diff --git a/python_tests/test_cached_extra_study_property.py b/python_tests/test_cached_extra_study_property.py
new file mode 100644
index 00000000..2ab8395a
--- /dev/null
+++ b/python_tests/test_cached_extra_study_property.py
@@ -0,0 +1,177 @@
+from unittest import TestCase
+import warnings
+
+import optuna
+from optuna import create_trial
+from optuna.distributions import UniformDistribution
+from optuna.exceptions import ExperimentalWarning
+from optuna.trial import TrialState
+
+from optuna_dashboard._cached_extra_study_property import _CachedExtraStudyProperty
+
+
+class _CachedExtraStudyPropertyTestCase(TestCase):
+    def setUp(self) -> None:
+        optuna.logging.set_verbosity(optuna.logging.ERROR)
+        warnings.simplefilter("ignore", category=ExperimentalWarning)
+
+    def test_same_distributions(self) -> None:
+        distributions = [
+            {
+                "x0": UniformDistribution(low=0, high=10),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+            {
+                "x0": UniformDistribution(low=0, high=10),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+        ]
+        params = [
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+        ]
+        trials = [
+            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
+            for d, p in zip(distributions, params)
+        ]
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+
+        self.assertEqual(len(cached_extra_study_property.intersection), 2)
+        self.assertEqual(len(cached_extra_study_property.union), 2)
+
+    def test_different_distributions(self) -> None:
+        distributions = [
+            {
+                "x0": UniformDistribution(low=0, high=10),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+            {
+                "x0": UniformDistribution(low=0, high=5),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+        ]
+        params = [
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+        ]
+        trials = [
+            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
+            for d, p in zip(distributions, params)
+        ]
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+
+        self.assertEqual(len(cached_extra_study_property.intersection), 1)
+        self.assertEqual(len(cached_extra_study_property.union), 3)
+
+    def test_dynamic_search_space(self) -> None:
+        distributions = [
+            {
+                "x0": UniformDistribution(low=0, high=10),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+            {
+                "x0": UniformDistribution(low=0, high=5),
+            },
+            {
+                "x0": UniformDistribution(low=0, high=10),
+                "x1": UniformDistribution(low=0, high=10),
+            },
+        ]
+        params = [
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+            {
+                "x0": 0.5,
+            },
+            {
+                "x0": 0.5,
+                "x1": 0.5,
+            },
+        ]
+        trials = [
+            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
+            for d, p in zip(distributions, params)
+        ]
+
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+
+        self.assertEqual(len(cached_extra_study_property.intersection), 0)
+        self.assertEqual(len(cached_extra_study_property.union), 3)
+
+    def test_no_intermediate_value(self) -> None:
+        intermediate_values = [
+            {},
+            {},
+        ]
+        trials = [
+            create_trial(
+                state=TrialState.COMPLETE,
+                value=0,
+                distributions={"x0": UniformDistribution(low=0, high=10)},
+                intermediate_values=iv,
+                params={"x0": 0.5},
+            )
+            for iv in intermediate_values
+        ]
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+        self.assertFalse(cached_extra_study_property.has_intermediate_values)
+
+    def test_some_trials_has_no_intermediate_value(self) -> None:
+        intermediate_values = [
+            {0: 0.3, 1: 1.2},
+            {},
+            {0: 0.3, 1: 1.2},
+        ]
+        trials = [
+            create_trial(
+                state=TrialState.COMPLETE,
+                value=0,
+                distributions={"x0": UniformDistribution(low=0, high=10)},
+                intermediate_values=iv,
+                params={"x0": 0.5},
+            )
+            for iv in intermediate_values
+        ]
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+        self.assertTrue(cached_extra_study_property.has_intermediate_values)
+
+    def test_all_trials_has_intermediate_value(self) -> None:
+        intermediate_values = [{0: 0.3, 1: 1.2}, {0: 0.3, 1: 1.2}]
+        trials = [
+            create_trial(
+                state=TrialState.COMPLETE,
+                value=0,
+                distributions={"x0": UniformDistribution(low=0, high=10)},
+                intermediate_values=iv,
+                params={"x0": 0.5},
+            )
+            for iv in intermediate_values
+        ]
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+        self.assertTrue(cached_extra_study_property.has_intermediate_values)
+
+    def test_no_trials(self) -> None:
+        trials = []
+        cached_extra_study_property = _CachedExtraStudyProperty()
+        cached_extra_study_property.update(trials)
+        self.assertFalse(cached_extra_study_property.has_intermediate_values)
diff --git a/python_tests/test_search_space.py b/python_tests/test_search_space.py
deleted file mode 100644
index df7fe9e2..00000000
--- a/python_tests/test_search_space.py
+++ /dev/null
@@ -1,115 +0,0 @@
-from unittest import TestCase
-import warnings
-
-import optuna
-from optuna import create_trial
-from optuna.distributions import UniformDistribution
-from optuna.exceptions import ExperimentalWarning
-from optuna.trial import TrialState
-
-from optuna_dashboard._search_space import _SearchSpace
-
-
-class SearchSpaceTestCase(TestCase):
-    def setUp(self) -> None:
-        optuna.logging.set_verbosity(optuna.logging.ERROR)
-        warnings.simplefilter("ignore", category=ExperimentalWarning)
-
-    def test_same_distributions(self) -> None:
-        distributions = [
-            {
-                "x0": UniformDistribution(low=0, high=10),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-            {
-                "x0": UniformDistribution(low=0, high=10),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-        ]
-        params = [
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-        ]
-        trials = [
-            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
-            for d, p in zip(distributions, params)
-        ]
-        search_space = _SearchSpace()
-        search_space.update(trials)
-
-        self.assertEqual(len(search_space.intersection), 2)
-        self.assertEqual(len(search_space.union), 2)
-
-    def test_different_distributions(self) -> None:
-        distributions = [
-            {
-                "x0": UniformDistribution(low=0, high=10),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-            {
-                "x0": UniformDistribution(low=0, high=5),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-        ]
-        params = [
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-        ]
-        trials = [
-            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
-            for d, p in zip(distributions, params)
-        ]
-        search_space = _SearchSpace()
-        search_space.update(trials)
-
-        self.assertEqual(len(search_space.intersection), 1)
-        self.assertEqual(len(search_space.union), 3)
-
-    def test_dynamic_search_space(self) -> None:
-        distributions = [
-            {
-                "x0": UniformDistribution(low=0, high=10),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-            {
-                "x0": UniformDistribution(low=0, high=5),
-            },
-            {
-                "x0": UniformDistribution(low=0, high=10),
-                "x1": UniformDistribution(low=0, high=10),
-            },
-        ]
-        params = [
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-            {
-                "x0": 0.5,
-            },
-            {
-                "x0": 0.5,
-                "x1": 0.5,
-            },
-        ]
-        trials = [
-            create_trial(state=TrialState.COMPLETE, value=0, distributions=d, params=p)
-            for d, p in zip(distributions, params)
-        ]
-        search_space = _SearchSpace()
-        search_space.update(trials)
-
-        self.assertEqual(len(search_space.intersection), 0)
-        self.assertEqual(len(search_space.union), 3)