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Part 2 is here. The severity or trustworthiness assessment, on which the error correcting capacity depends, requires an appropriate link qualitative or quantitative between the data and the data generating phenomenon, e.
Inductive inference, as Peirce conceives it i. Rather, the justification is sought in the manner of obtaining data. Justifying induction is a matter Sydtems showing that there exist methods with good error probabilities. For this it suffices that randomness be met only approximately, that inductive methods check their own assumptions, and that they can often detect and correct departures from randomness. But this is an idea which flies far away from the plain facts.
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Thirty throws of a die constitute an approximately random sample of all the throws of that die; and that the randomness should be approximate is all that is required. Peirce backs up his defense with robustness arguments.
What if, for example, a certain proportion of the population had twice the probability of being selected? This is particularly so if the sample mean is near 0 or 1. In other words, violating experimental assumptions may be shown to weaken the trustworthiness or severity of the proceeding, but this may only mean we learn a little less.
Nor must we lose sight of the constant tendency of the inductive process to correct itself.
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This is of its essence. This is the marvel of it. Still, Peirce cautions, we should not depend so much on the self-correcting virtue that we Correcting Error Reporting Systems our efforts to get a random and independent sample. But if our effort is not successful, and neither is our method robust, we will probably discover it. Peirce turns the tables on those skeptical about satisfying random sampling—or, more generally, satisfying the assumptions of a statistical model. But, as Peirce is quick to point out, this would equally vitiate deductive inferences about the expected ratio of successful bets.]
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