spearman_rank_correlation_coefficient.py

fromcollections.abcimportSequence


defassign_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) forindex, valueinenumerate(data))
ranks= [0] *len(data)

forposition, (_, index) inenumerate(ranked_data):
ranks[index] =position+1

returnranks


defcalculate_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-ryforrx, ryinzip(rank_var1, rank_var2)]

# Calculate the sum of squared differences
d_squared=sum(di**2fordiind)

# Calculate the Spearman's rank correlation coefficient
rho=1- (6*d_squared) / (n* (n**2-1))

returnrho


if__name__=="__main__":
importdoctest

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]) =}")