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I have a simple question. I'm not sure which one to use, whether it should be one tailed or two tailed test.

I have two sets of data - any type of measurements. First test is in perfect conditions and the second one is where the measurements are slightly different, some noise has been introduced. Comparing two second set of data to the first one I need to answer the following questions:

  1. Is the mean value of the second data significantly different?
  2. Is the second data significantly nosier?

For the first one I decided to use two-tailed t-test to compare the means, the reason why I chose two tailed test is the fact that we are not asked whether one is higher/lower/better than the other.

However with the second question I've got a little dilemma. I want to use F-Test to compare the variances, but I am slightly confused in deciding, which one to use - two or one tailed test? I think it should be one tailed test, as I am testing whether the second data is worse than the first one, what that means I am checking whether the variance in the second one is a lot higher. Am I correct or am I misunderstanding something here? Thank you.

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It is possible to use a one-tailed test since only deviations in one direction are expected in this case and because it is essentially an interpretation problem. More importantly, however, is that if you reject the second hypothesis, a different test needs to be chosen for the first, because t-test has an assumption of equality of variances. Finally, F-test for inequality of variances is extremely sensitive to data meeting distributional assumptions (normality), Levene's test is a more robust alternative.

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