SPSS command: SPSS BAYES CORRELATION

Bayesian Pearson correlation in your browser

Bayesian Pearson correlation tests whether two scale variables are linearly related and gives a posterior distribution for the population correlation ρ.

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

Worked example result

Bayesian Pearson Correlations · study × exam

BF₁₀ = 5.482

Pearson correlation = 0.485

Pair	N	Pearson correlation	BF10
study × exam	30	0.485	5.482
study × commute	30	−0.113	0.168
exam × commute	30	0.072	0.152

Bayesian Pearson Correlations

See the full worked example

What it tells you

Crosstabs runs the SPSS BAYES CORRELATION procedure on your device for every pair of the variables you choose, computing the posterior moments and the highest-density interval by deterministic quadrature rather than sampling.

For every pair, the Bayes factor for a correlation (BF10) against no correlation (BF01).
The posterior mode, mean and variance of ρ and a highest-density interval: the narrowest range holding the chosen probability.
Positive evidence that two variables are unrelated, when BF01 is large.

When to use it

Use it when

Two or more scale variables whose pairwise linear association you want to quantify, such as study time and grades.
Replication studies where demonstrating the absence of a correlation matters as much as finding one.
Small samples where a credible interval for ρ communicates uncertainty better than a p value.

Use something else when

Ordinal or heavily skewed variables: the classical Spearman correlation is more appropriate.
You need to control for a third variable: use partial correlation or Bayesian linear regression.
The relationship is clearly curved: Pearson's ρ only measures linear association.

How to run it in Crosstabs

01
Open your data
Open the file, switch to Statistics mode and choose Bayesian Pearson correlation in the Bayesian statistics group.
02
Choose the variables
Tick at least two numeric variables under Variables (at least two). Every pair is analysed with its own complete cases.
03
Pick the Bayes factor
Choose JZS (Wetzels & Wagenmakers) or Fractional (Kang et al.) and, for the fractional factor, set Fraction b between 0 and 1.
04
Set the prior on ρ
Under Prior on ρ keep Uniform (c = 0), choose Jeffreys-type (c = −1.5), or enter a Custom c; the prior is proportional to (1 − ρ²)^c.
05
Run
Set Credible interval (%), declare any workspace weight, and press Run Bayesian correlation.

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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 students with weekly study hours, an exam score built to rise with study time, and commute minutes generated independently of both, all from a fixed seed.

Bayesian Pearson Correlations

Pair	N	Pearson correlation	BF10	Posterior mean	95% HDI lower	95% HDI upper
study × exam	30	0.485	5.482	0.442	0.153	0.710
study × commute	30	−0.113	0.168	−0.101	−0.439	0.243
exam × commute	30	0.072	0.152	0.064	−0.280	0.405

JZS Bayes factor of Wetzels & Wagenmakers (2012); uniform prior on ρ (c = 0).

How to read it

Study hours and exam score correlate at r = 0.485, with moderate evidence for the alternative (BF10 = 5.482); the 95% highest-density interval for ρ is 0.153 to 0.710. For study hours and commute time (r = −0.113) the factor gives moderate evidence for the null (BF01 = 5.940) — a Bayes factor below 1 is positive evidence for no correlation, which a non-significant p value cannot provide.

Output tables explained

Bayesian Pearson Correlations: One row per pair: N, Pearson correlation, BF01, BF10, posterior mode, mean and variance of ρ, and the lower and upper bounds of the highest-density interval. Footnotes name the Bayes factor, the prior exponent c and the pairwise missing-value rule.
Prior and posterior of ρ: A plot per pair overlays the prior and posterior density of ρ; a selector switches between pairs.

Assumptions and notes

Each pair of variables is roughly bivariate normal and linearly related.
Cases are independent; missing values are excluded pair by pair, so N can differ between rows.
No Bayes factor or posterior is reported when |r| = 1, and the fractional factor needs b × N > 1.

How the results are validated

For every pair of a three-variable reference dataset, the JZS factor matches 30-digit mpmath quadrature to a relative 1e-8 and pingouin's bayesfactor_pearson(method = "wetzels") to 1e-7; posterior mode, mean, variance and interval bounds match the mpmath reference to 1e-8 under the uniform and c = −1.5 priors, and the fractional factor matches to 1e-8. Validation evidence

Questions

Why a highest-density interval instead of an equal-tailed one?

The posterior of ρ is skewed when the correlation is far from zero, so the highest-density interval is the narrowest range with the chosen probability and never excludes a more probable value in favour of a less probable one.

Will my numbers match SPSS exactly?

The Bayes factors use the same formulas. For the posterior, SPSS samples from a Fisher-z approximation, while Crosstabs integrates the posterior density directly, so posterior summaries can differ slightly from SPSS output in the later decimals.

What does the prior exponent c do?

With c = 0 every value of ρ between −1 and 1 is equally likely a priori. Negative c puts more weight near ±1; positive c concentrates the prior around zero. It affects the posterior, not the Bayes factor.

Can I get Spearman or Kendall correlations here?

No. This procedure covers Pearson's ρ only. Use Bivariate Correlations for Spearman's rho and Kendall's tau-b.

Run Bayesian Pearson Correlation 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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