Resolve "Include Mann-Whitney U rank test"

Closes #355 (closed)

mlair/helpers/statistics.py

@@ -10,6 +10,7 @@ import xarray as xr
 import pandas as pd
 from typing import Union, Tuple, Dict, List
 import itertools
+from collections import OrderedDict
 
 Data = Union[xr.DataArray, pd.DataFrame]
 
@@ -219,6 +220,47 @@ def calculate_error_metrics(a, b, dim):
     return {"mse": mse, "rmse": rmse, "mae": mae, "n": n}
 
 
+def mann_whitney_u_test(data: pd.DataFrame, reference_col_name: str, **kwargs):
+    """
+    Calculate Mann-Whitney u-test. Uses pandas' .apply() on scipy.stats.mannwhitneyu(x, y, ...).
+    :param data:
+    :type data:
+    :param reference_col_name: Name of column which is used for comparison (y)
+    :type reference_col_name:
+    :param kwargs:
+    :type kwargs:
+    :return:
+    :rtype:
+    """
+    res = data.apply(stats.mannwhitneyu, y=data[reference_col_name], **kwargs)
+    res = res.rename(index={0: "statistics", 1: "p-value"})
+    return res
+
+
+def represent_p_values_as_asteriks(p_values: pd.Series, threshold_representation: OrderedDict = None):
+    """
+    Represent p-values as asteriks based on its value.
+    :param p_values:
+    :type p_values:
+    :param threshold_representation:
+    :type threshold_representation:
+    :return:
+    :rtype:
+    """
+    if threshold_representation is None:
+        threshold_representation = OrderedDict([(1, "ns"), (0.05, "*"), (0.01, "**"), (0.001, "***")])
+
+    if not all(x > y for x, y in zip(list(threshold_representation.keys()), list(threshold_representation.keys())[1:])):
+        raise ValueError(
+            f"`threshold_representation' keys mus be in strictly "
+            f"decreasing order but is: {threshold_representation.keys()}")
+
+    asteriks = pd.Series().reindex_like(p_values)
+    for k, v in threshold_representation.items():
+        asteriks[p_values < k] = v
+    return asteriks
+
+
 class SkillScores:
     r"""
     Calculate different kinds of skill scores.