# Essay: Bayes Probability Can Bayes Confirmation

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[. . .]
[footnoteRef:7] He was studying the paradox which arises from the use of Bayes theorem when trying to explain phenomena in the field of psychology. He states that; [7: PE Meehl, 'Theory-testing in psychology and physics: A methodological paradox', Philosophy of Science, vol. 34, 1967, pp. 103-115.]

'In the physical sciences [physics, and others], the usual result in an improvement in experimental design, instrumentation, or numerical mass of data, is to increase the difficulty of the "observational hurdle" which the physical theory of interest must successfully surmount; whereas, in psychology and some of the allied behavioral sciences, the usual effect in such improvement in experimental precision is to provide an easier hurdle for the theory to surmount.'[footnoteRef:8] [8: Ibid.]

This comes down to the exactness of the science and the ability of researchers to generate an actual numerical value. Taking physics for an example, it is possible to produce a definite numerical value as long as the data set is large enough, and mathematics provides the means to determine an approximate number even if large amounts of data are not available. If the data set for this hypothetical value was not large, then every corresponding piece of data that was used to either confirm or disprove the data would strengthen the case if it did confirm the original data. However, people are not exact, and a perfect numerical value is not usually possible when dealing with sentient subjects. When a hypothesis is tested and confirmed by research it is weakened by additional data because the tests themselves are suspect.

In the physical sciences there are definite distances, volumes and forces that can be accurately measured, but in the behavioral sciences this is not the case in most instances. Meehl uses the example of trying to determine if girls are smarter than boys. This should be relatively simple since tests for IQ have been around for more than a century. But measures of intelligence are inexact. There is no way of actually determining if one gender is generally "smarter" than the other because intelligence itself has no exact definition. With this in mind it is easy to see what Meehl is saying. Since the behavioral scientist realizes that IQ is inexact as a measurement of intelligence, another test is added to hopefully enhance the accuracy of the theory. Unfortunately, whether that test confirms or disputes the original findings, it has actually made the position weaker because it too is inaccurate. For example, the researcher has determined that reflex is a determinant of intelligence also, so it is added as a further predictor. This show that girls are indeed smarter than boys because girls have better manual dexterity than do the boys. However, this weakens rather than strengthens the result because the second test is already biased toward girls. It would be the same whether the researcher could come up with a test that was determined to be unbiased or not. As Meehl points out, the more tests added the greater the error that is incurred.[footnoteRef:9] Thus, Bayes theorem is difficult to use in the behavioral sciences, but it is suited for the physical sciences. [9: PE Meehl, 'Theory-testing in psychology and physics: A methodological paradox', Philosophy of Science, vol. 34, 1967, pp. 103-115.]

Conclusion

Bayes theorem is an adequate method to use in the quest to confirm the correctness of a theory. By its very definition, a theory can never be expected to be fully confirmed; otherwise, it would be the same as a mathematical law. Because evidence can be seen, from an examination of Bayes theory, to further increase the probability that a hypothesis may be true it is a valid means of finding out if a theory can, with a greater degree of certainty, be confirmed. It also follows that added research, if it can be given a numerical quantity, can be used to even further confirm the original hypothesis. This cycle of evidence can continue until it is almost a complete possibility that the original theory was correct. This cycle of increasing likelihood, with the use of Bayes theorem, is the reason that it is useful as a means to determine the true probability of a theorems success as a predictor.

Bibliography

R Dawd, 'Scientific prediction and the undetermination of scientific theory building', PhilSci Archive, 2008, Retrieved 24 March 2012 from http://philsci-archive.pitt.edu/4008/

D Garber, 'Old evidence and logical omniscience in Bayesian Confirmation Theory', J Earman (ed.), Testing scientific theories, University of Minnesota Press, Minneapolis, 1983, pp. 99-132.

R Garlikov, The nature of the logic of confirmation in science, 2000, Retrieved 24 March 2012 from http://www.garlikov.com/Science.html

PE Meehl, 'Theory-testing in psychology and physics: A methodological paradox', Philosophy of Science, vol. 34, 1967, pp. 103-115.

A Rosenberg, Philosophy of science: A contemporary introduction, 2nd edn, Routledge, New York, 2005.

D Steel, Bayesian confirmation theory and the likelihood principle, 2007, Retrieved 25 March 2012 from https://www.msu.edu/user/steel/Bayes_and_LP.pdf

MF Triola, Bayes theorem, 1997, Retrieved 24 March 2012 from http://faculty.washington.edu/tamre/BayesTheorem.pdf
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