diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index 3de6af8eef694..83b096cfc2d05 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -853,11 +853,6 @@ def test_groupby_multi_corner(df):
 
 def test_omit_nuisance(df):
     grouped = df.groupby("A")
-
-    result = grouped.mean()
-    expected = df.loc[:, ["A", "C", "D"]].groupby("A").mean()
-    tm.assert_frame_equal(result, expected)
-
     agged = grouped.agg(np.mean)
     exp = grouped.mean()
     tm.assert_frame_equal(agged, exp)
@@ -876,14 +871,43 @@ def test_omit_nuisance(df):
         grouped.agg(lambda x: x.sum(0, numeric_only=False))
 
 
-def test_omit_nuisance_sem(df):
-    # GH 38774 - sem should work with nuisance columns
+@pytest.mark.parametrize(
+    "agg_function",
+    ["max", "min"],
+)
+def test_keep_nuisance_agg(df, agg_function):
+    # GH 38815
+    grouped = df.groupby("A")
+    result = getattr(grouped, agg_function)()
+    expected = result.copy()
+    expected.loc["bar", "B"] = getattr(df.loc[df["A"] == "bar", "B"], agg_function)()
+    expected.loc["foo", "B"] = getattr(df.loc[df["A"] == "foo", "B"], agg_function)()
+    tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "agg_function",
+    ["sum", "mean", "prod", "std", "var", "median"],
+)
+def test_omit_nuisance_agg(df, agg_function):
+    # GH 38774, GH 38815
     grouped = df.groupby("A")
-    result = grouped.sem()
-    expected = df.loc[:, ["A", "C", "D"]].groupby("A").sem()
+    result = getattr(grouped, agg_function)()
+    expected = getattr(df.loc[:, ["A", "C", "D"]].groupby("A"), agg_function)()
     tm.assert_frame_equal(result, expected)
 
 
+def test_omit_nuisance_warnings(df):
+    # GH 38815
+    with tm.assert_produces_warning(
+        FutureWarning, filter_level="always", check_stacklevel=False
+    ):
+        grouped = df.groupby("A")
+        result = grouped.skew()
+        expected = df.loc[:, ["A", "C", "D"]].groupby("A").skew()
+        tm.assert_frame_equal(result, expected)
+
+
 def test_omit_nuisance_python_multiple(three_group):
     grouped = three_group.groupby(["A", "B"])