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The relationship between n and Type 1 error may be less obvious: all else equal, as sample size increases, error rates also increase.The problem is exacerbated by the way reliability interacts with error rates, giving a non-monotonic relationship.
In the middle [of the reliability range, RCK], however, there exists a territory where effects are large enough to afford detection, but reliability is too low to prevent misattribution, leading to particularly high Type 1 error rates.Furthermore, this problem is independent of the statistical analysis approach used (frequentist vs Bayesian, parameter estimation) as long as reliability is not explicitly accounted for.
econometric studies attempting to control for SES [i.e. socioeconomic status, cf. above, RCK] hardly ever estimate or report the reliability of the actual survey item(s) used to operationalize the SES construct ....This is why Westfall and Yarkoni recommend structural equation modeling (SEM) in order to avoid the trap altogether. Lacking any estimations for the reliability, the researchers can then at least plot their results across a range of estimates to see how sensitive their findings are on reliability.
A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. (p.67)Thus:
The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either. (p.67)Similarly for inductive inference.
An inductive inference, too, is justified by conformity to general rules, and a general rule by conformity to accepted inductive inferences. Predictions are justified if they conform to valid canons of induction; and the canons are valid fi they accurately codify accepted inductive practice. (p.67)Applying this to inductive work, which is neglected as compared to deductive inference, is what Goodman calls the Constructive Task of Confirmation Theory (p.68). However, just as with defining any term, we tweak the usage and the definition to make sure that the definition picks out only the instances of usage an no others (p.69).
... the hypothesis says of all things what the evidence statement says of one thing .... (p.71)
The central idea for an improved definition is that, within certain limitations, what is asserted to be true for the narrow universe of the evidence statements is confirmed for the whole universe of discourse. (p.73)(to be continued)