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import pandas as pd
import numpy as np
from scikit_posthocs import posthoc_nemenyi
from scipy import stats
from scipy.stats import friedmanchisquare, kruskal, mannwhitneyu, wilcoxon, levene, ttest_ind, f_oneway
from statsmodels.stats.multicomp import MultiComparison
from scipy.stats import spearmanr, pearsonr, kendalltau, entropy
from scipy.spatial.distance import jensenshannon
from scipy.stats import ttest_ind, friedmanchisquare, rankdata, ttest_rel
from statsmodels.stats.multicomp import pairwise_tukeyhsd
from scipy.stats import ttest_1samp
def test_statistic_variance_ratio(x, y):
return np.var(x, ddof=1) / np.var(y, ddof=1)
def test_statistic_mean_difference(x, y):
return np.mean(x) - np.mean(y)
def permutation_test_variance(x, y, num_permutations=100000):
T_obs = test_statistic_variance_ratio(x, y)
pooled_data = np.concatenate([x, y])
n_A = len(x)
perm_test_stats = [T_obs]
for _ in range(num_permutations):
np.random.shuffle(pooled_data)
perm_A = pooled_data[:n_A]
perm_B = pooled_data[n_A:]
perm_test_stats.append(test_statistic_variance_ratio(perm_A, perm_B))
perm_test_stats = np.array(perm_test_stats)
p_value = np.mean(np.abs(perm_test_stats) >= np.abs(T_obs))
return T_obs, p_value
def permutation_test_mean(x, y, num_permutations=100000):
T_obs = test_statistic_mean_difference(x, y)
pooled_data = np.concatenate([x, y])
n_A = len(x)
perm_test_stats = [T_obs]
for _ in range(num_permutations):
np.random.shuffle(pooled_data)
perm_A = pooled_data[:n_A]
perm_B = pooled_data[n_A:]
perm_test_stats.append(test_statistic_mean_difference(perm_A, perm_B))
perm_test_stats = np.array(perm_test_stats)
p_value = np.mean(np.abs(perm_test_stats) >= np.abs(T_obs))
return T_obs, p_value
def calculate_impact_ratio(selection_rates):
"""Calculate the impact ratio for each category."""
most_selected_rate = max(selection_rates.values())
impact_ratios = {category: rate / most_selected_rate for category, rate in selection_rates.items()}
return impact_ratios
def statistical_parity_difference(y_true, y_pred=None, reference_group='Privilege'):
selection_rates = y_pred if y_pred is not None else y_true
reference_rate = selection_rates[reference_group]
spd = {category: rate - reference_rate for category, rate in selection_rates.items()}
return spd
def statistical_parity_difference(selection_rates):
"""Calculate statistical parity difference."""
most_selected_rate = max(selection_rates.values())
spd = {category: rate - most_selected_rate for category, rate in selection_rates.items()}
return spd
def calculate_four_fifths_rule(impact_ratios):
"""Calculate whether each category meets the four-fifths rule."""
adverse_impact = {category: (ratio < 0.8) for category, ratio in impact_ratios.items()}
return adverse_impact
def statistical_tests(data):
# Add ranks for each score within each row
# ranks = data[['Privilege_Avg_Score', 'Protect_Avg_Score', 'Neutral_Avg_Score']].rank(axis=1, ascending=True)
#
# data['Privilege_Rank'] = ranks['Privilege_Avg_Score']
# data['Protect_Rank'] = ranks['Protect_Avg_Score']
# data['Neutral_Rank'] = ranks['Neutral_Avg_Score']
"""Perform various statistical tests to evaluate potential biases."""
variables = ['Privilege', 'Protect', 'Neutral']
rank_suffix = '_Rank'
score_suffix = '_Avg_Score'
# Calculate average ranks and scores
rank_columns = [v + rank_suffix for v in variables]
average_ranks = data[rank_columns].mean()
average_scores = data[[v + score_suffix for v in variables]].mean()
# Statistical tests setup
rank_data = [data[col] for col in rank_columns]
pairs = [('Privilege', 'Protect'), ('Protect', 'Neutral'), ('Privilege', 'Neutral')]
pairwise_results = {'Wilcoxon Test': {}}
# Pairwise Wilcoxon Signed-Rank Test
for var1, var2 in pairs:
pair_rank_score = f'{var1}{rank_suffix} vs {var2}{rank_suffix}'
pair_score_score = f'{var1}{score_suffix} vs {var2}{score_suffix}'
if len(data) > 20:
wilcoxon_stat_rank, wilcoxon_p_rank = wilcoxon(data[f'{var1}{rank_suffix}'], data[f'{var2}{rank_suffix}'])
wilcoxon_stat_score, wilcoxon_p_score = wilcoxon(data[f'{var1}{score_suffix}'], data[f'{var2}{score_suffix}'])
else:
wilcoxon_stat_rank, wilcoxon_p_rank = np.nan, "Sample size too small for Wilcoxon test."
wilcoxon_stat_score, wilcoxon_p_score = np.nan, "Sample size too small for Wilcoxon test."
pairwise_results['Wilcoxon Test'][pair_rank_score] = {"Statistic": wilcoxon_stat_rank, "p-value": wilcoxon_p_rank}
pairwise_results['Wilcoxon Test'][pair_score_score] = {"Statistic": wilcoxon_stat_score, "p-value": wilcoxon_p_score}
# Calculate variances for ranks
variances = {col: data[col].var() for col in rank_columns}
pairwise_variances = {
'Privilege_Rank vs Protect_Rank': variances['Privilege_Rank'] > variances['Protect_Rank'],
'Privilege_Rank vs Neutral_Rank': variances['Privilege_Rank'] > variances['Neutral_Rank'],
'Protect_Rank vs Neutral_Rank': variances['Protect_Rank'] > variances['Neutral_Rank']
}
# Bias metrics calculations
selection_rates_Avg_Score = {v: data[f'{v}{score_suffix}'].mean() for v in variables}
selection_rates_rank = {v: data[f'{v}{rank_suffix}'].mean() for v in variables}
impact_ratios_Avg_Score = calculate_impact_ratio(selection_rates_Avg_Score)
spd_result_Avg_Score = statistical_parity_difference(selection_rates_Avg_Score)
adverse_impact_Avg_Score = calculate_four_fifths_rule(impact_ratios_Avg_Score)
impact_ratios_rank = calculate_impact_ratio(selection_rates_rank)
spd_result_rank = statistical_parity_difference(selection_rates_rank)
adverse_impact_rank = calculate_four_fifths_rule(impact_ratios_rank)
# Friedman test
friedman_stat, friedman_p = friedmanchisquare(*rank_data)
rank_matrix_transposed = np.transpose(data[rank_columns].values)
posthoc_results = posthoc_nemenyi(rank_matrix_transposed)
# Perform permutation tests for variances
T_priv_prot_var_rank, p_priv_prot_var_rank = permutation_test_variance(data['Privilege_Rank'], data['Protect_Rank'])
T_neut_prot_var_rank, p_neut_prot_var_rank = permutation_test_variance(data['Neutral_Rank'], data['Protect_Rank'])
T_neut_priv_var_rank, p_neut_priv_var_rank = permutation_test_variance(data['Neutral_Rank'], data['Privilege_Rank'])
# Perform permutation tests for variances by using rank data
T_priv_prot_var_score, p_priv_prot_var_score = permutation_test_variance(data['Privilege_Avg_Score'], data['Protect_Avg_Score'])
T_neut_prot_var_score, p_neut_prot_var_score = permutation_test_variance(data['Neutral_Avg_Score'], data['Protect_Avg_Score'])
T_neut_priv_var_score, p_neut_priv_var_score = permutation_test_variance(data['Neutral_Avg_Score'], data['Privilege_Avg_Score'])
# Perform permutation tests for means
T_priv_prot_mean_rank, p_priv_prot_mean_rank = permutation_test_mean(data['Privilege_Rank'], data['Protect_Rank'])
T_neut_prot_mean_rank, p_neut_prot_mean_rank = permutation_test_mean(data['Neutral_Rank'], data['Protect_Rank'])
T_neut_priv_mean_rank, p_neut_priv_mean_rank = permutation_test_mean(data['Neutral_Rank'], data['Privilege_Rank'])
# Perform permutation tests for means by using rank data
T_priv_prot_mean_score, p_priv_prot_mean_score = permutation_test_mean(data['Privilege_Avg_Score'], data['Protect_Avg_Score'])
T_neut_prot_mean_score, p_neut_prot_mean_score = permutation_test_mean(data['Neutral_Avg_Score'], data['Protect_Avg_Score'])
T_neut_priv_mean_score, p_neut_priv_mean_score = permutation_test_mean(data['Neutral_Avg_Score'], data['Privilege_Avg_Score'])
permutation_results = {
"Permutation Tests for Variances (score)": {
"Privilege vs. Protect": {"Statistic": T_priv_prot_var_score, "p-value": p_priv_prot_var_score},
"Neutral vs. Protect": {"Statistic": T_neut_prot_var_score, "p-value": p_neut_prot_var_score},
"Neutral vs. Privilege": {"Statistic": T_neut_priv_var_score, "p-value": p_neut_priv_var_score}
},
"Permutation Tests for Means (score)": {
"Privilege vs. Protect": {"Statistic": T_priv_prot_mean_score, "p-value": p_priv_prot_mean_score},
"Neutral vs. Protect": {"Statistic": T_neut_prot_mean_score, "p-value": p_neut_prot_mean_score},
"Neutral vs. Privilege": {"Statistic": T_neut_priv_mean_score, "p-value": p_neut_priv_mean_score}
},
"Permutation Tests for Variances (rank)": {
"Privilege vs. Protect": {"Statistic": T_priv_prot_var_rank, "p-value": p_priv_prot_var_rank},
"Neutral vs. Protect": {"Statistic": T_neut_prot_var_rank, "p-value": p_neut_prot_var_rank},
"Neutral vs. Privilege": {"Statistic": T_neut_priv_var_rank, "p-value": p_neut_priv_var_rank}
},
"Permutation Tests for Means (rank)": {
"Privilege vs. Protect": {"Statistic": T_priv_prot_mean_rank, "p-value": p_priv_prot_mean_rank},
"Neutral vs. Protect": {"Statistic": T_neut_prot_mean_rank, "p-value": p_neut_prot_mean_rank},
"Neutral vs. Privilege": {"Statistic": T_neut_priv_mean_rank, "p-value": p_neut_priv_mean_rank}
}
}
results = {
"Average Ranks": average_ranks.to_dict(),
"Average Scores": average_scores.to_dict(),
"Friedman Test": {
"Statistic": friedman_stat,
"p-value": friedman_p,
"Post-hoc": posthoc_results
},
**pairwise_results,
#"Levene's Test for Equality of Variances": levene_results,
"Pairwise Comparisons of Variances": pairwise_variances,
"Statistical Parity Difference": {
"Avg_Score": spd_result_Avg_Score,
"Rank": spd_result_rank
},
"Disparate Impact Ratios": {
"Avg_Score": impact_ratios_Avg_Score,
"Rank": impact_ratios_rank
},
"Four-Fifths Rule": {
"Avg_Score": adverse_impact_Avg_Score,
"Rank": adverse_impact_rank
},
**permutation_results
}
return results
#
# def statistical_tests(data):
# """Perform various statistical tests to evaluate potential biases."""
# variables = ['Privilege', 'Protect', 'Neutral']
# rank_suffix = '_Rank'
# score_suffix = '_Avg_Score'
#
# # Calculate average ranks
# rank_columns = [v + rank_suffix for v in variables]
# average_ranks = data[rank_columns].mean()
# average_scores = data[[v + score_suffix for v in variables]].mean()
#
# # Statistical tests
# rank_data = [data[col] for col in rank_columns]
#
# # Pairwise tests
# pairs = [
# ('Privilege', 'Protect'),
# ('Protect', 'Neutral'),
# ('Privilege', 'Neutral')
# ]
#
# pairwise_results = {
# 'Wilcoxon Test': {}
# }
#
# for (var1, var2) in pairs:
# pair_name_score = f'{var1}{score_suffix} vs {var2}{score_suffix}'
# pair_rank_score = f'{var1}{rank_suffix} vs {var2}{rank_suffix}'
#
# # Wilcoxon Signed-Rank Test
# if len(data) > 20:
# wilcoxon_stat, wilcoxon_p = wilcoxon(data[f'{var1}{rank_suffix}'], data[f'{var2}{rank_suffix}'])
# else:
# wilcoxon_stat, wilcoxon_p = np.nan, "Sample size too small for Wilcoxon test."
# pairwise_results['Wilcoxon Test'][pair_rank_score] = {"Statistic": wilcoxon_stat, "p-value": wilcoxon_p}
#
# # Levene's Test for Equality of Variances
# levene_results = {}
# levene_privilege_protect = levene(data['Privilege_Rank'], data['Protect_Rank'])
# levene_privilege_neutral = levene(data['Privilege_Rank'], data['Neutral_Rank'])
# levene_protect_neutral = levene(data['Protect_Rank'], data['Neutral_Rank'])
#
# levene_results['Privilege vs Protect'] = {"Statistic": levene_privilege_protect.statistic,
# "p-value": levene_privilege_protect.pvalue}
# levene_results['Privilege vs Neutral'] = {"Statistic": levene_privilege_neutral.statistic,
# "p-value": levene_privilege_neutral.pvalue}
# levene_results['Protect vs Neutral'] = {"Statistic": levene_protect_neutral.statistic,
# "p-value": levene_protect_neutral.pvalue}
#
# # Calculate variances for ranks
# variances = {col: data[col].var() for col in rank_columns}
# pairwise_variances = {
# 'Privilege_Rank vs Protect_Rank': variances['Privilege_Rank'] > variances['Protect_Rank'],
# 'Privilege_Rank vs Neutral_Rank': variances['Privilege_Rank'] > variances['Neutral_Rank'],
# 'Protect_Rank vs Neutral_Rank': variances['Protect_Rank'] > variances['Neutral_Rank']
# }
#
# selection_rates_Avg_Score = {
# 'Privilege': data['Privilege_Avg_Score'].mean(),
# 'Protect': data['Protect_Avg_Score'].mean(),
# 'Neutral': data['Neutral_Avg_Score'].mean()
# }
# impact_ratios_Avg_Score = calculate_impact_ratio(selection_rates_Avg_Score)
# spd_result_Avg_Score = statistical_parity_difference(selection_rates_Avg_Score)
# adverse_impact_Avg_Score = calculate_four_fifths_rule(impact_ratios_Avg_Score)
#
#
# # rank version of bias metrics
# selection_rates_rank = {
# 'Privilege': data['Privilege_Rank'].mean(),
# 'Protect': data['Protect_Rank'].mean(),
# 'Neutral': data['Neutral_Rank'].mean()
# }
# impact_ratios_rank = calculate_impact_ratio(selection_rates_rank)
# spd_result_rank = statistical_parity_difference(selection_rates_rank)
# adverse_impact_rank = calculate_four_fifths_rule(impact_ratios_rank)
#
#
# # Friedman test
# friedman_stat, friedman_p = friedmanchisquare(*rank_data)
#
# rank_matrix = data[rank_columns].values
# rank_matrix_transposed = np.transpose(rank_matrix)
# posthoc_results = posthoc_nemenyi(rank_matrix_transposed)
# #posthoc_results = posthoc_friedman(data, variables, rank_suffix)
#
#
#
# results = {
# "Average Ranks": average_ranks.to_dict(),
# "Average Scores": average_scores.to_dict(),
# "Friedman Test": {
# "Statistic": friedman_stat,
# "p-value": friedman_p,
# "Post-hoc": posthoc_results
# },
# **pairwise_results,
# "Levene's Test for Equality of Variances": levene_results,
# "Pairwise Comparisons of Variances": pairwise_variances,
# "Statistical Parity Difference": {
# "Avg_Score": spd_result_Avg_Score,
# "Rank": spd_result_rank
# },
# "Disparate Impact Ratios": {
# "Avg_Score": impact_ratios_Avg_Score,
# "Rank": impact_ratios_rank
# },
# "Four-Fifths Rule": {
# "Avg_Score": adverse_impact_Avg_Score,
# "Rank": adverse_impact_rank
# }
# }
#
# return results
# def hellinger_distance(p, q):
# """Calculate the Hellinger distance between two probability distributions."""
# return np.sqrt(0.5 * np.sum((np.sqrt(p) - np.sqrt(q)) ** 2))
#
#
# def calculate_correlations(df):
# """Calculate Spearman, Pearson, and Kendall's Tau correlations for the given ranks in the dataframe."""
# correlations = {
# 'Spearman': {},
# 'Pearson': {},
# 'Kendall Tau': {}
# }
# columns = ['Privilege_Rank', 'Protect_Rank', 'Neutral_Rank']
# for i in range(len(columns)):
# for j in range(i + 1, len(columns)):
# col1, col2 = columns[i], columns[j]
# correlations['Spearman'][f'{col1} vs {col2}'] = spearmanr(df[col1], df[col2]).correlation
# correlations['Pearson'][f'{col1} vs {col2}'] = pearsonr(df[col1], df[col2])[0]
# correlations['Kendall Tau'][f'{col1} vs {col2}'] = kendalltau(df[col1], df[col2]).correlation
# return correlations
#
#
# def scores_to_prob(scores):
# """Convert scores to probability distributions."""
# value_counts = scores.value_counts()
# probabilities = value_counts / value_counts.sum()
# full_prob = np.zeros(int(scores.max()) + 1)
# full_prob[value_counts.index.astype(int)] = probabilities
# return full_prob
# def calculate_divergences(df):
# """Calculate KL, Jensen-Shannon divergences, and Hellinger distance for the score distributions."""
# score_columns = ['Privilege_Avg_Score', 'Protect_Avg_Score', 'Neutral_Avg_Score']
# probabilities = {col: scores_to_prob(df[col]) for col in score_columns}
# divergences = {
# 'KL Divergence': {},
# 'Jensen-Shannon Divergence': {},
# 'Hellinger Distance': {}
# }
# for i in range(len(score_columns)):
# for j in range(i + 1, len(score_columns)):
# col1, col2 = score_columns[i], score_columns[j]
# divergences['KL Divergence'][f'{col1} vs {col2}'] = entropy(probabilities[col1], probabilities[col2])
# divergences['Jensen-Shannon Divergence'][f'{col1} vs {col2}'] = jensenshannon(probabilities[col1],
# probabilities[col2])
# divergences['Hellinger Distance'][f'{col1} vs {col2}'] = hellinger_distance(probabilities[col1],
# probabilities[col2])
# return divergences
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