-`parameters` which is a numeric vector of values for the parameters under investigation (here only $\delta$ and thus`parameters` is of length $1$ with`parameters[1] = delta`).

In our simple example, it boils down to:

-`indices1` which is an integer vector of size $n_x$ storing the indices of the data points belonging to the first sample in the current permuted version of the data.

A[**flipr**](https://permaverse.github.io/flipr/)-compatible version of the t-statistic is already implemented in[**flipr**](https://permaverse.github.io/flipr/) and ready to use as`stat_student` or its alias`stat_t`. Here, we are only going to use the $t$-statistic for this example, but we might be willing to use more than one statistic for a parameter or we might have several parameters under investigation, each one of them requiring a different test statistic. We therefore group all the test statistics that we need into a single list:

Finally we need to define a named list that tells[**flipr**](https://permaverse.github.io/flipr/) which test statistics among the ones declared in the`stat_functions` list should be used for each parameter under investigation. This is used to determine bounds on each parameter for the plausibility function. This list, often termed`stat_assignments`, should therefore have as many elements as there are parameters under investigation. Each element should be named after a parameter under investigation and should list the indices corresponding to the test statistics that should be used for that parameter in`stat_functions`. In our example, it boils down to:

In[**flipr**](https://permaverse.github.io/flipr/), the plausibility function is implemented as an[R6Class](https://r6.r-lib.org/reference/R6Class.html) object. Assume we observed two samples stored in lists`x` and`y`, we therefore instantiate a plausibility function for this data as follows:

```{r, eval=FALSE}

We use the`$get_value()` method for this purpose, which essentially evaluates the permutation $p$-value of a two-sided test by default:

```{r, eval=FALSE}

Let us instantiate the plausibility for the data simulated under scenario A:

```{r, eval=FALSE}

We can compute a point estimate of the mean difference and store it inside the plausibility function class via the`$set_point_estimate()` method:

```{r, eval=FALSE}

The computed value can then be accessed via the`$point_estimate` field:

or by displaying the list of parameters under investigation which is stored in the`$parameters` field.

```{r, eval=FALSE}

In this list, one can see that parameters come with an unknown range by default. We can however compute their bounds by defining a maximum confidence level through the`$set_max_conf_level()` method of the`PlausibilityFunction` class. When a plausibility function is instantiated, the default value for the`$max_conf_level` field is $0.99$. To set parameter bounds automatically, use the`$set_parameter_bounds()` method:

```{r, eval=FALSE}

We can now inspect again the list of parameters under investigation to see the updated bounds:

Once bounds are known for each parameter, it becomes possible to generate a grid for later evaluating the plausibility function. This is done through the`$set_grid()` method as follows:

```{r, eval=FALSE}

We can then take a look at the newly created grid:

```{r, eval=FALSE}

We can go a step further and evaluate the plausibility function on that grid using the`$evaluate_grid()` method as follows:

```{r, eval=FALSE}

Again, we can then take a look at the updated grid:

We can add to this grid the p-value computed from the t-test assuming normality of the data:

One can obtain a point estimate of the parameter under investigation by

searching which value of the parameter reaches the maximum of the

$p$-value function (which is $1$). One can use the`$set_point_estimate()` method to do that:

```{r, eval=FALSE}

The computed point estimate is then stored in the`$point_estimate` field and can be retrieved as:

investigation by searching for which values of the parameter the

$p$-value function remains above a pre-specified significance level

$\alpha$. This is achieved via the`$set_parameter_bounds()` method:

```{r, eval=FALSE}

function as it boils down to evaluating the $p$-value function in

$\delta_0$. Hence we can for instance test $H_0: \delta = 3$ against the

alternative $H_1: \delta \ne 3$ using the following piece of code:

```{r, include = FALSE}

bibliography:references.bib

```{r, include = FALSE}