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Jun 9 '17 at 9:28 history edited kjetil b halvorsen
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May 9 '17 at 13:54 history edited kjetil b halvorsen
edited tags
May 25 '14 at 19:54 history edited numentar CC BY-SA 3.0
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May 25 '14 at 19:47 comment added numentar I originally asked "how equal" as I couldn't think of a better way to put it. Considering that a t-test (according to many places, including wikipedia test the hypothesis that two populations have equal means, then this equality in this case isn't really equal. But the point is clear now. I have updated the initial post with a bit of background for the question.
May 19 '14 at 0:54 comment added Glen_b "But does this mean that the means are equal or that we have no evidence to suggest otherwise?" -- the second. In no way does it imply the first. Indeed, in a very practical sense it can almost never be the case (an exception might be where population parameters may be discrete for some reason).
May 18 '14 at 20:06 answer kjetil b halvorsen timeline score: 6
May 18 '14 at 20:02 comment added Horst Grünbusch This question asks the same in terms of confidence intervals. Those are generally more instructive than $p$-values, because they live on the scale you measured, so you should prefer the confidence intervals anyway.
May 18 '14 at 19:03 comment added Andy W I take "how equal" to be a bit of an odd way to put it. We can estimate the difference between the means, $\mu_A - \mu_B$, and estimate the uncertainty around that difference, but how does one thing be more equal than another. Typically we test the hypothesis $\mu_A - \mu_B = 0$, but in non-inferiority or equivalence testing we flip the hypothesis to be something like $|\mu_A - \mu_B| < 2$, e.g. the absolute value of the difference of the means is less than 2 (for one possible example). The number you choose should be based on other criteria - not based on the observed data.
May 18 '14 at 18:51 comment added numentar Thanks for the tip! I agree, my question is quite vague, but that's because I'm not sure how to formulate it properly or what terms to use in this case. At what significance level are the means equal? But the t-test already tells us the level at which the difference is not significant... I guess I needed to know what is the terminology that applies to this type of question. Equivalence testing sounds promising!
May 18 '14 at 18:38 comment added Andy W I've added the equivalence tag, and I would suggest you check out those other questions as well. For equivalence testing you typically need to specify the bounds for the hypothesis test where you would consider them to be equal. This may be good enough to "quantify how equal the means are" - but that statement is a bit vague.
May 18 '14 at 18:35 history edited Andy W
added equivalence tag
May 18 '14 at 18:08 history asked numentar CC BY-SA 3.0