diff --git a/arviz/stats/diagnostics.py b/arviz/stats/diagnostics.py
index 83e8e14d47..a7778953ec 100644
--- a/arviz/stats/diagnostics.py
+++ b/arviz/stats/diagnostics.py
@@ -994,7 +994,7 @@ def _multichain_statistics(ary):
     """
     ary = np.atleast_2d(ary)
     if _not_valid(ary, shape_kwargs=dict(min_draws=4, min_chains=1)):
-        return np.nan, np.nan, np.nan, np.nan, np.nan, np.nan, np.nan
+        return np.nan, np.nan, np.nan, np.nan, np.nan
     # ess mean
     ess_mean_value = _ess_mean(ary)
 
@@ -1033,8 +1033,6 @@ def _multichain_statistics(ary):
     return (
         mcse_mean_value,
         mcse_sd_value,
-        ess_mean_value,
-        ess_sd_value,
         ess_bulk_value,
         ess_tail_value,
         rhat_value,
diff --git a/arviz/stats/stats.py b/arviz/stats/stats.py
index 1df477f98b..f9494a34a4 100644
--- a/arviz/stats/stats.py
+++ b/arviz/stats/stats.py
@@ -1261,11 +1261,11 @@ def summary(
         circ_hdi_higher = circ_hdi.sel(hdi="higher", drop=True)
 
     if kind in ["all", "diagnostics"]:
-        mcse_mean, mcse_sd, ess_mean, ess_sd, ess_bulk, ess_tail, r_hat = xr.apply_ufunc(
-            _make_ufunc(_multichain_statistics, n_output=7, ravel=False),
+        mcse_mean, mcse_sd, ess_bulk, ess_tail, r_hat = xr.apply_ufunc(
+            _make_ufunc(_multichain_statistics, n_output=5, ravel=False),
             dataset,
             input_core_dims=(("chain", "draw"),),
-            output_core_dims=tuple([] for _ in range(7)),
+            output_core_dims=tuple([] for _ in range(5)),
         )
 
     # Combine metrics
@@ -1280,8 +1280,6 @@ def summary(
             f"hdi_{100 * (1 - alpha / 2):g}%",
             "mcse_mean",
             "mcse_sd",
-            "ess_mean",
-            "ess_sd",
             "ess_bulk",
             "ess_tail",
             "r_hat",
@@ -1294,8 +1292,6 @@ def summary(
                 hdi_higher,
                 mcse_mean,
                 mcse_sd,
-                ess_mean,
-                ess_sd,
                 ess_bulk,
                 ess_tail,
                 r_hat,
@@ -1304,7 +1300,7 @@ def summary(
             metrics_ = (mean, sd, hdi_lower, hdi_higher)
             metrics_names_ = metrics_names_[:4]
         elif kind == "diagnostics":
-            metrics_ = (mcse_mean, mcse_sd, ess_mean, ess_sd, ess_bulk, ess_tail, r_hat)
+            metrics_ = (mcse_mean, mcse_sd, ess_bulk, ess_tail, r_hat)
             metrics_names_ = metrics_names_[4:]
         metrics.extend(metrics_)
         metric_names.extend(metrics_names_)
@@ -1358,11 +1354,7 @@ def summary(
     elif round_to not in ("None", "none") and (fmt.lower() in ("long", "wide")):
         # Don't round xarray object by default (even with "none")
         decimals = {
-            col: 3
-            if col not in {"ess_mean", "ess_sd", "ess_bulk", "ess_tail", "r_hat"}
-            else 2
-            if col == "r_hat"
-            else 0
+            col: 3 if col not in {"ess_bulk", "ess_tail", "r_hat"} else 2 if col == "r_hat" else 0
             for col in summary_df.columns
         }
         summary_df = summary_df.round(decimals)
diff --git a/arviz/tests/base_tests/test_diagnostics.py b/arviz/tests/base_tests/test_diagnostics.py
index a843fd8356..135cd02e4b 100644
--- a/arviz/tests/base_tests/test_diagnostics.py
+++ b/arviz/tests/base_tests/test_diagnostics.py
@@ -426,16 +426,12 @@ def test_multichain_summary_array(self, draws, chains):
 
         mcse_mean_hat = mcse(ary, method="mean")
         mcse_sd_hat = mcse(ary, method="sd")
-        ess_mean_hat = ess(ary, method="mean")
-        ess_sd_hat = ess(ary, method="sd")
         ess_bulk_hat = ess(ary, method="bulk")
         ess_tail_hat = ess(ary, method="tail")
         rhat_hat = _rhat_rank(ary)
         (
             mcse_mean_hat_,
             mcse_sd_hat_,
-            ess_mean_hat_,
-            ess_sd_hat_,
             ess_bulk_hat_,
             ess_tail_hat_,
             rhat_hat_,
@@ -445,8 +441,6 @@ def test_multichain_summary_array(self, draws, chains):
                 (
                     mcse_mean_hat,
                     mcse_sd_hat,
-                    ess_mean_hat,
-                    ess_sd_hat,
                     ess_bulk_hat,
                     ess_tail_hat,
                     rhat_hat,
@@ -456,8 +450,6 @@ def test_multichain_summary_array(self, draws, chains):
                 (
                     mcse_mean_hat_,
                     mcse_sd_hat_,
-                    ess_mean_hat_,
-                    ess_sd_hat_,
                     ess_bulk_hat_,
                     ess_tail_hat_,
                     rhat_hat_,
@@ -466,8 +458,6 @@ def test_multichain_summary_array(self, draws, chains):
         else:
             assert_almost_equal(mcse_mean_hat, mcse_mean_hat_)
             assert_almost_equal(mcse_sd_hat, mcse_sd_hat_)
-            assert_almost_equal(ess_mean_hat, ess_mean_hat_)
-            assert_almost_equal(ess_sd_hat, ess_sd_hat_)
             assert_almost_equal(ess_bulk_hat, ess_bulk_hat_)
             assert_almost_equal(ess_tail_hat, ess_tail_hat_)
             if chains in (None, 1):
diff --git a/arviz/tests/base_tests/test_stats.py b/arviz/tests/base_tests/test_stats.py
index 34a1c9a7a2..4416ed7a70 100644
--- a/arviz/tests/base_tests/test_stats.py
+++ b/arviz/tests/base_tests/test_stats.py
@@ -240,8 +240,6 @@ def test_summary_wrong_group(centered_eight):
     "hdi_97%",
     "mcse_mean",
     "mcse_sd",
-    "ess_mean",
-    "ess_sd",
     "ess_bulk",
     "ess_tail",
     "r_hat",