# Article: Bayesian Hodges-Lehmann tests for statistical equivalence in the two-sample setting

**URL:** <https://discourse.datamethods.org/t/article-bayesian-hodges-lehmann-tests-for-statistical-equivalence-in-the-two-sample-setting/4969>\
**Category:** data analysis\
**Tags:** research-method, bayes, equivalence-testing\
**Created:** [October 3, 2021, 12:09pm UTC](https://discourse.datamethods.org/t/article-bayesian-hodges-lehmann-tests-for-statistical-equivalence-in-the-two-sample-setting/4969 "2021-10-03T12:09:01Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![R\_cubed](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/r_cubed/32/1518_2.png) [@R\_cubed](https://discourse.datamethods.org/u/R_cubed)\
**Post date:** [October 3, 2021, 12:09pm UTC](https://discourse.datamethods.org/t/article-bayesian-hodges-lehmann-tests-for-statistical-equivalence-in-the-two-sample-setting/4969/1 "2021-10-03T12:09:01Z")

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This was just published in August. I have not read the paper in its entirety, but I thought this would be of interest.

> **[Bayesian Hodges-Lehmann tests for statistical equivalence in the two-sample...](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8369333/)**
>
> Null hypothesis significance testing (NHST) is among the most frequently employed methods in the biomedical sciences. However, the problems of NHST and p-values have been discussed widely and various Bayesian alternatives have been proposed. Some...

Addendum: After reading, I thought the paper was a good example of using frequentist criteria to judge the output of a Bayesian method.

I would have liked to have seen the “second generation p-value” approach mentioned. I had thought that using a bootstrap CI of the HL estimate in the context of 2 pre-defined frequentist intervals would be adequate, but never pushed it too far.

But it pulls together a lot of theory and simulation results in one place.

Here is an earlier paper by the same author

> **[Bayesian and frequentist testing for differences between two groups with...](https://wires.onlinelibrary.wiley.com/doi/full/10.1002/wics.1523)**
>
> Visual representation of a Bayesian two-sample t-test. Bayesian two-sample tests have recently becomes increasingly popular through the on-going discussion about statistical significance, and we revi...