confidence interval One-sided paired samples T-test

Comments

• EJ

  October 2020

  Hi Jaiden,

  From memory: for the one-sided test, their are two bounds, but one is plus infinity or minus infinity, right? This sounds silly, but then again, if you want inference that makes sense you should become a Bayesian instead ;-)

  Cheers,

  E.J.
• Jaiden_Camryn

  October 2020 edited October 2020

  Hi E.J.,

  Thank you very much for your answer. I am also doing Bayesian inference in this paper. The frequentist stats are for the benefit of my thesis advisors and co-authors so we can understand each other. I come from a very frequentist lab but since I participated to your workshop I am slowly trying to convince them to adopt Bayesian. They have finally downloaded Jasp!

  About the one-sided tests, I did report the lower bound - infinity in my draft but they said they had never seen this and you need two bounds. But I can't see any mathematical logics in it and I have myself never found such an interval reported in APA style. Just wondered if someone had because I am now expected to calculate the two bounds for a one-sided test and it bothers me.

  Cheers,

  J.C.
• EJ

  October 2020

  Well there *are* two bounds -- and one of them is at -infinity. I have a footnote on this in some paper, let me check...Yes, see footnote 3 and earlier associated text in https://link.springer.com/article/10.3758/s13423-017-1343-3

  A quick Google search also gives this: https://www.mathworks.com/matlabcentral/answers/90110-one-sided-t-test-function-gives-inf-as-part-of-the-confidence-interval

  and this: https://www.analytics-toolkit.com/glossary/confidence-limit/

  and this: https://www.power-analysis.com/precision_confidence_level.htm

  and this: https://www2.isye.gatech.edu/~yxie77/isye2028/lecture7.pdf

  Cheers,

  E.J.
• Jaiden_Camryn

  October 2020

  Thank you very much. For my analyses, I obtained a confidence interval with a minus infinity lower bound when the Bayesian t-test gave me a credible interval with two values. I now realize that they should not be compared as they do not estimate the same thing. It is still a bit tricky to think in Bayesian rather than to compare with frequentist.

  In addition, the frequentist interpretation of a CI is that we can be 95% confident that the true (unknown) estimate would lie within the lower and upper limits of the interval. When one is infinity, that does not sound precise at all. But I am still not clear on how the Bayesian credible interval provides 2 values for the interval in a one-sided hypothesis test. In my case, the analysis showed a Bayes Factor of 10.93 (median = 0.39; 95CI [0.19-0.67]) using Oosterwijk’s recommendation as an informed prior.

  Thanks again,

  Cheers,

  Jaiden
• EJ

  October 2020

  Hi Jaiden,

  Well, the Bayesian one-sided test simply truncates the prior distribution (and therefore the posterior distribution as well) to be on one side of 0. But that still gives a well-defined posterior distribution, and 95% of the central mass of that distribution will lie between two bounds. It is the frequentist result that is counterintuitive here.

  E.J.
• Jaiden_Camryn

  October 2020

  Ok, thank you for clarifying.

  Jaiden
• RobShaver

  October 2020

  Hey Jaiden,

  "In addition, the frequentist interpretation of a CI is that we can be 95% confident that the true (unknown) estimate would lie within the lower and upper limits of the interval."

  Isn't that what the frequentist CI claims to be but is not? See the cited article by EJ, Table 1 (https://doi.org/10.3758/s13423-017-1343-3  ).

  Maybe for convenience you could use a 90% frequentist CI to reflect a one-sided test base on an alpha-level of .05 like in TOST procedures: "In any one-sided test, for an alpha level of .05, one can reject H0 when the 90% confidence interval (CI) around the observed estimate is in the predicted direction and does not contain the value the estimate is being tested against (e.g., 0)" (Lakens et al. 2018, p. 260, https://doi.org/10.1177/2515245918770963)

  Best

  Robin