Statistical Bias & Sampling Artifacts

Abstractions about distortions introduced by measurement, search, or sampling — inflated coefficient variance from collinearity, false discoveries from unadjusted search in the look-elsewhere effect, directional errors like Type S error and underfitting, and perceptual sampling artifacts like the wagon-wheel effect.

6 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Collinearity Inflation — The pathological ballooning of individual regression-coefficient variance when predictors carry overlapping information — a near-singular predictor cross-product matrix that degrades per-predictor attribution while leaving joint prediction untouched, unfixable by more data.
• Look-Elsewhere Effect — Discount an exciting best-of-many find by the size of the search that produced it — converting a local p-value at one scanned peak into a global p-value asking whether any peak this extreme would occur anywhere, via the trials factor.
• Mental Rotation — The cognitive process of imagining an object rotating continuously through intermediate orientations to align it with a comparison object before judging a match — diagnosed by reaction time that scales linearly with angular disparity.
• Type S Error — Quantify the risk that a statistically significant estimate points the wrong way by computing, before data collection, the probability that a two-sided significance filter is cleared from the opposite tail when the true effect is near zero relative to noise.
• Underfitting — The failure mode where a model's hypothesis class is too restrictive to capture the structure genuinely present in the data — high bias, with training and test error both elevated and close together — curable only by a richer functional form, not by more data or regularization.
• Wagon-Wheel Effect — A rapidly spinning spoked wheel appears to slow, freeze, or reverse because a periodic feature sampled at discrete intervals above its Nyquist limit produces a lower-frequency alias — the apparent motion being the slowest rotation consistent with the snapshots, not the true speed.