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I have two samples both taken from uniform distributions. The two samples differ in size. My first question is can I use the t-test to test the hypothesis that the two distributions are the same.

Now suppose that one distribution is the other distribution but translated by an unknown but relatively small amount. How can I then test the previous hypothesis allowing for the unknown shift?

Nick
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    Yes, the t test is fine for this. Your estimate of the shift can just be the estimated difference in means. – Demetri Pananos Mar 14 '20 at 19:25
  • t-test performs well under departures from normality, but you could use the Mann-Whitney test (Wilcoxon rank sum test) to see if there's an appreciable difference. –  Mar 15 '20 at 03:12
  • Details at https://stats.stackexchange.com/questions/258374/why-my-simulation-shows-t-test-does-not-need-to-have-normal-distribution-assumpt/258388, (but all this assumes that you really want to test the *means* of the distributions, you didn't specify ... – kjetil b halvorsen Sep 20 '21 at 21:31

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