statpsych (version 2.0.0)

ci.bayes.cor: Bayesian credible interval for a Pearson or partial correlation with a skeptical prior

Description

Computes an approximate Bayesian credible interval for a Pearson or partial correlation with a skeptical prior. The skeptical prior distribution is Normal with a mean of 0 and a small standard deviation. A skeptical prior assumes that the population correlation is within a range of small values (-r to r). If a skeptic is 95% confident that the population correlation is between -r and r, then the prior standard deviation can be set to r/1.96. A correlation that is less than .2 in absolute value is typically considered to be "small", and the prior standard deviation could then be set to .2/1.96. A correlation value that is considered to be small will depend on the application. Set s = 0 for a Pearson correlation.

For more details, see Section 1.33 of Bonett (2021, Volume 2)

Usage

ci.bayes.cor(alpha, prior_sd, cor, s, n)

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean (Bayesian estimate of correlation)

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

Arguments

alpha

alpha level for 1-alpha credibility interval

prior_sd

standard deviation of skeptical prior distribution

cor

estimated Pearson or partial correlation

s

number of control variables

n

sample size

References

Bonett2021statpsych

Examples

ci.bayes.cor(.05, .1, .536, 0, 50)

# Should return:
# Posterior mean     LL     UL
#         0.1874  0.028 0.3375

ci.bayes.cor(.05, .1, .536, 0, 300)

# Should return:
# Posterior mean     LL     UL
#         0.4195 0.3352 0.4971