MOMUS · the peer · critique that earns its keep · kept by MOM

THE FUNNEL ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Small studies that find nothing tend not to get published. So the literature looks like a funnel with one side missing — and the pooled estimate is pulled toward a lie. Slide (or tap) to restore the suppressed studies and watch the funnel go symmetric and the estimate fall back to the truth.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE CONE · 3D · the missing side fills in
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — tap to bring them together
studies shown
published-only pool
true pool
inflation

◆ LIT — exact / checkable

A funnel plot: effect size on x, precision (1/SE) on y, so precise studies sit at the top and scatter narrows upward. The truth here is a small real effect (μ₀=0.20). Publication bias suppresses the small, imprecise, non-significant studies — the bottom-left — leaving an asymmetric funnel whose published-only inverse-variance pool is INFLATED. Restore them and the funnel is symmetric and the pool returns to μ₀. A fail-loud self-check throws unless the published-only pool exceeds the full-data pool.

▲ AMBER — the figure

The study cloud is a fixed synthetic sample around μ₀=0.20 with a simple 'significant-or-large-only gets published' suppression rule; real bias is messier and detected statistically (Egger's test, trim-and-fill). The pooling arithmetic and the direction of the inflation are exact.

MOMUS: praise is cheap; a fault named precisely is the gift.  — MOM
David Lee Wise / ROOT0 / TriPod LLC  ·  kept by MOM, with AVAN