diff --git a/arviz/plots/backends/bokeh/khatplot.py b/arviz/plots/backends/bokeh/khatplot.py
index c09ff99f36..a424680a16 100644
--- a/arviz/plots/backends/bokeh/khatplot.py
+++ b/arviz/plots/backends/bokeh/khatplot.py
@@ -21,7 +21,7 @@ def plot_khat(
     figsize,
     xdata,
     khats,
-    sample_size,
+    good_k,
     kwargs,
     threshold,
     coord_labels,
@@ -55,10 +55,8 @@ def plot_khat(
     if hlines_kwargs is None:
         hlines_kwargs = {}
 
-    if sample_size is None:
+    if good_k is None:
         good_k = 0.7
-    else:
-        good_k = min(1 - 1 / np.log10(sample_size), 0.7)
 
     hlines_kwargs.setdefault("hlines", [0, good_k, 1])
 
@@ -137,7 +135,7 @@ def plot_khat(
     xmax = len(khats)
 
     if show_bins:
-        bin_edges = np.array([ymin, threshold, 1, ymax])
+        bin_edges = np.array([ymin, good_k, 1, ymax])
         bin_edges = bin_edges[(bin_edges >= ymin) & (bin_edges <= ymax)]
         hist, _, _ = histogram(khats, bin_edges)
         for idx, count in enumerate(hist):
diff --git a/arviz/plots/backends/matplotlib/khatplot.py b/arviz/plots/backends/matplotlib/khatplot.py
index f6628b3ae6..af30bc832d 100644
--- a/arviz/plots/backends/matplotlib/khatplot.py
+++ b/arviz/plots/backends/matplotlib/khatplot.py
@@ -20,7 +20,7 @@ def plot_khat(
     figsize,
     xdata,
     khats,
-    sample_size,
+    good_k,
     kwargs,
     threshold,
     coord_labels,
@@ -62,10 +62,8 @@ def plot_khat(
     backend_kwargs.setdefault("figsize", figsize)
     backend_kwargs["squeeze"] = True
 
-    if sample_size is None:
+    if good_k is None:
         good_k = 0.7
-    else:
-        good_k = min(1 - 1 / np.log10(sample_size), 0.7)
 
     hlines_kwargs = matplotlib_kwarg_dealiaser(hlines_kwargs, "hlines")
     hlines_kwargs.setdefault("hlines", [0, good_k, 1])
@@ -157,7 +155,7 @@ def plot_khat(
         )
 
     if show_bins:
-        bin_edges = np.array([ymin, 0.5, 0.7, 1, ymax])
+        bin_edges = np.array([ymin, good_k, 1, ymax])
         bin_edges = bin_edges[(bin_edges >= ymin) & (bin_edges <= ymax)]
         hist, _, _ = histogram(khats, bin_edges)
         for idx, count in enumerate(hist):
diff --git a/arviz/plots/khatplot.py b/arviz/plots/khatplot.py
index e2bc0bbdad..6e4383ae8f 100644
--- a/arviz/plots/khatplot.py
+++ b/arviz/plots/khatplot.py
@@ -1,6 +1,7 @@
 """Pareto tail indices plot."""
 
 import logging
+import warnings
 
 import numpy as np
 from xarray import DataArray
@@ -163,19 +164,20 @@ def plot_khat(
         color = "C0"
 
     if isinstance(khats, np.ndarray):
-        _log.warning(
+        warnings.warn(
             "support for arrays will be deprecated, please use ELPDData."
             "The reason for this, is that we need to know the numbers of draws"
-            "sampled from the posterior"
+            "sampled from the posterior",
+            FutureWarning,
         )
         khats = khats.flatten()
         xlabels = False
         legend = False
         dims = []
-        sample_size = None
+        good_k = None
     else:
         if isinstance(khats, ELPDData):
-            sample_size = khats.n_samples
+            good_k = khats.good_k
             khats = khats.pareto_k
         if not isinstance(khats, DataArray):
             raise ValueError("Incorrect khat data input. Check the documentation")
@@ -197,7 +199,7 @@ def plot_khat(
         figsize=figsize,
         xdata=xdata,
         khats=khats,
-        sample_size=sample_size,
+        good_k=good_k,
         kwargs=kwargs,
         threshold=threshold,
         coord_labels=coord_labels,
diff --git a/arviz/stats/stats.py b/arviz/stats/stats.py
index f2dc579203..e1484c3e92 100644
--- a/arviz/stats/stats.py
+++ b/arviz/stats/stats.py
@@ -819,8 +819,17 @@ def loo(data, pointwise=None, var_name=None, reff=None, scale=None):
 
     if not pointwise:
         return ELPDData(
-            data=[loo_lppd, loo_lppd_se, p_loo, n_samples, n_data_points, warn_mg, scale],
-            index=["elpd_loo", "se", "p_loo", "n_samples", "n_data_points", "warning", "scale"],
+            data=[loo_lppd, loo_lppd_se, p_loo, n_samples, n_data_points, warn_mg, scale, good_k],
+            index=[
+                "elpd_loo",
+                "se",
+                "p_loo",
+                "n_samples",
+                "n_data_points",
+                "warning",
+                "scale",
+                "good_k",
+            ],
         )
     if np.equal(loo_lppd, loo_lppd_i).all():  # pylint: disable=no-member
         warnings.warn(
@@ -838,6 +847,7 @@ def loo(data, pointwise=None, var_name=None, reff=None, scale=None):
             loo_lppd_i.rename("loo_i"),
             pareto_shape,
             scale,
+            good_k,
         ],
         index=[
             "elpd_loo",
@@ -849,6 +859,7 @@ def loo(data, pointwise=None, var_name=None, reff=None, scale=None):
             "loo_i",
             "pareto_k",
             "scale",
+            "good_k",
         ],
     )
 
diff --git a/arviz/stats/stats_utils.py b/arviz/stats/stats_utils.py
index 7a5772f920..1f0f8c9892 100644
--- a/arviz/stats/stats_utils.py
+++ b/arviz/stats/stats_utils.py
@@ -454,10 +454,9 @@ def get_log_likelihood(idata, var_name=None, single_var=True):
 
 Pareto k diagnostic values:
                          {{0:>{0}}} {{1:>6}}
-(-Inf, 0.5]   (good)     {{2:{0}d}} {{6:6.1f}}%
- (0.5, 0.7]   (ok)       {{3:{0}d}} {{7:6.1f}}%
-   (0.7, 1]   (bad)      {{4:{0}d}} {{8:6.1f}}%
-   (1, Inf)   (very bad) {{5:{0}d}} {{9:6.1f}}%
+(-Inf, {{8:.1f}}]   (good)     {{2:{0}d}} {{5:6.1f}}%
+   ({{8:.1f}}, 1]   (bad)      {{3:{0}d}} {{6:6.1f}}%
+   (1, Inf)   (very bad) {{4:{0}d}} {{7:6.1f}}%
 """
 SCALE_DICT = {"deviance": "deviance", "log": "elpd", "negative_log": "-elpd"}
 
@@ -488,11 +487,14 @@ def __str__(self):
             base += "\n\nThere has been a warning during the calculation. Please check the results."
 
         if kind == "loo" and "pareto_k" in self:
-            bins = np.asarray([-np.inf, 0.5, 0.7, 1, np.inf])
+            bins = np.asarray([-np.inf, self.good_k, 1, np.inf])
             counts, *_ = _histogram(self.pareto_k.values, bins)
             extended = POINTWISE_LOO_FMT.format(max(4, len(str(np.max(counts)))))
             extended = extended.format(
-                "Count", "Pct.", *[*counts, *(counts / np.sum(counts) * 100)]
+                "Count",
+                "Pct.",
+                *[*counts, *(counts / np.sum(counts) * 100)],
+                self.good_k,
             )
             base = "\n".join([base, extended])
         return base