diff --git a/R/parallelization-vignette.R b/R/parallelization-vignette.R
new file mode 100644
index 0000000..be3c291
--- /dev/null
+++ b/R/parallelization-vignette.R
@@ -0,0 +1,91 @@
+## code to prepare `parallelization-vignette` dataset goes here
+
+# Setup -------------------------------------------------------------------
+
+library(flipr)
+library(future)
+library(parallel)
+library(progressr)
+library(tictoc)
+
+ngrid_in <- 50L
+nperms <- 5000
+n1 <- 10
+set.seed(1234)
+x <- rnorm(n1, mean = 1, sd = 1)
+y <- rnorm(n1, mean = 4, sd = 1)
+
+null_spec <- function(y, parameters) {
+  purrr::map(y, ~ .x - parameters[1])
+}
+
+stat_functions <- list(stat_t)
+
+stat_assignments <- list(delta = 1)
+
+# Inference on the mean without parallelization --------------------------------
+
+pf <- PlausibilityFunction$new(
+  null_spec = null_spec,
+  stat_functions = stat_functions,
+  stat_assignments = stat_assignments,
+  x, y
+)
+
+pf$set_point_estimate(mean(y) - mean(x))
+
+pf$set_nperms(nperms)
+pf$set_parameter_bounds(
+  point_estimate = pf$point_estimate,
+  conf_level = pf$max_conf_level
+)
+
+pf$set_grid(
+  parameters = pf$parameters,
+  npoints = ngrid_in
+)
+
+tic()
+pf$evaluate_grid(grid = pf$grid)
+time_without_parallelization <- toc()$callback_msg
+
+# Inference on the mean with parallelization -----------------------------------
+
+ncores <- 4
+plan(multisession, workers = ncores)
+cl <- makeCluster(ncores)
+setDefaultCluster(cl)
+progressr::handlers(global = TRUE)
+
+pf <- PlausibilityFunction$new(
+  null_spec = null_spec,
+  stat_functions = stat_functions,
+  stat_assignments = stat_assignments,
+  x, y
+)
+
+pf$set_point_estimate(mean(y) - mean(x))
+
+pf$set_nperms(nperms)
+pf$set_parameter_bounds(
+  point_estimate = pf$point_estimate,
+  conf_level = pf$max_conf_level
+)
+
+pf$set_grid(
+  parameters = pf$parameters,
+  npoints = ngrid_in
+)
+
+tic()
+pf$evaluate_grid(grid = pf$grid)
+time_with_parallelization <- toc()$callback_msg
+
+df_parallelization <- list(
+  delta = pf$grid$delta,
+  time_par = time_with_parallelization,
+  time_without_par = time_without_parallelization
+)
+
+saveRDS(df_parallelization, "data-raw/df_parallelization.rds")
+
diff --git a/R/sysdata.rda b/R/sysdata.rda
index b998cc9..2270f22 100644
Binary files a/R/sysdata.rda and b/R/sysdata.rda differ
diff --git a/data-raw/build-sysdata.R b/data-raw/build-sysdata.R
index b54d5a6..16f9918 100644
--- a/data-raw/build-sysdata.R
+++ b/data-raw/build-sysdata.R
@@ -6,11 +6,13 @@ df_mean <- readRDS("data-raw/df_mean.rds")
 df_sd <- readRDS("data-raw/df_sd.rds")
 df_fisher <- readRDS("data-raw/df_fisher.rds")
 df_tippett <- readRDS("data-raw/df_tippett.rds")
+df_parallelization <- readRDS("data-raw/df_parallelization.rds")
 usethis::use_data(
   alpha_estimates,
   pfa, pfb, pfc,
   df_mean, df_sd,
   df_fisher, df_tippett,
+  df_parallelization,
   overwrite = TRUE,
   internal = TRUE
 )
diff --git a/data-raw/df_parallelization.rds b/data-raw/df_parallelization.rds
new file mode 100644
index 0000000..0c46cc2
Binary files /dev/null and b/data-raw/df_parallelization.rds differ
diff --git a/vignettes/parallelization.Rmd b/vignettes/parallelization.Rmd
index 69b6a74..7ae24ed 100644
--- a/vignettes/parallelization.Rmd
+++ b/vignettes/parallelization.Rmd
@@ -12,18 +12,64 @@ knitr::opts_chunk$set(
   collapse = TRUE,
   comment = "#>"
 )
+load("../R/sysdata.rda")
+time_without_parallelization <- df_parallelization$time_without_par
+time_with_parallelization <- df_parallelization$time_par
 ```
 
 The [**flipr**](https://lmjl-alea.github.io/flipr/) package uses functions contained in the [**furrr**](https://future.futureverse.org/index.html) package for parallel processing. The setting of parallelization has to be done on the user side. We illustrate here how to achieve asynchronous evaluation. We use the [**future**](https://future.futureverse.org/index.html) package to set the plan, the **parallel** package to define a default cluster, and the [**progressr**](https://progressr.futureverse.org/index.html) package to report progress updates.
 
-By setting the desired number of cores, we define the number of background R sessions that will be used to evaluate expressions in parallel. This number is used to set the multisession plan with the function `future::plan()` and to define a default cluster with `parallel::setDefaultCluster()`. Then, to enable the visualization of evaluation progress, we can put the code in the `progressr::with_progress()` function, or more simply set it for all the following code with the `progressr::handlers()` function. After these settings, [**flipr**](https://lmjl-alea.github.io/flipr/) functions can be used, as shown in this example.
-
 ```{r setup}
 library(flipr)
 ```
 
+## Computation without parallel processing
+
+To show the benefit of parallel processing, we compare here the processing times necessary to evaluate a grid with a plausibility function. First, here is the computation without parallelization.
+
+```{r, eval=FALSE}
+set.seed(1234)
+x <- rnorm(10, 1, 1)
+y <- rnorm(10, 4, 1)
+
+null_spec <- function(y, parameters) {
+  purrr::map(y, ~ .x - parameters[1])
+}
+stat_functions <- list(stat_t)
+stat_assignments <- list(delta = 1)
+
+pf <- PlausibilityFunction$new(
+  null_spec = null_spec,
+  stat_functions = stat_functions,
+  stat_assignments = stat_assignments,
+  x, y
+)
+
+pf$set_point_estimate(mean(y) - mean(x), overwrite = TRUE)
+pf$set_parameter_bounds(
+  point_estimate = pf$point_estimate, 
+  conf_level = pf$max_conf_level
+)
+pf$set_grid(
+  parameters = pf$parameters, 
+  npoints = 50L
+)
+
+tictoc::tic()
+pf$evaluate_grid(grid = pf$grid)
+time_without_parallelization <- tictoc::toc()
+```
+
+```{r}
+time_without_parallelization 
+```
+
+## Computation with parallel processing
+
+By setting the desired number of cores, we define the number of background R sessions that will be used to evaluate expressions in parallel. This number is used to set the multisession plan with the function `future::plan()` and to define a default cluster with `parallel::setDefaultCluster()`. Then, to enable the visualization of evaluation progress, we can put the code in the `progressr::with_progress()` function, or more simply set it for all the following code with the `progressr::handlers()` function. After these settings, [**flipr**](https://lmjl-alea.github.io/flipr/) functions can be used, as shown in this example.
+
 ```{r, eval=FALSE}
-ncores <- 3
+ncores <- 4
 future::plan(multisession, workers = ncores)
 cl <- parallel::makeCluster(ncores)
 parallel::setDefaultCluster(cl)
@@ -55,13 +101,22 @@ pf$set_grid(
   parameters = pf$parameters, 
   npoints = 50L
 )
+
+tictoc::tic()
 pf$evaluate_grid(grid = pf$grid)
+time_with_parallelization <- tictoc::toc()
 
 parallel::stopCluster(cl)
 ```
 
 It is good practice to shut down the workers with the `parallel::stopCluster()` function at the end of the code.
 
+```{r}
+time_with_parallelization
+```
+
+This experiment proves that we can save a lot of computation time when using parallel processing, as we gained approximately 33 seconds in this example to evaluate the plausibility function.
+
 Finally, to return to a sequential plan with no progress updates, the following code can be used.
 
 ```{r, eval=FALSE}