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Science and Hypothesis, The Value of Science ..

When a theory makes a false prediction, sometimes it can be difficult to know whether we should reject the theory or whether there is something wrong with the auxiliary hypotheses. For example, astronomers in the 19th century found that Newtonian physics could not fully explain planet Mercury's orbit. It turns out that this is because Newtonian physics is wrong, and you need relativity to give a more accurate prediction of the orbit. However, when astronomers discovered Uranus in 1781, they also found out that its orbit was different from the predictions of Newtonian physics. But then scientists realized that it could be explained if there was an additional planet which affected Uranus, and Neptune was subsequently discovered as a result.

in The Foundations of Science: Science and Hypothesis, ..

Thus, for example, biological taxonomy and descriptions of historical events usually employ formal systems of that embody significant hypotheses about presumed similarities of nature or origin.

hypothesis and, if the prediction is successful, ..

The characterization of thedifference between the prediction and the observed data provides guidancefor localization and redesign.

If a hypothesis cannot be tested, we cannot find evidence to show that it is probable or not. In that case it cannot be part of scientific knowledge. Consider the hypothesis that there are ghosts which we cannot see and can never interact with, and which can never be detected either directly or indirectly. This hypothesis is defined in such a way to exclude the possibility of testing. It might still be true and there might be such ghosts, but we would never be in a position to know and so this cannot be a scientific hypothesis.

The confusion of many users of statistical methods (which has also driven the - still ongoing - discussion about NHST, "null hypothesis significance testing" in the "soft" or - better - weak "sciences" [like Psychology]) is probably due to mixing up two distinct approaches to testing hypotheses - Fisher's significance test on one side and Neyman-Pearson's theory of statistical decision on the other - into an "inconsistent hybrid that every decent statistician would reject" (Gigerenzer, 1993). A prototypical study, at least in Psychology, works like this: The researcher has an assumption, call it A, that there is some effect. He/she assumes a medium effect size (Cohen's d=0.5; poor theory, probably, but anyway...) and calculates the sample size for this assumed effect to be indicated sensitively, say with Power=0.8 (this is a kind of Neyman-Pearson). Then he/she collects data, runs a standard (central) t- or F-Test, setting a strawman null hypothesis of "no effect" and if pis Fisher, but not testing the actual hypothesis) and accepts A (which is not ok, as any effect size different from null gets support from rejecting the null, unless all other alternatives can be ruled out). This latter conclusion is neither Fisher, nor Neyman-Pearson, it is simply not correct.

Science and Hypothesis: Henri Poincar, W

The HD method tells us how to test a hypothesis, and a scientific hypothesis must be one that is capable of being tested.

"Law of Universal Gravitation," for example, has a lot of predictive power, since it can be used to explain great portions of both celestial and terrestrial motion.

Question 2: Is there any record on what Popper's position was regarding null hypothesis testing (after Fisher and Neyman-Pearson) and the Bayesian approach as tools to gain knowledge in the sciences?

Lederberg(1993), “DENDRAL: A Case Study of the First Expert System for ScientificHypothesis Formation.”  61:209-261.
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Two key concepts in the scientific approach are theory and hypothesis

How then can one be certain that one is questioning the right thing?The Popperian answer is that we cannot have absolute certainty here,but repeated tests usually show where the trouble lies. Evenobservation statements, Popper maintains, are fallible, and science inhis view is not a quest for certain knowledge, but an evolutionaryprocess in which hypotheses or conjectures are imaginatively proposedand tested in order to explain facts or to solve problems. Popperemphasises both the importance of questioning the background knowledgewhen the need arises, and the significance of the fact thatobservation-statements are theory-laden, and hence fallible. For whilefalsifiability is simple as a logical principle, in practice it isexceedingly complicated—no single observation can ever be takento falsify a theory, for there is always the possibility (a) that theobservation itself is mistaken, or (b) that the assumed backgroundknowledge is faulty or defective.

when a hypothesis makes a prediction and that prediction fails, ..

(d) The fourth and final step is the testing of a theory by theempirical application of the conclusions derived from it. If suchconclusions are shown to be true, the theory is corroborated (butnever verified). If the conclusion is shown to be false, then this istaken as a signal that the theory cannot be completely correct(logically the theory is falsified), and the scientist begins hisquest for a better theory. He does not, however, abandon thepresent theory until such time as he has a better one to substitutefor it. More precisely, the method of theory-testing is as follows:certain singular propositions are deduced from the newtheory—these are predictions, and of special interest are thosepredictions which are ‘risky’ (in the sense of beingintuitively implausible or of being startlingly novel) andexperimentally testable. From amongst the latter the scientist nextselects those which are not derivable from the current or existingtheory—of particular importance are those which contradict thecurrent or existing theory. He then seeks a decision as regards theseand other derived statements by comparing them with the results ofpractical applications and experimentation. If the new predictions areborne out, then the new theory is corroborated (and the oldone falsified), and is adopted as a working hypothesis. If thepredictions are not borne out, then they falsify the theory from whichthey are derived. Thus Popper retains an element of empiricism: forhim scientific method does involve making an appeal to experience. Butunlike traditional empiricists, Popper holds that experience cannotdetermine theory (i.e., we do not argue or infer fromobservation to theory), it rather delimits it: it shows whichtheories are false, not which theories are true. Moreover, Popper alsorejects the empiricist doctrine that empirical observations are, orcan be, infallible, in view of the fact that they are themselvestheory-laden.

Testing Hypotheses: Prediction and Prejudice - …

After a fix hypothesis is generatedand added to the system, the simulator is run again with the redesignedcomponent to determine if it now makes the correct prediction.

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