but sample 2 is the exact same data with random values deleted? I don't see the question or why this is of interest. $\endgroup$ – AdamO Jun 30 '14 at 21:16
  • $\begingroup$ Well, my research is about analysts' stock recommendations. So I want to see whether there is a reaction in the stock returns around the data of such recommendations. However, some research showed that analysts' recommendations piggyback from earnings announcements. So I have deleted the recommendations which fell on the same day of an earnings announcement. That is why I have two samples: one with all the recommendations and one with filtered recommendations. I hope this makes it more clear.. $\endgroup$ – DavidjeK Jun 30 '14 at 21:29
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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).

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  • $\begingroup$ Well, first I would like to thank you for all the support! I think I get what you want mean, however, I'm quite new to this. I hope someone can help me a bit further: I have a variable with all the Cumulative Abnormal Returns for the recommendations. Should I make another variable with an 1 on the returns that will be filtered out? And when this is the case, should I then do: full_recommendations=c(1)+c(2)*dum_earnings*full-recommendations? $\endgroup$ – DavidjeK Jul 1 '14 at 14:31
  • $\begingroup$ I performed the test, however, I used full_recommendations=c(1)+c(2)*dum_earnings, which resulted in the following output link. As you can see it is not significant (this result I also hoped for). However, which tests would you advise? And how should I interpret these results? Normal it is 0.77 percent and during a recommendation 0.89 percent? $\endgroup$ – DavidjeK Jul 1 '14 at 15:08
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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?)

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  • $\begingroup$ I have asked the Stats Department, but they couldn't support me before the deadline of the thesis.. $\endgroup$ – DavidjeK Jul 1 '14 at 14:45

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