From Brad Efron in [1]: "The frequentist aims for universally acceptable conclusions, ones that will stand up to adversarial scrutiny. The FDA for example doesn

From Brad Efron in [1]: "The frequentist aims for universally acceptable conclusions, ones that will stand up to adversarial scrutiny. The FDA for example doesn’t care about Pfizer’s prior opinion of how well it’s new drug will work, it wants objective proof. Pfizer, on the other hand may care very much about its own opinions in planning future drug development." Significance requirements should be approached differently depending on the use-case. The above are two extreme cases: FDA authorized a new drug where significance guarantees should be rigorously obtained beforehand, and at the other extreme, exploratory data-analysis inside a private company, where data-scientists may use fancy priors or unproven techniques to fish for potential discoveries in the data. Now how much significance guarantee should be required from a lab scientist is unclear to me. Why not let lab scientists publish their lab notebook with all experiments/remarks/conjectures without any significance requirement? The current situation looks pretty much like this anyway with many papers with significance claims that are not reproducible. We should ask the question of how much the requirement of statistical significance hinders the science exploratory process. Maybe the current situation is fine, maybe we should new journals for "lab notebooks" with no significance requirements, etc. On the other hand, in the mathematical literature, wrong claims are published often, see [2] for some examples. But mathematicians do not seem to as critical of this as the public is critical of non-reproducible papers in life sciences. Wrong mathematical proofs can be fixed, wrong proofs that can't be fixed sometimes still have a fruitful argument in it that could be helpful elsewhere. More importantly, the most difficult task is to come up with what to prove; if the proof is wrong or lacks an argument it can still be pretty useful. [1]: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.179.1454&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.179... [2]: https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat...