diff --git a/array_api_tests/test_statistical_functions.py b/array_api_tests/test_statistical_functions.py
index c88d0a53..390245c7 100644
--- a/array_api_tests/test_statistical_functions.py
+++ b/array_api_tests/test_statistical_functions.py
@@ -147,9 +147,13 @@ def test_prod(x, data):
                 _dtype = dh.default_float
     else:
         _dtype = dtype
-    # We ignore asserting the out dtype if what we expect is undefined
-    # See https://github.com/data-apis/array-api-tests/issues/106
-    if not isinstance(_dtype, _UndefinedStub):
+    if isinstance(_dtype, _UndefinedStub):
+        # If a default uint cannot exist (i.e. in PyTorch which doesn't support
+        # uint32 or uint64), we skip testing the output dtype.
+        # See https://github.com/data-apis/array-api-tests/issues/106
+        if _dtype in dh.uint_dtypes:
+            assert dh.is_int_dtype(out.dtype)  # sanity check
+    else:
         ph.assert_dtype("prod", x.dtype, out.dtype, _dtype)
     _axes = sh.normalise_axis(kw.get("axis", None), x.ndim)
     ph.assert_keepdimable_shape(
@@ -248,7 +252,14 @@ def test_sum(x, data):
                 _dtype = dh.default_float
     else:
         _dtype = dtype
-    ph.assert_dtype("sum", x.dtype, out.dtype, _dtype)
+    if isinstance(_dtype, _UndefinedStub):
+        # If a default uint cannot exist (i.e. in PyTorch which doesn't support
+        # uint32 or uint64), we skip testing the output dtype.
+        # See https://github.com/data-apis/array-api-tests/issues/160
+        if _dtype in dh.uint_dtypes:
+            assert dh.is_int_dtype(out.dtype)  # sanity check
+    else:
+        ph.assert_dtype("sum", x.dtype, out.dtype, _dtype)
     _axes = sh.normalise_axis(kw.get("axis", None), x.ndim)
     ph.assert_keepdimable_shape(
         "sum", x.shape, out.shape, _axes, kw.get("keepdims", False), **kw