ci.bayes.prop: Bayesian credible interval for a proportion

In statpsych: Statistical Methods for Psychologists

Bayesian credible interval for a proportion

Description

Computes a Bayesian credible interval for a population proportion using the mean and standard deviation of a prior Beta distribution along with sample information. The mean and standard deviation of the posterior Beta distribution are also reported. For a noninformative prior, set the prior mean to .5 and the prior standard deviation to 1/sqrt(12) (which corresponds to a Beta(1,1) distribution). The prior variance must be less than m(1 - m) where m is the prior mean.

For more details, see Section 1.18 of Bonett (2021, Volume 3)

Usage

ci.bayes.prop(alpha, prior_mean, prior_sd, f, n)

Arguments

alpha	alpha level for 1-alpha credibility interval
prior_mean	mean of prior Beta distribution
prior_sd	standard deviation of prior Beta distribution
f	number of participants who have the attribute
n	sample size

Value

Returns a 1-row matrix. The columns are:

• Posterior mean - posterior mean of Beta distribution

• Posterior SD - posterior standard deviation of Beta distribution

• LL - lower limit of the credible interval

• UL - upper limit of the credible interval

References

\insertRef

Gelman2004statpsych

\insertRef

Bonett2021statpsych

Examples

ci.bayes.prop(.05, .25, .1, 120, 300)

# Should return:
# Posterior mean Posterior SD        LL        UL
#      0.3916208   0.02742595 0.3387206 0.4458133

statpsych documentation built on Jan. 13, 2026, 1:07 a.m.