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The vocabulary, precisely

Every term on this site, defined the way an applied statistician would, and cited to the source you can take to your methods section.

ruleCredible interval vs. confidence interval

A 95% credible interval is a direct probability statement: given the prior and data, θ has a 95% chance of lying in that range. A 95% confidence interval is indirect: if the whole study were repeated infinitely, 95% of the produced intervals would contain the true θ. Most intuitions about "95% confident" describe the credible interval, not the confidence interval (see Gill, 2007, Ch. 1–2).

timelineHDI vs. equal-tailed interval

The equal-tailed interval cuts 2.5% of posterior mass off each end. The highest-density interval (HDI) finds the narrowest 95% region, every point inside has higher density than every point outside. On a skewed posterior they differ, and the HDI reports the most credible values of θ (Kruschke, 2015, Ch. 4).

boltKL divergence (information gained)

The Kullback–Leibler divergence from prior to posterior, DKL(Post‖Prior), measures: in nats, how far your belief moved. Zero means the data changed nothing; larger values mean the data did work. It is a single honest number for "how informative was this study" (Kullback & Leibler, 1951).

crop_freeRegion of Practical Equivalence (ROPE)

A band around a null value defined by the researcher as "close enough to not matter." Comparing how much posterior mass falls inside versus outside separates statistical detectability from practical importance: a distinction p-values collapse together (Kruschke & Liddell, 2018).

straightenCohen's h vs. Cohen's d

Cohen's h = 2·arcsin(√p₁) − 2·arcsin(√p₂) is the effect size for two proportions (used on the Compare page). Cohen's d is for two means, standardised by the pooled SD. Both share the ≈0.2 / 0.5 / 0.8 small/medium/large conventions (Cohen, 1988).

device_hubConjugate prior

A prior chosen so that, combined with a specific likelihood, the posterior stays in the same distributional family. Beta↔Binomial, Normal↔Normal, Gamma↔Poisson, Dirichlet↔Multinomial, Normal-IW↔MVN are the classic pairs. Conjugacy is why the "Models" pages compute exact posteriors (Gelman et al., 2013, §2.4).

scaleBayes factor

The ratio of how well two hypotheses predicted the observed data. Unlike a p-value it can quantify evidence for a null, essential when a media study finds "no effect" and must say whether that is informative or just underpowered (Kass & Raftery, 1995; Jeffreys, 1961).

compressShrinkage

The tendency of a posterior estimate to sit between the raw sample statistic and the prior mean, pulled toward the prior in proportion to prior confidence and inversely to sample size, the mechanism that keeps small pilot samples from overclaiming (McElreath, 2020, Ch. 2).

query_statsPredictive check

Simulating new data from the prior (prior predictive) or the fitted posterior (posterior predictive) and comparing with what you observed. A misfit is evidence the model or question is wrong, the Bayesian analog of model diagnosis (Gelman, Meng & Stern, 1996; Gelman et al., 2013, Ch. 6).

device_hubWeakly informative prior

A prior that constrains θ to a plausible range without strong commitment to a value, designed to be dominated by data when n is large. e.g. Beta(1,1) on a proportion, or a wide Normal on a log-odds. Refined in Gelman, Jakulin, Pittau & Su (2008).

data_explorationRandom-effects meta-analysis

Each study's true effect is treated as drawn from a distribution around an overall effect, with between-study SD τ capturing heterogeneity. More defensible than fixed-effect pooling when effects genuinely vary (Borenstein et al., 2010; Higgins & Thompson, 2002).

straightenReferential / default priors (Jeffreys)

Jeffreys' invariant priors (e.g., Beta(0.5,0.5) for a proportion) formalise "letting the data speak" while staying transformation-invariant. They are a principled default, but still a choice to be sensitivity-checked (Jeffreys, 1961; Gill, 2007, Ch. 3).

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