Andrew likes to discourage false precision through reporting too many digits for estimates. I think this is good advice, especially for abstracts, summaries, and the primary outputs of much research.

I thought this was a particularly striking example of meaningless precision from the world of finance:

Specifically, for the AllianzGI Structured Alpha 1000 LLC fund, in one instance, Bond-Nelson materially reduced losses in a stress scenario from -22.0557450847078% to -12.0557450847078%.

My attention was brought to this by Matt Levine writing at Bloomberg, who further comments:

What. If you had invested one trillion dollars in that fund, in the hypothetical stress scenario you would lose $220,557,450,847.078, according to the “real” calculation. “Bummer,” you would say; “I can’t believe I lost two hundred twenty billion, five hundred fifty-seven million, four hundred fifty thousand, eight hundred forty-seven dollars and seven and four-fifths cents. I had big plans for that four-fifths of a penny!” But the fund’s managers nefariously sent you a risk report saying that in that stress scenario you would only lose 12.0557450847078% of your money, and not the more accurate 22.0557450847078% reported by their true stress tests.

This is perhaps the purest case I’ve seen of using extra digits to convey, as Levine says, that one did “Some Real Math” to get the number. It is like the digits are supposed to be a costly, and thus more honest, signal about the calculation.

In some cases, reporting many digits can indeed be a costly signal — in that if they aren’t based on the stated calculations, it may be possible to figure out that they are impossible (e.g., via a granularity-related inconsistency of means aka GRIM test). This is perhaps one argument for at least reporting excess digits in tables (though not abstracts and press releases certainly!). Perhaps this argument is somewhat outdated if data and analysis code are provided in addition to results in a paper or report itself, though this remains not always the case.

Here it also seems that perhaps the evidence that this was just fraud is clearer because some real calculations were done to get all those digits, but then either leading digits were changed or the the numbers were just divided by two. Or maybe the fraud would have been clear anyway, but we can definitely imagine how these extra digits can provide some evidence about exactly what happened.

For those following the intersection of error, fraud, and Excel spreadsheets, there are some more details in the complaint about some of the specific labor-intensive (!) steps for how to manipulate a bunch of spreadsheets.

[This post is by Dean Eckles.]