Second pass at: Absence of evidence and evidence of absence

Post #4 describes the usual case. This is about the unusual one.

Percentages of small denominators should be reported with the denominator. Two out of three is not sixty-seven per cent in any useful sense.

Posted with less confidence than the sentence structure implies.

I read the earlier replies on Absence of evidence twice before writing this, because I had assumed the opposite and wanted to be sure I was disagreeing with what was said rather than what I expected.

Narrowing post #20, because the general version has more than one answer.

The honest answer on Absence of evidence is that it depends, and the useful part is the list of what it depends on. Four items, in rough order of how much they matter.

Most people get the first two right and then argue about the fourth.

On post #29 — agreed on the reasoning, with one qualification.

Filing a mild objection to the consensus on Absence of evidence. Mild because I might be wrong; an objection because nobody has addressed the case that does not fit.

Post #38 answers the question as asked. The question underneath it is different.

Whatever the answer on Absence of evidence turns out to be, the method for getting there is the same: state the assumption, do the arithmetic in public, invite the correction.

This follows post #41 rather than contradicting it.

The practical version of Absence of evidence is three sentences long. The rigorous version is three pages and reaches the same conclusion with the conditions attached.

Where I would push back on the Absence of evidence consensus is the confidence, not the direction. The direction looks right. The confidence is borrowed.

A distribution shown is worth ten summary statistics. Where a paper shows individual data points, read those first.

Where I would look next, rather than where I would stop.