`RoBTT`

is used to estimate a Robust Bayesian
T-Test. The input either requires the vector of observations for
each group, `x1, x2`

, or the summary statistics (in case only
the `"normal"`

likelihood is used).

```
RoBTT(
x1 = NULL,
x2 = NULL,
mean1 = NULL,
mean2 = NULL,
sd1 = NULL,
sd2 = NULL,
N1 = NULL,
N2 = 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 = 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(),
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

- 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))`

.- 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)).- 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 methodology.

Generic `summary.RoBTT()`

, `print.RoBTT()`

, and `plot.RoBTT()`

functions are
provided to facilitate manipulation with the ensemble.

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)
}
```