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According to Karl Popper, only falsifiable hypotheses are truly scientific (quoting Wikipedia):

no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive: it shows the theory, from which the implication is derived, to be false.

In keeping with these theoretical premises, which statistical framework is more appropriate, the frequentist or the Bayesian?

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    $\begingroup$ Regarding your edit, please notice that "single counterexample" is single counterexample no matter of your methodology, it has nothing to do with statistical hypothesis test! $\endgroup$ – Tim May 5 '17 at 13:12
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    $\begingroup$ Popper did not like the use of probabilities in science, so would not have approved of either statistical approach. His attempt to develop a propensity probability did not make much sense in the real word. See the related hsm.stackexchange.com/questions/3176/… $\endgroup$ – Henry May 5 '17 at 17:03
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    $\begingroup$ I recall Deborah Mayo's drawn some connections between frequentist inference & Poppper's ideas (see her blog). (But for me, & I'm sure for many statisticians, it's the theoretical premises promulgated by philosophers of science that ought to be judged in light of the successes of both statistical frameworks. "Anything goes!" :)) $\endgroup$ – Scortchi - Reinstate Monica May 10 '17 at 19:40
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Karl Popper has argued for a general mindset that should be employed by a scientist. The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about scientific method. However this does not mean that is is the only way how you could conduct hypothesis tests! In Bayesian framework you could use Bayes factors to compare the "null" model with alternative model so to falsify your hypothesis (this is how most Bayesian equivalents to frequentist tests, like BEST, work). So you can perform hypothesis tests in Bayesian framework and Karl Popper has nothing to do with Bayesian vs. frequentist debate.

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    $\begingroup$ +1 for "Karl Popper has nothing to do with Bayesian vs. frequentist debate". But I'd add that Andrew Gelman has been arguing that frequentist hypothesis testing is not as Popperian as people think (or like think), because Popper teaches us to try to falsify the hypotheses we believe & cherish, whereas frequentist hypothesis testing usually involves trying to falsify aka reject the hypothesis we do not believe & do not cherish, i.e. the "null hypothesis". $\endgroup$ – amoeba May 5 '17 at 12:56
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    $\begingroup$ @amoeba As a characterization of how testing is sometimes (often?) taught in universities, that is correct. However, I have no books on my shelves that characterize the null hypothesis in that way. Few of the frequentist books even mention "beliefs"! Indeed, I think none even frame this enterprise in terms of "try to falsify." They discuss testing, comparison, evaluation, and the like. The null hypothesis is distinguished because it is the one for which a sampling distribution of the statistic is known: that concept has nothing to do with "belief." $\endgroup$ – whuber May 5 '17 at 13:14
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    $\begingroup$ @whuber I am not here to defend Andrew Gelman's views (I often disagree with them). However, in practice, at least in science, researchers would usually have some opinions (beliefs) about the null/alternative. Sometimes the null corresponds to the "status quo", and in this case hypothesis testing seems to follow Popperian framework rather closely. But often the null is more of a strawman that needs to be rejected merely in order to be able to argue in favour of the alternative; this is what Gelman talks about. In any case, researchers usually do prefer to reject H0, hence my "trying to" :-) $\endgroup$ – amoeba May 5 '17 at 13:23
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    $\begingroup$ Good answer. In addition when using Bayesian statistics to do hypothesis testing, you can cotrol for frequentist errors and you get the best of both approaches. As such the question may be missleading - it is not an either or. E.g, see figshare. doi.org/10.6084/m9.figshare.4819597.v3 $\endgroup$ – user36160 May 10 '17 at 17:21
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It depends on what you mean that Popper had nothing to with debate.

IN some sense it is half correct

In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he was intimately connected with these issues. The foundations of probability is generally considered to be his best work.

  1. Developed and helped make rigorous Von Mises frequentist theory
  2. Developed A confirmation Logic, using Popper Functions.
  3. Argued against Inductive logic, and standard bayesian inference; that is nonsense (see his paper on this

  4. Developed his own probability calculus similar to A Renyi

  5. Ultimately was interested in the debate, because he rejected both conceptions; arguing to a return to Kolmogorov interpretation of probability= the neo-classical physical interpretation called propensity theory

  6. Connected these issues to QM
  7. Generally considered to amongst the greatest mathematical philosophers of probability (if not the greatest in some cases) and probabilistic logicians
  8. More than half of his best work (read David Miller, who was close confident, contribution in the newly published cambridge companion to Popper)
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    $\begingroup$ I don't quite follow what you are saying. $\endgroup$ – Michael R. Chernick May 5 '17 at 14:57
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    $\begingroup$ Welcome to Cross Validated & thanks for your contribution! You might want to look at how to merge your accounts, & then keep using the same one rather than creating a new one for each answer. Also note that this isn't a conversation-style forum but a Q&A site, so it's better (1) to edit your answer to make additional points, & (2) if you want to address issues raised in other answers link to them (clicking on 'share' underneath an answer provides a link you can copy) - among other reasons answers get shuffled about, so it won't ... $\endgroup$ – Scortchi - Reinstate Monica May 5 '17 at 15:08
  • $\begingroup$ ... remain clear to which you're referring. $\endgroup$ – Scortchi - Reinstate Monica May 5 '17 at 15:10

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