fix: correct Spearman correlation for tied values

Author: deepshekhardas

maths/spearman_rank_correlation_coefficient.py

@@ -1,26 +1,35 @@
 from collections.abc import Sequence
 
 
-def assign_ranks(data: Sequence[float]) -> list[int]:
+def assign_ranks(data: Sequence[float]) -> list[float]:
     """
-    Assigns ranks to elements in the array.
+    Assigns ranks to elements in the array, using averaged ranks for ties.
 
     :param data: List of floats.
-    :return: List of ints representing the ranks.
+    :return: List of floats representing the ranks.
 
     Example:
     >>> assign_ranks([3.2, 1.5, 4.0, 2.7, 5.1])
-    [3, 1, 4, 2, 5]
+    [3.0, 1.0, 4.0, 2.0, 5.0]
 
     >>> assign_ranks([10.5, 8.1, 12.4, 9.3, 11.0])
-    [3, 1, 5, 2, 4]
+    [3.0, 1.0, 5.0, 2.0, 4.0]
+
+    >>> assign_ranks([1.0, 2.0, 2.0, 4.0])
+    [1.0, 2.5, 2.5, 4.0]
     """
+    n = len(data)
     ranked_data = sorted((value, index) for index, value in enumerate(data))
-    ranks = [0] * len(data)
-
-    for position, (_, index) in enumerate(ranked_data):
-        ranks[index] = position + 1
-
+    ranks = [0.0] * n
+    i = 0
+    while i < n:
+        j = i
+        while j < n - 1 and ranked_data[j + 1][0] == ranked_data[i][0]:
+            j += 1
+        avg_rank = (i + j) / 2.0 + 1
+        for k in range(i, j + 1):
+            ranks[ranked_data[k][1]] = avg_rank
+        i = j + 1
     return ranks
 
 
@@ -50,8 +59,14 @@ def calculate_spearman_rank_correlation(
     >>> y = [5, 1, 2, 9, 5]
     >>> calculate_spearman_rank_correlation(x, y)
     0.6
+    >>> calculate_spearman_rank_correlation([1], [1])
+    Traceback (most recent call last):
+        ...
+    ValueError: Need at least 2 data points
     """
     n = len(variable_1)
+    if n < 2:
+        raise ValueError("Need at least 2 data points")
     rank_var1 = assign_ranks(variable_1)
     rank_var2 = assign_ranks(variable_2)