Statistical fallacies

Errors in reading data and evidence: samples, averages, correlations, and what the numbers do not say.

Reading a test result or a piece of evidence without accounting for how common the thing being tested for actually is.

A filter that selects on two traits at once makes those traits look negatively related inside the selected group.

Treating a statistical association as evidence of cause without ruling out confounders, reverse causation, selection, or chance.

Concluding something about an individual from a statistic that describes the group they belong to.

Reporting a mean that hides a skewed distribution, so the average ends up describing almost nobody in the data.

Running analyses until one crosses the significance threshold, then reporting that one as though it were the only test.

Extreme results tend to be followed by ordinary ones for purely statistical reasons, and that drift gets mistaken for an effect.

A pattern that holds in every subgroup can reverse once the subgroups are pooled, so the combined number tells the opposite story.

Small groups produce more extreme results by chance alone, so they crowd both the top and the bottom of any ranking.

Finding a pattern in the data first, then presenting it as the thing you set out to test.