t_test_b: t-test

In bayesics: Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

t-test

Description

One and two sample t-tests on vectors of data

Usage

t_test_b(
  x,
  y,
  mu,
  paired = FALSE,
  data,
  heteroscedastic = TRUE,
  prior_mean_mu,
  prior_mean_nu = 0.001,
  prior_var_shape = 0.001,
  prior_var_rate = 0.001,
  CI_level = 0.95,
  ROPE = 0.1,
  improper = FALSE,
  plot = TRUE,
  seed = 1,
  mc_error = 0.002
)

Arguments

x	Either a (non-empty) numeric vector of data values, or a formula of the form outcome ~ grouping variable.
y	an optional (non-empty) numeric vector of data values
mu	optional. If supplied, t_test_b will return the posterior probabilty that the population mean (ignored in 2 sample inference) is less than this value.
paired	logical. If TRUE, provide both x and y as vectors.
data	logical. Only used if x is a formula.
heteroscedastic	logical. Set to FALSE to assume all groups have equal variance.
prior_mean_mu	numeric. Hyperparameter for the a priori mean of the group means.
prior_mean_nu	numeric. Hyperparameter which scales the precision of the group means.
prior_var_shape	numeric. Twice the shape parameter for the inverse gamma prior on the residual variance(s). I.e., \sigma^2\sim IG(prior_var_shape/2,prior_var_rate/2).
prior_var_rate	numeric. Twice the rate parameter for the inverse gamma prior on the residual variance(s). I.e., \sigma^2\sim IG(prior_var_shape/2,prior_var_rate/2).
CI_level	numeric. Credible interval level.
ROPE	numeric. Used to compute posterior probability that Cohen's D +/- ROPE
improper	logical. Should we use an improper prior that is proportional to the inverse of the variance?
plot	logical. Should the resulting inverse gamma distribution be plotted?
seed	integer. Always set your seed!!!
mc_error	The number of posterior draws will ensure that with 99% probability the bounds of the credible intervals will be within \pm mc_error\times 4s_y, that is, within 100mc_error% of the trimmed range of y. (Ignored for single population inference.)

Details

A one and two sample t-test is nothing more than a special case of one-way anova. See aov_b for details.

Value

Either an aov_b object, if two samples are being compared, or a list with the following elements:

• Variable

• Post Mean

• Lower (bound of credible interval)

• Upper (bound of credible interval)

• Prob Dir (Probability of Direction)

Examples

# Single population
t_test_b(rnorm(50))
# or an alternative input format
t_test_b(outcome ~ 1,
         data = data.frame(outcome = rnorm(50)))

# Two populations
t_test_b(rnorm(50),
         rnorm(15,1))

# or an alternative input format
t_test_b(outcome ~ group_variable,
         data = 
           data.frame(outcome = c(rnorm(50),
                                  rnorm(15,1)),
                      group_variable = rep(c("a","b"),
                                           c(50,15))))

bayesics documentation built on March 11, 2026, 5:07 p.m.