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1. Other people who relate Peircean induction and Neyman-Pearson exams are Isaac Levi (1980 ) and Ian Hacking (1980 ). See also Mayo 1993 and 1996.
2. This statement of (b) is considered by Laudan because the strong thesis of self-correcting. A less strong thesis would replace (b) with (b’): science has approaches for figuring out unambiguously whether an alternate T’ is nearer to the reality than the usual refuted T.
3. When the p-value weren’t really small, then your difference could be considered statistically minor (generally small values are .1 or fewer).
We’d then regard H0 as in line with data x but we may decide to go further and see how big an elevated risk r which has therefore been eliminated with severity. We all do so by locating a risk increase, so that, Prob(d(x) d(x) risk increase r ) is high, say. Then your assertion: the danger increase r passes rich in severity, we’d argue.
If there have been a discrepancy from hypothesis H0 of r (or even more), then, rich in probability, 1-p. the information could be statistically significant at level p .
x isn’t statistically significant at level p .
Therefore, x is evidence than any discrepancy from H0 is under r .
For any general management of effect size. see Mayo and Spanos (forthcoming).
2005 Charles S. Peirce Society