diff --git a/botorch/models/utils/assorted.py b/botorch/models/utils/assorted.py
index fa1e62f30a..fadab8da66 100644
--- a/botorch/models/utils/assorted.py
+++ b/botorch/models/utils/assorted.py
@@ -167,7 +167,7 @@ def check_min_max_scaling(
             msg = "contained"
         if msg is not None:
             msg = (
-                f"Input data is not {msg} to the unit cube. "
+                f"Data (input features) not {msg} to the unit cube. "
                 "Please consider min-max scaling the input data."
             )
             if raise_on_fail:
@@ -197,7 +197,7 @@ def check_standardization(
         if Y.shape[-2] <= 1:
             if mean_not_zero:
                 msg = (
-                    f"Data is not standardized (mean = {Ymean}). "
+                    f"Data (outcome observations) not standardized (mean = {Ymean}). "
                     "Please consider scaling the input to zero mean and unit variance."
                 )
                 if raise_on_fail:
@@ -208,7 +208,8 @@ def check_standardization(
             std_not_one = torch.abs(Ystd - 1).max() > atol_std
             if mean_not_zero or std_not_one:
                 msg = (
-                    f"Data is not standardized (std = {Ystd}, mean = {Ymean}). "
+                    "Data (outcome observations) not standardized "
+                    f"(std = {Ystd}, mean = {Ymean})."
                     "Please consider scaling the input to zero mean and unit variance."
                 )
                 if raise_on_fail:
diff --git a/test/models/utils/test_assorted.py b/test/models/utils/test_assorted.py
index 459893363e..21533f762f 100644
--- a/test/models/utils/test_assorted.py
+++ b/test/models/utils/test_assorted.py
@@ -158,14 +158,14 @@ def test_check_standardization(self):
         check_standardization(Y=y, raise_on_fail=True)
 
         # check nonzero mean for case where >= 2 observations per batch
-        msg_more_than_1_obs = r"Data is not standardized \(std ="
+        msg_more_than_1_obs = r"Data \(outcome observations\) not standardized \(std ="
         with self.assertWarnsRegex(InputDataWarning, msg_more_than_1_obs):
             check_standardization(Y=Yst + 1)
         with self.assertRaisesRegex(InputDataError, msg_more_than_1_obs):
             check_standardization(Y=Yst + 1, raise_on_fail=True)
 
         # check nonzero mean for case where < 2 observations per batch
-        msg_one_obs = r"Data is not standardized \(mean ="
+        msg_one_obs = r"Data \(outcome observations\) not standardized \(mean ="
         y = torch.ones((3, 1, 2), dtype=torch.float32)
         with self.assertWarnsRegex(InputDataWarning, msg_one_obs):
             check_standardization(Y=y)