Fix permutation tests calculating p-values with z-score

frouros/callbacks/batch/permutation_test.py

@@ -4,9 +4,10 @@
 from typing import Any, Callable, Dict, List, Optional, Tuple
 
 import numpy as np  # type: ignore
+from scipy.stats import norm  # type: ignore
 
 from frouros.callbacks.batch.base import BatchCallback
-from frouros.utils.stats import permutation
+from frouros.utils.stats import permutation, z_score
 
 
 class PermutationTestOnBatchData(BatchCallback):
@@ -120,7 +121,14 @@ def _calculate_p_value(  # pylint: disable=too-many-arguments
             random_state=random_state,
             verbose=verbose,
         )
-        p_value = (observed_statistic < permuted_statistic).mean()  # type: ignore
+        permuted_statistic = np.array(permuted_statistic)
+        # Use z-score to calculate p-value
+        observed_z_score = z_score(
+            value=observed_statistic,
+            mean=permuted_statistic.mean(),  # type: ignore
+            std=permuted_statistic.std(),  # type: ignore
+        )
+        p_value = norm.sf(np.abs(observed_z_score)) * 2
         return permuted_statistic, p_value
 
     def on_compare_end(self, **kwargs) -> None:

frouros/tests/integration/test_callback.py

@@ -54,13 +54,13 @@
     "detector_class, expected_distance, expected_p_value",
     [
         (BhattacharyyaDistance, 0.55516059, 0.0),
-        (EMD, 3.85346006, 0.0),
-        (HellingerDistance, 0.74509099, 0.0),
-        (HINormalizedComplement, 0.78, 0.0),
-        (JS, 0.67010107, 0.0),
-        (KL, np.inf, 0.0),
-        (MMD, 0.69509004, 0.0),
-        (PSI, 461.20379435, 0.0),
+        (EMD, 3.85346006, 9.21632493e-101),
+        (HellingerDistance, 0.74509099, 3.13808126e-50),
+        (HINormalizedComplement, 0.78, 1.31340683e-55),
+        (JS, 0.67010107, 2.30485343e-63),
+        (KL, np.inf, np.nan),
+        (MMD, 0.69509004, 2.53277069e-137),
+        (PSI, 461.20379435, 4.45088795e-238),
     ],
 )
 def test_batch_permutation_test_data_univariate_different_distribution(
@@ -100,7 +100,11 @@ def test_batch_permutation_test_data_univariate_different_distribution(
     distance, callback_logs = detector.compare(X=X_test_univariate)
 
     assert np.isclose(distance, expected_distance)
-    assert np.isclose(callback_logs[permutation_test_name]["p_value"], expected_p_value)
+    assert np.isclose(
+        callback_logs[permutation_test_name]["p_value"],
+        expected_p_value,
+        equal_nan=True,
+    )
 
 
 @pytest.mark.parametrize(

frouros/utils/stats.py

@@ -262,5 +262,23 @@ def permutation(  # pylint: disable=too-many-arguments,too-many-locals
             iterable=tqdm(permuted_data) if verbose else permuted_data,
         ).get()
 
-    # FIXME: explore if abs must be used in permuted_statistic  # pylint: disable=fixme
     return permuted_statistics
+
+
+def z_score(
+    value: np.ndarray,
+    mean: float,
+    std: float,
+) -> np.ndarray:
+    """Z-score method.
+
+    :param value: value to use to compute the z-score
+    :type value: np.ndarray
+    :param mean: mean value
+    :type mean: float
+    :param std: standard deviation value
+    :type std: float
+    :return: z-score
+    :rtype: np.ndarray
+    """
+    return (value - mean) / std