Create Spearman's rank correlation coefficient (#11155)

* Create spearman_rank_correlation_coefficient.py

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* Update maths/spearman_rank_correlation_coefficient.py

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
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Harsh Kumar 2023-11-25 19:50:42 +05:30 committed by GitHub
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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]) = }")