backed by Kruschke · McElreath · Gelman · Jeffreys

Belief, updated by data.

Bayes Lab is a working statistics lab for media and mass communication research. Set a prior belief about an audience, hand it real survey data, and watch the exact posterior distribution, credible intervals, Bayes factors, and predictive probabilities compute themselves, live, from the underlying gamma and beta functions.

monitor_heart Live: a prior meeting respondents, one at a time

Posterior of the population proportion θ as each new respondent arrives. Grey = prior. Blue shading = 95% HDI.
respondents seen
0
posterior mean θ
95% HDI

The same exact math, on every data shape

Four conjugate models, each rendered live from first principles. No approximation below the posterior, only closed-form updates.

toggle_on Beta–Binomial

Binary attitude item: "yes/no" response. β posterior: Beta(α₀+x, β₀+n−x).

straighten Normal–Normal

Continuous Likert composite. Posterior precision = prior precision + n/σ².

bar_chart Gamma–Poisson

Count of exposures. Rate λ posterior is Gamma(a₀+S, b₀+n).

linear_scale Correlation (Fisher z)

Association between two continuous media variables, back-transformed to ρ.

Why a Bayesian workflow, in one paragraph

A frequentist p-value can only tell you how surprising your data would be under a specific null. A Bayesian analysis answers the questions researchers actually ask: what should I now believe about my audience, and how confident am I? It combines theory with evidence, yields a full distribution of plausible effects (a credible interval you can interpret directly), and can even quantify evidence for a null hypothesis, something a p-value can never do.

0.95
mass of the posterior inside a 95% credible interval (a direct probability)
6
conjugate measurement models: binary, continuous, count, ordinal, correlation, categorical
18
validated media-communication scales with reference priors built in
0
simulation hidden behind the math for the conjugate models, exact closed forms

Explore the lab, in whatever order suits you

Every section is interactive, mathematically exact, and grounded in a real media-research context.

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Foundations

What a prior actually is, Bayes' theorem in research vocabulary, conjugate priors, and why "no prior" is a myth.

Start here arrow_forward
poll

Measurement Models

Six conjugate models for the data shapes media research actually produces, from binary attitudes to Likert scales to exposure counts.

Open the lab arrow_forward
fact_check

Media Scales

Cultivation, parasocial interaction, third-person effect, agenda-setting, framing, spiral of silence, and more, with reference priors.

See your constructs arrow_forward
balance

Testing & Decisions

Bayes factors, ROPE, prior & posterior predictive checks, and prior-sensitivity analysis: evidence for and against effects.

Test an effect arrow_forward
compare_arrows

Compare Groups

Heavy vs. light viewers, exposure groups, ad-vs-no-ad, posterior differences, Cohen's h, odds ratios, and probability of superiority.

Compare audiences arrow_forward
data_exploration

Bayesian Meta-Analysis

Combine effect sizes across studies with a random-effects model, the modern engine behind cultivation evidence reviews.

Combine studies arrow_forward
straighten

Planning & Power

Prior elicitation you can defend to reviewers, and sample-size planning by posterior precision rather than long-run p-values.

Plan a study arrow_forward
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Reference & Glossary

The vocabulary, precisely: credible vs. confidence intervals, HDI, KL divergence, ROPE, conjugate priors, with full citations.

Look it up arrow_forward

Written for a methods reviewer, not just a coder

Every estimate is paired with the sentence a reviewer would accept, because a Bayesian result is only as defensible as the prior that seeded it and the model that digested it.

translate From p-values to probabilities

"p < .05" becomes "given this data, there is a 93% chance the effect exceeds zero."

rule Evidence for the null

A Bayes factor can support "no meaningful effect", essential when a media-effects null must be shown informative, not just underpowered.

tune Transparency by construction

The prior is written down before the data. A reviewer can evaluate it, criticise it, and see how much it changed the answer.

What the actual models look like

This is not toy math. The same models run here in exact closed form are the ones you'd fit in brms, Stan, or JASP for a real study.

functions Beta-Binomial (a binary attitude item)

# brms: Bayesian glm for a yes/no survey item
brm(attitude_shift ~ 1,
    family = bernoulli(),
    prior = set_prior("beta(6, 14)",
                 class = "Intercept"),
    data = survey)

Exact conjugate update: posterior = Beta(α₀ + x, β₀ + n − x).

functions Normal-Normal (a continuous Likert composite)

# Stan: unknown mean, known-ish sampling SD
data { int N; vector[N] y; real mu0; real s0; }
parameters { real mu; }
model {
  mu ~ normal(mu0, s0);
  y  ~ normal(mu, sigma_est);
}

Posterior precision = prior precision + n·(1/σ²): the conjugate normal-normal result shown live on the Models page.