unspurious.

Reference

The glossary.

Every illusion, bias and term in the compendium, defined in a sentence — each linked to the entry or tool that explains it in full.

Anscombe's quartet

Four datasets built by Francis Anscombe (1973) with nearly identical mean, variance, correlation and regression line, but completely different shapes when plotted — the classic case for graphing data rather than trusting summary statistics alone.

see also: the Datasaurus dozen

Base-rate fallacy

Judging the probability of a condition from a test's accuracy while ignoring how rare the condition is — confusing P(positive | sick) with P(sick | positive).

also: base rate neglect, false positive paradox, prosecutor's fallacy

Benford's Law

In data spanning many orders of magnitude, the leading digit is small far more often than large — a 1 about 30% of the time. Used to flag possible fraud, and often misapplied to data it doesn't fit.

also: first-digit law, Newcomb–Benford law

Berkson's paradox

A spurious negative association created between two independent traits when the sample is selected on something both traits influence — a collider.

also: collider bias, Berkson's bias, admission-rate bias

Collider

A variable that two others both point into. Conditioning on a collider — by selecting or filtering on it — opens a false association between its causes.

also: collision node

Confounder

A variable that influences both the supposed cause and the supposed effect, creating an association that is not causal unless the confounder is held fixed.

also: lurking variable, common cause

Ecological fallacy

Inferring something about individuals from statistics about the groups they belong to. What is true of populations can be false of every person in them.

also: aggregation fallacy

Friendship paradox

On average, your friends have more friends than you do — because sampling people through their friendships favours the highly-connected.

also: Feld's paradox

Gambler's fallacy

The belief that independent random events are “due” to correct — that after a run of one outcome, the other becomes more likely. A fair coin or wheel has no memory, so each outcome stays equally likely. Also called the Monte Carlo fallacy.

also: Monte Carlo fallacy, the maturity of chances

Goodhart's law

When a measure becomes a target, it ceases to be a good measure. Rewarding a proxy metric makes people optimise the metric rather than the goal it stood for, so the two come apart.

also: McNamara fallacy, Campbell's law, the cobra effect

Inspection paradox

Observations made by arriving into, or sitting inside, intervals and groups oversample the large ones in proportion to their size.

also: length-biased sampling, waiting-time paradox, size-biased sampling

Lord's paradox

Analysing change scores and analysing baseline-adjusted outcomes can give contradictory verdicts from the same before-and-after data.

also: change-score vs ANCOVA paradox

Monty Hall problem

A probability puzzle in which switching your choice after the host reveals a losing option wins two-thirds of the time — because the host's reveal is constrained, and constraint carries information.

also: three doors problem, Monty Hall paradox

P-hacking

Trying many analyses of one dataset and reporting whichever crosses the significance threshold — whether deliberately or through a garden of forking paths.

also: data dredging, specification searching, the garden of forking paths

Positive predictive value (PPV)

The probability that a positive test result is correct. It depends on the test's accuracy and on how common the condition is in the population tested.

also: precision, posterior probability

Regression to the mean

Extreme measurements tend to be followed by less extreme ones, because part of any extreme is luck that does not repeat. Often mistaken for a real effect.

also: reversion to the mean

Relative vs. absolute risk

Relative risk states a change as a proportion of a baseline (“+50%”); absolute risk gives the real change in cases. A relative figure is uninterpretable without the baseline it omits — the press's favourite omission.

also: relative risk reduction, number needed to treat

Sensitivity & specificity

Sensitivity is the share of truly positive cases a test catches; specificity is the share of truly negative cases it clears. Neither tells you what a positive result is worth.

also: true positive rate, true negative rate

Simpson's paradox

A trend present in every subgroup of data reverses or disappears when the subgroups are combined.

also: Yule–Simpson effect, amalgamation paradox, reversal paradox

Specification curve

A plot of the result of every reasonable analysis of a dataset at once, used to see whether a finding survives defensible changes or vanishes with them.

also: multiverse analysis

Spurious correlation

A statistical association between two variables that are not causally related — usually because both are driven by a third factor, or because both trend over time and drift in step. Strong correlations arise from unrelated random data surprisingly often.

also: spurious relationship, correlation is not causation

Survivorship bias

Drawing conclusions only from the people or things that passed a survival filter, while the failures — the informative ones — remain invisible.

also: survival bias, survivor bias

Texas sharpshooter fallacy

Firing many shots, then drawing the target around the tightest cluster — treating chance patterns found after the fact as if they were predicted.

also: multiple comparisons problem, cluster illusion

Truncated axis

A chart whose quantitative axis does not begin at zero, visually exaggerating differences. A genuine distortion for length-based encodings like bars.

also: y-axis truncation, baseline manipulation

Will Rogers phenomenon

Moving an element from one group to another can raise the average of both groups at once — progress that exists only on paper.

also: stage migration

Winner's curse

The tendency for a value selected for being most extreme — a winning auction bid, or a statistically significant result — to overestimate the truth. With publication bias, it inflates the effects reported in the scientific literature.

also: publication bias, file-drawer problem