SPSS command: SPSS BAYES ANOVA

Bayesian one-way ANOVA in your browser

Bayesian one-way ANOVA compares a model in which group means differ with the intercept-only model and reports the Bayes factor between them.

Try with example data Run on your own file

Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

Crosstabs runs the SPSS BAYES ANOVA procedure on your device with four g-prior Bayes factors, the classical ANOVA table, and posterior distributions for every group mean and the error variance.

Whether a factor explains the outcome at all: BF10 compares the group model with the intercept-only model.
Evidence that all groups share one mean, through BF01 — useful when a non-significant F leaves you unsure.
A posterior mean and credible interval for each group mean, and for the error variance.
R² and the classical F test, so Bayesian and frequentist results can be reported together.

When to use it

Use it when

One scale outcome across three or more independent groups, such as yield by fertilizer or score by teaching method.
You need to argue that groups do not differ, for example equivalence of regional samples.
You want interval estimates for each group mean that can be read as probabilities.

Use something else when

Only two groups: Bayesian independent samples gives the posterior of the difference directly.
Several factors or covariates: use Bayesian linear regression with factors, or GLM Univariate.
Repeated measurements of the same people: use Bayesian repeated-measures ANOVA.

How to run it in Crosstabs

01
Open your data
Open the file, switch to Statistics mode and choose Bayesian one-way ANOVA in the Bayesian statistics group.
02
Set Dependent and Factor
Choose a numeric Dependent (scale) variable and a Factor with between 2 and 50 categories.
03
Pick the Bayes factor
Under Bayes factor choose JZS (Zellner–Siow), Zellner (fixed g, blank g = N), Hyper-g (a, default 3) or Rouder (scale s, default 1).
04
Pick the prior for the posterior
Keep Reference, p(θ, σ²) ∝ 1/σ², or choose Conjugate normal–inverse-gamma and set Shape a0, Scale b0, Prior mean and Prior variance (× σ²).
05
Run
Set Credible interval (%), declare any workspace weight, and press Run Bayesian one-way ANOVA. Cases missing either variable are excluded listwise.

Run Bayesian One-Way ANOVA in your browser

Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Try with example data

Data

30 synthetic field plots, 10 for each of three fertilizer blends (A, B, C); the outcome is yield in kilograms per plot, drawn from normal distributions with a common spread and a fixed seed.

ANOVA: yield

Source	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	115.99	2	57.99	6.710	.004
Within Groups	233.35	27	8.64
Total	349.33	29

Bayes Factor

N	R²	BF10	BF01
30	0.332	6.397	0.156

JZS method (Zellner–Siow Cauchy prior), model against the intercept-only model.

Posterior Distribution Characterization for Group Means

blend	Posterior mode	Posterior mean	Posterior variance	95% CrI lower	95% CrI upper
A	30.07	30.07	0.933	28.16	31.98
B	33.18	33.18	0.933	31.27	35.09
C	34.81	34.81	0.933	32.90	36.72

Reference prior p(θ, σ²) ∝ 1/σ²; equal-tailed credible intervals.

How to read it

The classical table gives F(2, 27) = 6.71, p = .004, R² = 0.332. The JZS Bayes factor comparing the blend model with the intercept-only model shows moderate evidence for the alternative (BF10 = 6.397). The posterior table then gives a 95% credible interval for each blend's mean yield, from 30.07 kg for A to 34.81 kg for C; the omnibus factor itself does not say which blends differ.

Output tables explained

ANOVA: Between- and within-groups sums of squares, df, mean squares, F and significance for the chosen dependent variable.
Bayes Factor: N, R², BF10 and BF01 for the group model against the intercept-only model; a footnote states the g-prior method and its setting.
Posterior Distribution Characterization for Group Means: Mode, mean, variance and equal-tailed credible interval for each group mean under the reference or conjugate prior.
Posterior Distribution Characterization for Error Variance: The Inverse-Gamma posterior of the error variance, with its shape and rate in a footnote; plots show each mean and the variance.

Assumptions and notes

Observations are independent, and each case belongs to one group.
Residuals are roughly normal with a common variance across groups; there is no Welch-type option here.
The Bayes factor is an omnibus comparison: it does not identify which groups differ, and no post hoc comparisons are produced.

How the results are validated

The JZS and Rouder (s = 0.5) factors match 30-digit mpmath quadrature to a relative 1e-8 and R BayesFactor 0.9.12.4.8 lmBF on k − 1 dummy columns to 1e-8; Zellner and hyper-g factors match closed forms to 1e-12 and 1e-8. Group-mean and error-variance posteriors match the reference to 1e-10 (credible limits 1e-9) under both the reference and conjugate priors. Validation evidence

Questions

Why does my Bayes factor differ from JASP or anovaBF?

SPSS places a g-prior on the k − 1 coefficients of the whole model, while BayesFactor's anovaBF (used by JASP) uses a per-level fixed-effect prior with a different scale. Both are valid; they are different priors, so the numbers differ.

Which g-prior should I use?

JZS (Zellner–Siow) is a robust default. Zellner's fixed g is simple but sensitive to g; hyper-g and Rouder's scale s let you tune how large an effect the alternative expects.

How do I find which groups differ?

Compare the group-mean credible intervals, or run Bayesian independent samples on the pairs you care about. For multiplicity-adjusted pairwise tests, use One-Way ANOVA's post hoc options.

Does a frequency weight work?

Yes. A declared frequency weight with whole numbers is treated as replicated cases. Fractional weights and sampling weights are refused.

Run Bayesian One-Way ANOVA on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

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