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Perform Frequentist and Bayesian t-tests with Effect Size Estimation

Source: R/t_test_all.r
t_test_all.Rd

This function performs frequentist and Bayesian t-tests, with options for effect size estimation, confidence intervals, Bayesian credible intervals, probability of direction (pd), and Bayes factors.

Usage

t_test_all(
  x,
  y = NULL,
  var.label = c("x", "y"),
  paired = F,
  var.equal = FALSE,
  mu = 0,
  ci = c("freq", "bayes_central", "bayes_hdi"),
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  alpha = 0.05,
  pd = FALSE,
  bf = FALSE,
  cor = TRUE,
  mean_x_EAP = FALSE,
  mean_x_MAP = FALSE,
  mean_x_MED = FALSE,
  diff_EAP = FALSE,
  diff_MAP = FALSE,
  diff_MED = FALSE,
  cohens_d = NULL,
  cohens_d_EAP = FALSE,
  cohens_d_MAP = FALSE,
  cohens_d_MED = FALSE,
  cohens_dz = TRUE,
  cohens_dz_EAP = FALSE,
  cohens_dz_MAP = FALSE,
  cohens_dz_MED = FALSE,
  rscale_est = Inf,
  rscale_bf = "medium",
  iterations = 10000,
  map_density_n = 512,
  verbose = TRUE,
  detailed = FALSE,
  fullbayes = FALSE
)

Arguments

x

A numeric vector representing the first sample.

y

An optional numeric vector representing the second sample. If NULL, a one-sample t-test is performed (default: NULL).

var.label

A character vector of length two specifying labels for x and y.

paired

Logical. If TRUE, a paired t-test is performed (default: FALSE).

var.equal

Logical. If TRUE, the two-sample t-test assumes equal variances (default: FALSE).

mu

A numeric value specifying the null hypothesis mean difference.

ci

Character. Specifies the type of confidence or credible interval: "freq" (frequentist confidence interval), "bayes_central" (Bayesian central credible interval), or "bayes_hdi" (highest density interval based on the posterior distribution) (default: "freq").

alternative

Character. Specifies the alternative hypothesis for the frequentist test: "two.sided", "less", or "greater" (default: "two.sided").

conf.level

Numeric. The confidence level for frequentist intervals or credibility level for Bayesian intervals (default: 0.95).

alpha

Numeric. Significance level. Defaults to 0.05.

pd

Logical. If TRUE, computes the probability of direction (pd) based on posterior distributions (default: FALSE).

bf

Logical. If TRUE, computes Bayes factors for the presence of a difference versus the null hypothesis (default: FALSE).

cor

Logical. If TRUE, computes Pearson correlation for paired samples.

mean_x_EAP

Logical. If TRUE, computes the expected a posteriori (EAP) estimate of the mean of x (default: FALSE).

mean_x_MAP

Logical. If TRUE, computes the maximum a posteriori (MAP) estimate of the mean of x (default: FALSE).

mean_x_MED

Logical. If TRUE, computes the median of the posterior distribution (MED) for the mean of x (default: FALSE).

diff_EAP

Logical. If TRUE, computes the expected a posteriori (EAP) estimate of the mean difference (default: FALSE).

diff_MAP

Logical. If TRUE, computes the maximum a posteriori (MAP) estimate of the mean difference (default: FALSE).

diff_MED

Logical. If TRUE, computes the median of the posterior distribution (MED) for the mean difference (default: FALSE).

cohens_d

Logical. If TRUE, computes Cohen's d for independent samples.

cohens_d_EAP

Logical. If TRUE, computes the expected a posteriori (EAP) estimate of Cohen's d (default: FALSE).

cohens_d_MAP

Logical. If TRUE, computes the maximum a posteriori (MAP) estimate of Cohen's d (default: FALSE).

cohens_d_MED

Logical. If TRUE, computes the median of the posterior distribution (MED) for Cohen's d (default: FALSE).

cohens_dz

Logical. If TRUE, computes Cohen's dz for paired samples.

cohens_dz_EAP

Logical. If TRUE, computes the expected a posteriori (EAP) estimate of Cohen's dz (default: FALSE).

cohens_dz_MAP

Logical. If TRUE, computes the maximum a posteriori (MAP) estimate of Cohen's dz (default: FALSE).

cohens_dz_MED

Logical. If TRUE, computes the median of the posterior distribution (MED) for Cohen's dz (default: FALSE).

rscale_est

Numeric or character. Specifies the Cauchy prior scale for Bayesian estimation of the posterior distribution. Options: "ultrawide", "wide", "medium", or a positive real number (default: Inf). Passed to BayesFactor::ttestBF().

rscale_bf

Numeric or character. Specifies the Cauchy prior scale for Bayes factor calculation. Options: "ultrawide", "wide", "medium", or a positive real number (default: "medium"). Passed to BayesFactor::ttestBF().

iterations

Integer. Number of MCMC iterations for Bayesian estimation.

map_density_n

Integer. Number of bins for MAP density estimation.

verbose

Logical. If TRUE, prints additional messages.

detailed

Logical. Whether to return detailed results (TRUE) or minimal output (FALSE, default).

fullbayes

Logical. Whether to show only Bayesian results (TRUE) or both frequentist and Bayesian results (FALSE, default).

Value

A data frame containing test statistics, effect sizes, confidence intervals, and Bayesian estimates.

Examples

set.seed(123)
x <- rnorm(30,0, 1)
y <- x + rnorm(30,0.5, 1)

# Welch's t-test with effect size estimation
t_test_all(x, y)
#> 
#> -----------------------------------------------
#> Two-sample t-test
#> (Welch's method applied in the frequentist analysis)
#> -----------------------------------------------
#> H0: mu_x - mu_y = 0, H1: mu_x - mu_y != 0
#> 
#> n_x = 30, n_y = 30
#> 
#> t = -2.416334, df = 56.0632, p = 0.01895871
#> r_(x,y) = NA
#> -----------------------------------------------
#> Mean of x = -0.04710376
#> Mean of y = 0.6312346
#> -----------------------------------------------
#> Diff (x-y) = -0.6783383
#> CI = [-1.240695, -0.1159818]
#> -----------------------------------------------
#> Cohen's d = -0.6238948
#> CI = [-1.13992, -0.1027481]
#> -----------------------------------------------
#> Note:
#> The CI represents the frequentist confidence interval.
#> (Confidence level = 0.95)

# Welch's t-test with Bayesian independent t-test (Bayes factor and pd)
# and 95% highest density intervals
t_test_all(x, y, diff_MAP = TRUE, cohens_d_MAP = TRUE,
           bf = TRUE, pd = TRUE, ci = "bayes_hdi", rscale_bf = "medium")
#> 
#> -----------------------------------------------
#> Two-sample t-test
#> (Welch's method applied in the frequentist analysis)
#> -----------------------------------------------
#> H0: mu_x - mu_y = 0, H1: mu_x - mu_y != 0
#> 
#> n_x = 30, n_y = 30
#> 
#> t = -2.416334, df = 56.0632, p = 0.01895871
#> r_(x,y) = NA
#> pd = 0.9902
#> 
#> BF_10 = 2.869844 in favor of H1 (anecdotal)
#> rscale = 0.7071068
#> Note: BF is sensitive to the rscale parameter of the prior.
#> -----------------------------------------------
#> Mean of x = -0.04710376
#> Mean of y = 0.6312346
#> -----------------------------------------------
#> Diff (x-y) = -0.6783383
#> MAP of diff = -0.6916485
#> CI = [-1.22348, -0.1196791]
#> -----------------------------------------------
#> Cohen's d = -0.6238948
#> MAP of delta = -0.6500264
#> CI = [-1.142792, -0.1035713]
#> -----------------------------------------------
#> Note:
#> The CI represents the Bayesian posterior highest density interval.
#> (Probability = 0.95)
#> Note:
#> The posterior was approximated using 10000 samples,
#> given prior rscale = Inf.

# Paired t-test with effect size estimation
t_test_all(x, y, paired = TRUE)
#> 
#> -----------------------------------------------
#> Paired t-test
#> -----------------------------------------------
#> H0: mu_x - mu_y = 0, H1: mu_x - mu_y != 0
#> 
#> N = 30 (pairs)
#> 
#> t = -4.448914, df = 29, p = 0.0001169206
#> r_(x,y) = 0.7175137
#> -----------------------------------------------
#> Mean of x = -0.04710376
#> Mean of y = 0.6312346
#> -----------------------------------------------
#> Diff (x-y) = -0.6783383
#> CI = [-0.9901802, -0.3664964]
#> -----------------------------------------------
#> Cohen's d_z = -0.8122568
#> CI = [-1.224918, -0.3995955]
#> -----------------------------------------------
#> Note:
#> The CI represents the frequentist confidence interval.
#> (Confidence level = 0.95)

# Paired t-test with Bayesian paired t-test (Bayes factor and pd)
# and 95% central credible intervals
t_test_all(x, y, paired = TRUE, diff_MAP = TRUE, cohens_dz_MAP = TRUE,
           bf = TRUE, pd = TRUE, ci = "bayes_central", rscale_bf = "medium")
#> 
#> -----------------------------------------------
#> Paired t-test
#> -----------------------------------------------
#> H0: mu_x - mu_y = 0, H1: mu_x - mu_y != 0
#> 
#> N = 30 (pairs)
#> 
#> t = -4.448914, df = 29, p = 0.0001169206
#> r_(x,y) = 0.7175137
#> pd = 0.9999
#> 
#> BF_10 = 225.371 in favor of H1 (extreme)
#> rscale = 0.7071068
#> Note: BF is sensitive to the rscale parameter of the prior.
#> -----------------------------------------------
#> Mean of x = -0.04710376
#> Mean of y = 0.6312346
#> -----------------------------------------------
#> Diff (x-y) = -0.6783383
#> MAP of diff = -0.6957117
#> CI = [-0.9809708, -0.3694457]
#> -----------------------------------------------
#> Cohen's d_z = -0.8122568
#> MAP of delta_z = -0.8325525
#> CI = [-1.231449, -0.4140352]
#> -----------------------------------------------
#> Note:
#> The CI represents the Bayesian central posterior interval.
#> (Probability = 0.95)
#> Note:
#> The posterior was approximated using 10000 samples,
#> given prior rscale = Inf.