bayesics (version 2.0.2)

prop_test_b: Bayesian test of Equal or Given Proportions

Description

prop_test_b either makes inference on a single population proportion, or else compares two population proportions. binom_test_b is the same as prop_test_b.

Usage

prop_test_b(
  n_successes,
  n_failures,
  n_total,
  p,
  predict_for_n,
  ROPE,
  prior = "jeffreys",
  prior_shapes,
  CI_level = 0.95,
  PI_level = 0.95,
  plot = TRUE,
  seed = 1,
  mc_error = 0.002
)

Value

(returned invisible) A list with the following:

• successes, failures: Number of successes and failures

• posterior_mean, posterior_mean_pop1, posterior_mean_pop2: posterior means for the population proportion

• CI, CI_pop1, CI_pop2: Credible interval for the population proportion

• Pr_oddsratio_in_ROPE: (2 sample analysis only) Posterior probability that the odds ratio is in the ROPE

• PI, PI_pop1, PI_pop2: Prediction interval for the number of trials given in predict_for_n

• Pr_less_than_p: (1 sample analysis only) If p was supplied, the posterior probability that the population proportion is less than p

• prop_plot: Prior and posterior plot of population proportion(s)

• posterior_parameters: Posterior beta shape parameters for the population proportion(s)

Arguments

n_successes

integer/numeric vector of length 1 (for 1 population) or 2 (for 2 populations) providing the number of "successes"

n_failures

Similar to n_successes, but for failures. Only provide this OR n_total.

n_total

Similar to n_successes, but for total number of trials. Only provide this OR n_failures.

p

optional. If provided and inference is being made for a single population, prop_test_b will return the posterior probability that the population proportion is less than this value.

predict_for_n

Number in a future trial. If missing, prop_test_b will use the observed number of trials.

ROPE

ROPE for odds ratio if inference is being made for two populations. Provide either a single value or a vector of length two. If the former, the ROPE will be taken as (1/ROPE,ROPE). If the latter, these will be the bounds of the ROPE.

prior

Either "jeffreys" (Beta(1/2,1/2)) or "uniform" (Beta(1,1)). This is ignored if prior_shapes is provided.

prior_shapes

Vector of length two, giving the shape parameters for the beta distribution that will act as the prior on the population proportions.

CI_level, PI_level

The posterior probability to be contained in the credible and prediction intervals respectively.

plot

logical. Should a plot be shown?

seed

Always set your seed! (Unused for a single population proportion.)

mc_error

The number of posterior draws will ensure that with 99% probability the bounds of the credible intervals of \(p_1 - p_2\) will be within \(\pm\) mc_error. (Ignored for a single population proportion.)

Details

The likelihood is given by $$ y \sim \text{Binom}(n,p), $$ and the prior on \(p\) is $$ p \sim Beta(a,b), $$ where \(a\) and \(b\) are given by the argument prior_shapes. If prior_shapes is missing and prior = "jeffreys", then a Jeffreys prior will be used (\(Beta(1/2,1/2)\)), and if prior = "uniform", then a uniform prior will be used (\(Beta(1,1)\)).

Examples

# \donttest{
# Single population
prop_test_b(14,
            19)
# or another way of the same thing;
prop_test_b(14,
            n_total = 14 + 19)

# A null value compared against can be added:
prop_test_b(14,
            19,
            p = 0.5)

# Two populations
prop_test_b(c(14,22),
            c(19,45))
# or equivalently
prop_test_b(c(14,22),
            n_total = c(14,22) + c(19,45))
# }