Please, I have the next doubt:
I have two samples (two different treatments) , and I want to prove that there is no difference in the average outcome.
I test the data using the two one-sided test for equivalence (tost function of r package equivalence) , where H0: means are different, H1: means are equal. (Confidence level 95%)
p value around 0.63, H0 can not be rejected
But if I reverse the hypothesis, with the t-test (t.test of r), H0* = means are equal, H1*=means are different (Confidence level 95%)
I get p value around 0.7, H0* can not be rejected
Please confirm or discards these interpretations:
(1) Data is not conclusive: we can not discard that the means are equal and that the means are diferent.
(2) But because one p value is 0.6, and the other is 0.7, H0* is "less rejectable" than H0. so I should be inclined to think that is more probable that the means are equal
Hello Glen
Regarding : where H0: means are different, H1: means are equal.
H0 is the Null Hypothesis that means no difference. The probability of finding a difference when no difference exists or presents.
Generally, you cannot use statistics to prove something. It's only about finding out how likely you expect differences between data and a model larger than the one observed. How this is to be interpreted is a different story, but it's never a proof.
Regarding your question, interpretation (1) is correct.
Rather than trying to interpret p-values I would simply have a look at the confidence interval (CI) for the mean difference. If the 96%CI or the 99%CI is fully within a small band of "irrelevancy" (0±d, with d being "irrelevantly" small), the data provides sufficient evidence that the mean difference is at least so close to zero that it is practically irrelevant. If the CI exceeds this band, the data is not sufficiently conclusive.
- Badges
- Science topic
- Similar topics
- Philosophy
- Esthetics
- Interpretation