diff --git a/DESCRIPTION b/DESCRIPTION
index 54ef2c9..08fbd68 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -15,7 +15,8 @@ Imports:
     dplyr (>= 1.0.7),
     ggplot2 (>= 3.3.5),
     JuliaConnectoR (>= 1.0.0),
-    rlang (>= 0.4.11)
+    rlang (>= 0.4.11),
+    tidyr (>= 1.0.0)
 Encoding: UTF-8
 LazyData: true
 Roxygen: list(markdown = TRUE)
diff --git a/R/joint_significance_probability.R b/R/joint_significance_probability.R
new file mode 100644
index 0000000..0657b3e
--- /dev/null
+++ b/R/joint_significance_probability.R
@@ -0,0 +1,15 @@
+#' Compute the posterior probability of having at least one relevant factor
+#'
+#' @param fit An object of class anova_bnp_model.
+#' @return The corresponding probability.
+#' @export
+joint_significance_probability <- function(fit) {
+  prob <-
+    fit$gamma_post |>
+    dplyr::arrange(dplyr::pick(dplyr::starts_with("group"))) |>
+    dplyr::slice_head(n = 1) |>
+    tidyr::pivot_longer(-prob) |>
+    dplyr::summarise(prob = mean(prob) * all(!value))
+  out <- 1 - prob
+  return(out)
+}
diff --git a/extra/demo_bernoulli.R b/extra/demo_bernoulli.R
index f15602f..78a1166 100644
--- a/extra/demo_bernoulli.R
+++ b/extra/demo_bernoulli.R
@@ -19,3 +19,6 @@ group_codes(fit)
 
 # Show the posterior distribution of gamma
 gamma_post(fit)
+
+# Perform our Dunnet-like test
+joint_significance_probability(fit)
diff --git a/extra/demo_berpoi.R b/extra/demo_berpoi.R
index ce9d409..46aec54 100644
--- a/extra/demo_berpoi.R
+++ b/extra/demo_berpoi.R
@@ -19,3 +19,6 @@ group_codes(fit)
 
 # Show the posterior distribution of gamma
 gamma_post(fit)
+
+# Perform our Dunnet-like test
+joint_significance_probability(fit)
diff --git a/extra/demo_normal.R b/extra/demo_normal.R
index 1a726db..72234b6 100644
--- a/extra/demo_normal.R
+++ b/extra/demo_normal.R
@@ -19,3 +19,6 @@ group_codes(fit)
 
 # Show the posterior distribution of gamma
 gamma_post(fit)
+
+# Perform our Dunnet-like test
+joint_significance_probability(fit)