Statistical Hypothesis Tests & Diagnostics

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Abstractions about testing statistical models and hypotheses, spanning time-series diagnostic tests (augmented Dickey-Fuller test, Ljung-Box test, CUSUM), regression and similarity diagnostics (Breusch-Pagan test, Fisher kernel), and inferential-methodology critiques (misuse of p-values, one- and two-tailed tests, approximate Bayesian computation).

9 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.

• Approximate Bayesian Computation — A family of likelihood-free Bayesian methods that simulates data under proposed parameters and approximates a posterior from closeness to observed summaries.
• Augmented Dickey–Fuller Test — A regression-based time-series hypothesis test whose null is a unit root, augmenting the Dickey–Fuller equation with lagged differences to absorb serial correlation under a declared deterministic specification and lag order.
• Breusch–Pagan test — A Lagrange-multiplier regression diagnostic testing whether disturbance variance in a fitted linear model depends systematically on specified covariates rather than remaining constant.
• Counternull — A nonnull effect value or set that matches a designated null's p-value under a specified test of the observed data.
• CUSUM — A sequential change-detection method that accumulates signed deviations from a reference value, resets or branches according to a declared rule, and signals when the cumulative evidence crosses a decision threshold.
• Fisher Kernel — A model-based similarity equal to the Fisher-information-normalized inner product of two observations' log-likelihood gradients under a common fitted generative model.
• Ljung–Box Test — A portmanteau hypothesis test that combines sample autocorrelations through a chosen lag to assess whether a time series or fitted-model residuals retain serial correlation across that lag set.
• Misuse of p-values — Inferential errors that treat a p-value as evidence about hypothesis probability, causation, effect magnitude, practical importance, replicability, or categorical truth beyond its model-conditional tail-probability meaning.
• One- and Two-Tailed Tests — Hypothesis-test designs that allocate rejection probability to one prespecified direction or to extreme departures in both directions according to the scientific alternative.