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I am looking for a way to combine two one-tail t-tests into the appropriate F-test (I think?) in R.

Currently, I have been using a one-tailed t-test to check if the mean of the population before a date is equal to the mean. I programmed a simple one-tail t-test because my standard deviations are calculated separately from the sample. I plug-in (mean before), (mean after), (std. dev. before), (std. dev. after), (sample size) (with Gibbard-Satterthwaite errors) and check if (mean before) < (mean after) is significant.

Now, I wish to test the hypothesis that in the first sample (mean before) < (mean after) while in a second sample, reject (mean before) < (mean after). How can I do this? (I'll be using R to implement it.)

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