Create Spearman's rank correlation coefficient (TheAlgorithms#11155)

* Create spearman_rank_correlation_coefficient.py

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* Update maths/spearman_rank_correlation_coefficient.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 3 people

maths/spearman_rank_correlation_coefficient.py

@@ -0,0 +1,82 @@
+from collections.abc import Sequence
+
+
+def assign_ranks(data: Sequence[float]) -> list[int]:
+    """
+    Assigns ranks to elements in the array.
+
+    :param data: List of floats.
+    :return: List of ints representing the ranks.
+
+    Example:
+    >>> assign_ranks([3.2, 1.5, 4.0, 2.7, 5.1])
+    [3, 1, 4, 2, 5]
+
+    >>> assign_ranks([10.5, 8.1, 12.4, 9.3, 11.0])
+    [3, 1, 5, 2, 4]
+    """
+    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
+
+    return ranks
+
+
+def calculate_spearman_rank_correlation(
+    variable_1: Sequence[float], variable_2: Sequence[float]
+) -> float:
+    """
+    Calculates Spearman's rank correlation coefficient.
+
+    :param variable_1: List of floats representing the first variable.
+    :param variable_2: List of floats representing the second variable.
+    :return: Spearman's rank correlation coefficient.
+
+    Example Usage:
+
+    >>> x = [1, 2, 3, 4, 5]
+    >>> y = [5, 4, 3, 2, 1]
+    >>> calculate_spearman_rank_correlation(x, y)
+    -1.0
+
+    >>> x = [1, 2, 3, 4, 5]
+    >>> y = [2, 4, 6, 8, 10]
+    >>> calculate_spearman_rank_correlation(x, y)
+    1.0
+
+    >>> x = [1, 2, 3, 4, 5]
+    >>> y = [5, 1, 2, 9, 5]
+    >>> calculate_spearman_rank_correlation(x, y)
+    0.6
+    """
+    n = len(variable_1)
+    rank_var1 = assign_ranks(variable_1)
+    rank_var2 = assign_ranks(variable_2)
+
+    # Calculate differences of ranks
+    d = [rx - ry for rx, ry in zip(rank_var1, rank_var2)]
+
+    # Calculate the sum of squared differences
+    d_squared = sum(di**2 for di in d)
+
+    # Calculate the Spearman's rank correlation coefficient
+    rho = 1 - (6 * d_squared) / (n * (n**2 - 1))
+
+    return rho
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example usage:
+    print(
+        f"{calculate_spearman_rank_correlation([1, 2, 3, 4, 5], [2, 4, 6, 8, 10]) = }"
+    )
+
+    print(f"{calculate_spearman_rank_correlation([1, 2, 3, 4, 5], [5, 4, 3, 2, 1]) = }")
+
+    print(f"{calculate_spearman_rank_correlation([1, 2, 3, 4, 5], [5, 1, 2, 9, 5]) = }")