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I want to determine if method A provides the same results as method B. I obtain 2 sets of measurements using both method A and B. I therefore have 2 means that I want to compare using the paired t-test. I know that if the calculated T-value is higher than the chosen critical T-value, the null hypothesis can be rejected, therefore accepting the alternate hypothesis which is that the two means are significantly different. But what if the calculated T-value is lower than the chosen critical T-value? If we don't reject the null hypothesis, can we conclude that, statistically, method A and B are the same?

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marked as duplicate by Michael Chernick, Juho Kokkala, Peter Flom Jan 31 '17 at 11:47

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  • $\begingroup$ It just means you can't reach a confident conclusion. Being "statistically the same" is a very confusing phrase without any obvious meaning. $\endgroup$ – David Lane Jan 31 '17 at 1:49
  • $\begingroup$ There may be better ways of doing this. In the health field people plot difference against sum in a so-called Bland and Altman plot. Various statistics can be derived from that. $\endgroup$ – mdewey Jan 31 '17 at 9:06
  • $\begingroup$ You are asking two different questions here. The title question is about t-tests, the question in the text is a duplicate. $\endgroup$ – Peter Flom Jan 31 '17 at 11:46