Bayesian Correlation (Bayes Factor)

The Bayesian correlation test computes a Bayes factor comparing a model in which the population Pearson correlation is zero against one in which it follows a stretched beta prior on [−1, 1].

베이즈 상관 검정은 모상관이 0인 모형과 [−1, 1] 위의 늘린 베타 사전분포를 따르는 모형을 베이즈 인자로 비교해 상관의 증거를 평가하는 방법이다.

How strong is the evidence for or against a correlation between two variables?

두 변수 사이에 상관이 있는지, 없는지에 대한 증거는 얼마나 강한가요?

The Bayes factor BF10 for a correlation states how many times more likely the observed correlation is under a nonzero-correlation model than under a zero-correlation model. With a uniform prior on the correlation, values below 1/3 give moderate evidence that the variables are uncorrelated.

When to use Bayesian Correlation (Bayes Factor)

• You want to quantify evidence for a null correlation
• You report correlations and want a continuous evidence measure
• Sample size is modest and p values alone are hard to interpret

When to use something else

• The relationship is monotone but nonlinear or has outliers; use a rank correlation instead
• You need to control for other variables; use Bayesian regression instead

Assumptions and requirements

• Pairs are independent
• Variables are approximately bivariate normal
• The relationship is linear

What the analysis reports

• Pearson r and sample size
• BF10 and BF01
• Evidence category
• Classical p value for comparison

How to report it

A Bayesian Pearson correlation gave r = [value], N = [value], BF10 = [value], indicating [category] evidence for [a / no] correlation.

Related methods

• Pearson Correlation Analysis
• Bayesian Linear Regression

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