Personally, I think the dichotomy between hypothesis-testing and likelihood-quantification is a false one. The “P=0.05” cutoff we use to “reject” a hypothesis is an arbitrary one. When I read papers, I never “accept” or “reject” hypotheses but rather consider likelihood quantification as a measure of the weight of evidence or a distance of the data from some null hypothesis, as measured by some statistic. I encourage everyone else to consider this probabilistic worldview when viewing our paper: we aimed to quantify probabilities of this system occurring in nature, and P-values were convenient and commonly understood ways of communicating quantiles.
This paragraph does a lot of lifting. Conflating p-values and probabilities is the science equivalent of a code smell.
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