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=10000): 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=10000): 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): """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}' 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 = { # 'Privilege vs Protect': levene(data['Privilege_Rank'], data['Protect_Rank']), # 'Privilege vs Neutral': levene(data['Privilege_Rank'], data['Neutral_Rank']), # 'Protect vs Neutral': levene(data['Protect_Rank'], data['Neutral_Rank']) # } # # levene_results = {key: {"Statistic": res.statistic, "p-value": res.pvalue} for key, res in levene_results.items()} # 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, p_priv_prot_var = permutation_test_variance(data['Privilege_Rank'], data['Protect_Rank']) T_neut_prot_var, p_neut_prot_var = permutation_test_variance(data['Neutral_Rank'], data['Protect_Rank']) T_neut_priv_var, p_neut_priv_var = permutation_test_variance(data['Neutral_Rank'], data['Privilege_Rank']) # Perform permutation tests for means T_priv_prot_mean, p_priv_prot_mean = permutation_test_mean(data['Privilege_Rank'], data['Protect_Rank']) T_neut_prot_mean, p_neut_prot_mean = permutation_test_mean(data['Neutral_Rank'], data['Protect_Rank']) T_neut_priv_mean, p_neut_priv_mean = permutation_test_mean(data['Neutral_Rank'], data['Privilege_Rank']) permutation_results = { "Permutation Tests for Variances": { "Privilege vs. Protect": {"Statistic": T_priv_prot_var, "p-value": p_priv_prot_var}, "Neutral vs. Protect": {"Statistic": T_neut_prot_var, "p-value": p_neut_prot_var}, "Neutral vs. Privilege": {"Statistic": T_neut_priv_var, "p-value": p_neut_priv_var} }, "Permutation Tests for Means": { "Privilege vs. Protect": {"Statistic": T_priv_prot_mean, "p-value": p_priv_prot_mean}, "Neutral vs. Protect": {"Statistic": T_neut_prot_mean, "p-value": p_neut_prot_mean}, "Neutral vs. Privilege": {"Statistic": T_neut_priv_mean, "p-value": p_neut_priv_mean} } } 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