import pandas as pd import numpy as np from scipy.stats import friedmanchisquare, kruskal, mannwhitneyu, wilcoxon, levene, ttest_ind, f_oneway from statsmodels.stats.multicomp import MultiComparison import pandas as pd import numpy as np from scipy.stats import spearmanr, pearsonr, kendalltau, entropy from scipy.spatial.distance import jensenshannon 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 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() # Statistical tests rank_data = [data[col] for col in rank_columns] kw_stat, kw_p = kruskal(*rank_data) # Pairwise tests pairwise_results = {} pairs = [ ('Privilege', 'Protect'), ('Protect', 'Neutral'), ('Privilege', 'Neutral') ] pairwise_results = { 'Mann-Whitney U Test': {}, 'Wilcoxon Test': {}, 'Levene\'s Test': {}, 'T-Test': {} } for (var1, var2) in pairs: pair_name_rank = f'{var1}{rank_suffix} vs {var2}{rank_suffix}' pair_name_score = f'{var1}{score_suffix} vs {var2}{score_suffix}' # # Mann-Whitney U Test # mw_stat, mw_p = mannwhitneyu(data[f'{var1}{rank_suffix}'], data[f'{var2}{rank_suffix}']) # pairwise_results['Mann-Whitney U Test'][pair_name_rank] = {"Statistic": mw_stat, "p-value": mw_p} # # # 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_name_rank] = {"Statistic": wilcoxon_stat, "p-value": wilcoxon_p} # # Levene's Test for equality of variances # levene_stat, levene_p = levene(data[f'{var1}{score_suffix}'], data[f'{var2}{score_suffix}']) # pairwise_results['Levene\'s Test'][pair_name_score] = {"Statistic": levene_stat, "p-value": levene_p} # T-test for independent samples t_stat, t_p = ttest_ind(data[f'{var1}{score_suffix}'], data[f'{var2}{score_suffix}']) #equal_var=(levene_p > 0.05)) pairwise_results['T-Test'][pair_name_score] = {"Statistic": t_stat, "p-value": t_p} # ANOVA and post-hoc tests if applicable score_columns = [v + score_suffix for v in variables] score_data = [data[col] for col in score_columns] anova_stat, anova_p = f_oneway(*score_data) if anova_p < 0.05: mc = MultiComparison(data.melt()['value'], data.melt()['variable']) tukey_result = mc.tukeyhsd() tukey_result_summary = tukey_result.summary().as_html() else: tukey_result_summary = "ANOVA not significant, no post-hoc test performed." results = { #"Average Ranks": average_ranks.to_dict(), "Friedman Test": { "Statistic": friedmanchisquare(*rank_data).statistic, "p-value": friedmanchisquare(*rank_data).pvalue }, "Kruskal-Wallis Test": {"Statistic": kw_stat, "p-value": kw_p}, **pairwise_results, "ANOVA Test": {"Statistic": anova_stat, "p-value": anova_p}, "Tukey HSD Test": tukey_result_summary } return results