diff --git a/tests/scipy_stats_test.py b/tests/scipy_stats_test.py
index 83827db78..3b1ea21d5 100644
--- a/tests/scipy_stats_test.py
+++ b/tests/scipy_stats_test.py
@@ -885,7 +885,7 @@ class LaxBackedScipyStatsTests(jtu.JaxTestCase):
   )
   def testKde(self, inshape, dtype, outsize, weights, method, func):
     if method == "callable":
-      method = lambda kde: jax.numpy.power(kde.neff, -1./(kde.d+4))
+      method = lambda kde: kde.neff ** -1./(kde.d+4)
 
     def scipy_fun(dataset, points, w):
       w = np.abs(w) if weights else None
@@ -915,11 +915,12 @@ class LaxBackedScipyStatsTests(jtu.JaxTestCase):
       rng(inshape, dtype), rng(outshape, dtype), rng(inshape[-1:], dtype)]
     self._CheckAgainstNumpy(
         scipy_fun, lax_fun, args_maker, tol={
-            np.float32: 1e-2 if jtu.device_under_test() == "tpu" else 1e-3,
-            np.float64: 1e-14
+            np.float32: 2e-2 if jtu.device_under_test() == "tpu" else 1e-3,
+            np.float64: 3e-14
         })
     self._CompileAndCheck(
-        lax_fun, args_maker, rtol={np.float32: 3e-07, np.float64: 4e-15})
+        lax_fun, args_maker, rtol={np.float32: 3e-5, np.float64: 3e-14},
+        atol={np.float32: 3e-4, np.float64: 3e-14})
 
   @jtu.sample_product(
     shape=[(15,), (3, 15), (1, 12)],