Watch out for naively (because implicitly based on flat-prior) Bayesian statements based on classical confidence intervals! (Comptroller of the Currency edition)

Laurent Belsie writes:

An economist formerly with the Consumer Financial Protection Bureau wrote a paper on whether a move away from forced arbitration would cost credit card companies money. He found that the results are statistically insignificant at the 95 percent (and 90 percent) confidence level.

But the Office of the Comptroller of the Currency used his figures to argue that although statistically insignificant at the 90 percent level, “an 88 percent chance of an increase of some amount and, for example, a 56 percent chance that the increase is at least 3 percentage points, is economically significant because the average consumer faces the risk of a substantial rise in the cost of their credit cards.”

The economist tells me it’s a statistical no-no to draw those inferences and he references your paper with John Carlin, “Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors,” Perspectives on Psychological Science, 2014.

My question is: Is that statistical mistake a really subtle one and a common faux pas among economists – or should the OCC know better? If a lobbying group or a congressman made a rookie statistical mistake, I wouldn’t be surprised. But a federal agency?

The two papers in question are here and here.

My reply:

I don’t think it’s appropriate to talk about that 88 percent etc. for reasons discussed in pages 71-72 of this paper.

I can’t comment on the economics or the data, but if it’s just a question of summarizing the regression coefficient, you can’t say much more than to just give the 95% conf interval (estimate +/- 2 standard errors) and go from there.

Regarding your question: Yes, this sort of mistake is subtle and can be made by many people, including statisticians and economists. It’s not a surprise to see even a trained professional making this sort of error.

The general problem I have with noninformatively-derived Bayesian probabilities is that they tend to be too strong.

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