`RoBTT`

is used to estimate a robust Bayesian
t-test or truncated Bayesian t-test (if `truncation`

is used).
The input either requires the vector of observations for
each group, `x1, x2`

, or the summary statistics (only if the normal
likelihood models are used).

```
RoBTT(
x1 = NULL,
x2 = NULL,
mean1 = NULL,
mean2 = NULL,
sd1 = NULL,
sd2 = NULL,
N1 = NULL,
N2 = NULL,
truncation = NULL,
prior_delta = prior(distribution = "cauchy", parameters = list(location = 0, scale =
sqrt(2)/2)),
prior_rho = prior(distribution = "beta", parameters = list(alpha = 1, beta = 1)),
prior_nu = if (is.null(truncation)) prior(distribution = "exp", parameters = list(rate
= 1)),
prior_delta_null = prior(distribution = "spike", parameters = list(location = 0)),
prior_rho_null = prior(distribution = "spike", parameters = list(location = 0.5)),
prior_nu_null = prior_none(),
prior_mu = NULL,
prior_sigma2 = NULL,
chains = 4,
iter = 10000,
warmup = 5000,
thin = 1,
parallel = FALSE,
control = set_control(),
convergence_checks = set_convergence_checks(),
save = "all",
seed = NULL,
silent = TRUE,
...
)
```

- x1
vector of observations of the first group

- x2
vector of observations of the second group

- mean1
mean of the first group

- mean2
mean of the first group

- sd1
standard deviation of the first group

- sd2
standard deviation of the first group

- N1
sample size of the first group

- N2
sample size of the first group

- truncation
an optional list specifying truncation applied to the data. Defaults to

`NULL`

, i.e., no truncation was applied and the full likelihood is applied. Alternative the truncation can be specified via a named list with:`"x"`

where

`x`

is a vector of two values specifying the lower and upper truncation points common across the groups`"x1"`

and`"x2"`

where

`x1`

is a vector of two values specifying the lower and upper truncation points for the first group and`x2`

is a vector of two values specifying the lower and upper truncation points for the second group.`"sigma"`

where

`sigma`

corresponds to the number of standard deviations from the common mean where the truncation points should be set.`"sigma1"`

and`"sigma2"`

where

`sigma1`

corresponds to the number of standard deviations from the mean of the first group where the truncation points should be set and`sigma2`

corresponds to the number of standard deviations from the mean of the second group where the truncation points should be set.

- prior_delta
prior distributions for the effect size

`delta`

parameter that will be treated as belonging to the alternative hypothesis. Defaults to`prior(distribution = "Cauchy", parameters = list(location = 0, scale = sqrt(2)/2))`

.- prior_rho
prior distributions for the precision allocation

`rho`

parameter that will be treated as belonging to the alternative hypothesis. Defaults to`prior(distribution = "beta", parameters = list(alpha = 1, beta = 1))`

.- prior_nu
prior distribution for the degrees of freedom + 2

`nu`

parameter that will be treated as belonging to the alternative hypothesis. Defaults to`prior(distribution = "exp", parameters = list(rate = 1))`

if no`truncation`

is specified. If`truncation`

is specified, the default is`NULL`

(i.e., use only normal likelihood).- prior_delta_null
prior distribution for the

`delta`

parameter that will be treated as belonging to the null hypothesis. Defaults to point distribution with location at 0 (`prior(distribution = "point", parameters = list(location = 0))`

).- prior_rho_null
prior distribution for the

`rho`

parameter that will be treated as belonging to the null hypothesis. Defaults to point distribution with location at 0.5 (`prior(distribution = "point", parameters = list(location = 0.5))`

).- prior_nu_null
prior distribution for the

`nu`

parameter that will be treated as belonging to the null hypothesis. Defaults to`prior_none`

( (i.e., normal likelihood)).- prior_mu
prior distribution for the grand mean parameter. Defaults to

`NULL`

which sets Jeffreys prior for the grand mean in case of no truncation or an unit Cauchy prior distributions for the grand mean in case of truncation (which greatly improves sampling efficiency).- prior_sigma2
prior distribution for the grand variance parameter. Defaults to

`NULL`

which sets Jeffreys prior for the variance in case of no truncation or an exponential prior distribution for the variance in case of truncation (which greatly improves sampling efficiency).- chains
a number of chains of the MCMC algorithm.

- iter
a number of sampling iterations of the MCMC algorithm. Defaults to

`10000`

, with a minimum of`4000`

.- warmup
a number of warmup iterations of the MCMC algorithm. Defaults to

`5000`

.- thin
a thinning of the chains of the MCMC algorithm. Defaults to

`1`

.- parallel
whether the individual models should be fitted in parallel. Defaults to

`FALSE`

. The implementation is not completely stable and might cause a connection error.- control
allows to pass control settings with the

`set_control()`

function. See`?set_control`

for options and default settings.- convergence_checks
automatic convergence checks to assess the fitted models, passed with

`set_convergence_checks()`

function. See`?set_convergence_checks`

for options and default settings.- save
whether all models posterior distributions should be kept after obtaining a model-averaged result. Defaults to

`"all"`

which does not remove anything. Set to`"min"`

to significantly reduce the size of final object, however, some model diagnostics and further manipulation with the object will not be possible.- seed
a seed to be set before model fitting, marginal likelihood computation, and posterior mixing for reproducibility of results. Defaults to

`NULL`

- no seed is set.- silent
whether all print messages regarding the fitting process should be suppressed. Defaults to

`TRUE`

. Note that`parallel = TRUE`

also suppresses all messages.- ...
additional arguments.

See Maier et al. (2022)
for more details
regarding the robust Bayesian t-test methodology and the corresponding
vignette (`vignette("Introduction_to_RoBTT", package = "RoBTT")`

).

See Godmann et al. (2024)
for more details
regarding the truncated Bayesian t-test methodology and the corresponding
vignette (`vignette("Truncated_t_test", package = "RoBTT")`

).

Generic `summary.RoBTT()`

, `print.RoBTT()`

, and `plot.RoBTT()`

functions are provided to facilitate manipulation with the ensemble.

Godmann HR, Bartoš F, Wagenmakers E (2024).
“A truncated t-test: Excluding outliers without biasing the Bayes factor.”
PsyArxiv Preprint.

Maier M, Bartoš F, Quintana DS, van den Bergh D, Marsman M, Ly A, Wagenmakers E (2022).
“Model-averaged Bayesian t-tests.”
doi:10.31234/osf.io/d5zwc
, PsyArxiv Preprint.

```
if (FALSE) {
# using the example data from Darwin
data("fertilization", package = "RoBTT")
fit <- RoBTT(
x1 = fertilization$Self,
x2 = fertilization$Crossed,
prior_delta = prior("cauchy", list(0, 1/sqrt(2))),
prior_rho = prior("beta", list(3, 3)),
seed = 1,
chains = 1,
warmup = 1000,
iter = 2000,
control = set_control(adapt_delta = 0.95)
)
# summary can provide many details about the model
summary(fit)
}
```