I'm doing some equivalency testing with both the CI approach and TOST to demostrate the equivalency of two scanning methods. For most of my samples, results align as one would expect, i.e. if the CI lies within the upper and lower bounds, the p-values calculated with two one-sided t-test are <0,05. However, I have two samples, where it doesnt't match at all. CIs are outside the upper and lower bounds, but p < 0,001. I wondered whether that might be because the distribution of the values is not normal and skewed to the left (mean difference is -0,27, lower bound -0,09, upper bound 0,09, 90% CI -0,418;-0,128).

Does anyone have an idea what I'm doing wrong?

Thanks!