diff --git a/tests/integration/test_property.py b/tests/integration/test_property.py
new file mode 100644
index 00000000..054ddabd
--- /dev/null
+++ b/tests/integration/test_property.py
@@ -0,0 +1,59 @@
+"""Tests that are common to all properties."""
+
+import numpy as np
+import pytest
+
+from sdmetrics.demos import load_demo
+from sdmetrics.reports.multi_table import _properties as multi_table_properties
+from sdmetrics.reports.single_table import _properties as single_table_properties
+
+REAL_DATA_ST, SYNTHETIC_DATA_ST, METADATA_ST = load_demo(modality='single_table')
+REAL_DATA_MT, SYNTHETIC_DATA_MT, METADATA_MT = load_demo(modality='multi_table')
+SINGLE_TABLE_PROPERTIES = [
+    property
+    for property_name, property in vars(single_table_properties).items()
+    if property_name != 'BaseSingleTableProperty' and isinstance(property, type)
+]
+MULTI_TABLE_PROPERTIES = [
+    property
+    for property_name, property in vars(multi_table_properties).items()
+    if property_name != 'BaseMultiTableProperty' and isinstance(property, type)
+]
+
+
+@pytest.mark.parametrize('property', SINGLE_TABLE_PROPERTIES)
+def test_shuffling_data_single_table(property):
+    """Test the property score is the same when shuffling the data for single-table."""
+    # Setup
+    property_instance = property()
+
+    # Run
+    score = property_instance.get_score(REAL_DATA_ST, SYNTHETIC_DATA_ST, METADATA_ST)
+    score_shuffled = property_instance.get_score(
+        REAL_DATA_ST.sample(frac=1), SYNTHETIC_DATA_ST.sample(frac=1), METADATA_ST
+    )
+
+    # Assert
+    assert score_shuffled == score
+
+
+@pytest.mark.parametrize('property', MULTI_TABLE_PROPERTIES)
+def test_shuffling_data_multi_table(property):
+    """Test the property score is the same when shuffling the data for multi-table."""
+    # Setup
+    property_instance = property()
+    real_data_shuffled = {
+        table_name: table.sample(frac=1) for table_name, table in REAL_DATA_MT.items()
+    }
+    synthetic_data_shuffled = {
+        table_name: SYNTHETIC_DATA_MT[table_name].sample(frac=1) for table_name in SYNTHETIC_DATA_MT
+    }
+
+    # Run
+    score = property_instance.get_score(REAL_DATA_MT, SYNTHETIC_DATA_MT, METADATA_MT)
+    score_shuffled = property_instance.get_score(
+        real_data_shuffled, synthetic_data_shuffled, METADATA_MT
+    )
+
+    # Assert
+    assert np.isclose(score, score_shuffled, rtol=1e-12)