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I am analysing data from an experiment consisting of 4 treatments, and I am interested in treatment differences of DNA damage caused by a toxicant. I have consulted a statistician to discuss some of the statistical intricacies. He insists that p-values are not a measure of evidence and are misused in science and evidence-based research. So far, so good. Instead, he wants me to use likelihood ratios. I have been at this for weeks now, but I cannot figure out how I would compare treatments to each other. From my understanding, likelihood ratios are used to compare different models. However, I have only one model, and now I want to see which treatments differ. Can somebody explain how one would go about this using likelihood ratios? Or are there any other suggestions that could help?

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    $\begingroup$ This paper will likely be relevant for you, as it explained how Bayesian likelihoods comparison can be used instead of classical frequentist tests using the p-value: nature.com/articles/s41593-020-0660-4 $\endgroup$ Commented Jul 18, 2023 at 14:58
  • $\begingroup$ Welcome to CV. The lack of response to your question suggests that there are not many adherents of the Likelihood school on this site. It is a pity that the statistician you consulted was so negative on the conventional statistical approaches involving estimated effects (both point and confidence intervals) and p-values. ctd ... $\endgroup$ Commented Jul 19, 2023 at 20:31
  • $\begingroup$ ... As the ASA Presidential taskforce states about p-values and significance tests "They are important tools that have advanced science through their proper application." Tools can still be useful even if other people misuse them. magazine.amstat.org/blog/2021/08/01/… $\endgroup$ Commented Jul 19, 2023 at 20:33

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