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How am I supposed to interpret the confidence interval for a two tailed Student's t test?

I understand that the confidence interval in a one tailed t test reveals the likely range of difference between the two population means. When running a two tailed t test in Matlab, the confidence interval still looks like a likely range of the difference between population means.

Does this confidence interval still convey the significance of intervals that do not cross zero?

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Yes, why shouldn't it?

  • You can always compare confidence intervals to points (like 0)
  • You shouldn't compare confidence intervals to other confidence intervals
  • Only one out of 20 95% confidence intervals will not contain the true population parameter (and 1 out of 100 99% CI etc.)

All of the above is true for one tailed and two tailed confidence intervals.

You should know that one-tailed t-tests are almost never used.

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  • $\begingroup$ Not so sure about one-tailed tests being almost never used. They make sense in many cases. And when using Bayesian inferences, probability statements are almost all directional. $\endgroup$ – Frank Harrell Oct 1 '17 at 12:36
  • $\begingroup$ They wouldn't be called confidence intervals in a Bayesian frameworks though, would they? $\endgroup$ – David Ernst Oct 1 '17 at 13:20
  • $\begingroup$ I was referring to posterior probabilities for specific assertions. If you want an uncertainty interval that would be the credible interval, which unlike a confidence interval has a definition that makes sense. It is the interval that we are e.g. 0.95 certain the true unknown parameter lies. Frequentist confidence interval is virtually uninterpretable. $\endgroup$ – Frank Harrell Oct 1 '17 at 13:27
  • $\begingroup$ My point was that the title mentions confidence intervals specifically. $\endgroup$ – David Ernst Oct 1 '17 at 13:55
  • $\begingroup$ And point is that we need to get away from them when we can. $\endgroup$ – Frank Harrell Oct 3 '17 at 12:16

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