diff --git a/R/loo_compare.R b/R/loo_compare.R
index fdf0e368..326fb9e7 100644
--- a/R/loo_compare.R
+++ b/R/loo_compare.R
@@ -327,7 +327,7 @@ loo_order_stat_check <- function(loos, ord) {
 
   if (max(elpd_diff) <= order_stat) {
     # flag warning if we suspect no model is theoretically better than the baseline
-    warning("Difference in performance potentially due to chance.",
+    warning("Difference in performance potentially due to chance. ",
             "See McLatchie and Vehtari (2023) for details.",
             call. = FALSE)
   }
diff --git a/tests/testthat/test_compare.R b/tests/testthat/test_compare.R
index 7f720b22..d21e0731 100644
--- a/tests/testthat/test_compare.R
+++ b/tests/testthat/test_compare.R
@@ -62,7 +62,8 @@ test_that("loo_compare throws appropriate warnings", {
   })
   expect_warning(
     loo_compare(w_list),
-    "Difference in performance potentially due to chance"
+    "Difference in performance potentially due to chance. See McLatchie and Vehtari (2023) for details.",
+    fixed = TRUE
   )
 
   w_list_short <- lapply(1:4, function(x) {