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) mw_stat, mw_p = mannwhitneyu(rank_data[0], rank_data[1]) # Wilcoxon Signed-Rank Test between pairs if len(data) > 20: wilcoxon_stat, wilcoxon_p = wilcoxon(rank_data[0], rank_data[1]) else: wilcoxon_stat, wilcoxon_p = np.nan, "Sample size too small for Wilcoxon test." # Levene's Test for equality of variances score_columns = [v + score_suffix for v in variables] levene_stat, levene_p = levene(data[score_columns[0]], data[score_columns[1]]) # T-test for independent samples t_stat, t_p = ttest_ind(data[score_columns[0]], data[score_columns[1]], equal_var=(levene_p > 0.05)) # ANOVA and post-hoc tests if applicable 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}, "Mann-Whitney U Test": {"Statistic": mw_stat, "p-value": mw_p}, "Wilcoxon Test Between Pairs": {"Statistic": wilcoxon_stat, "p-value": wilcoxon_p}, "Levene's Test": {"Statistic": levene_stat, "p-value": levene_p}, "T-Test (Independent)": {"Statistic": t_stat, "p-value": t_p}, "ANOVA Test": {"Statistic": anova_stat, "p-value": anova_p}, "Tukey HSD Test": tukey_result_summary } return results def result_evaluation(test_results): """Evaluate the results of statistical tests to provide insights on potential biases.""" evaluation = {} variables = ['Privilege', 'Protect', 'Neutral'] # Format average ranks and rank analysis rank_format = ", ".join([f"{v}: {test_results['Average Ranks'][f'{v}_Rank']:.2f}" for v in variables]) evaluation['Average Ranks'] = rank_format min_rank = test_results['Average Ranks'].idxmin() max_rank = test_results['Average Ranks'].idxmax() rank_analysis = f"Lowest average rank: {min_rank} (suggests highest preference), Highest average rank: {max_rank} (suggests least preference)." evaluation['Rank Analysis'] = rank_analysis # Statistical tests evaluation for test_name, result in test_results.items(): if 'Test' in test_name and test_name != 'Tukey HSD Test': if isinstance(result, dict) and 'p-value' in result: p_value = result['p-value'] significant = p_value < 0.05 test_label = test_name.replace('_', ' ').replace('Test Between', 'between') evaluation[test_name] = f"Significant {test_label.lower()} observed (p = {p_value:.5f}), indicating potential biases." if significant else f"No significant {test_label.lower()}." else: evaluation[test_name] = "Test result format error or incomplete data." # Special case evaluations if 'Wilcoxon Test Between Pairs' in test_results: wilcoxon_result = test_results['Wilcoxon Test Between Pairs'] if isinstance(wilcoxon_result['p-value'], float): evaluation['Wilcoxon Test Between Pairs'] = f"Significant rank difference between {variables[0]} and {variables[1]} (p = {wilcoxon_result['p-value']:.5f}), indicating bias." if wilcoxon_result['p-value'] < 0.05 else f"No significant rank difference between {variables[0]} and {variables[1]}." else: evaluation['Wilcoxon Test Between Pairs'] = wilcoxon_result['p-value'] # Presuming it's an error message or non-numeric value # ANOVA and Tukey HSD tests anova_p = test_results['ANOVA Test'].get('p-value', 1) # Default to 1 if p-value is missing evaluation['ANOVA Test'] = f"No significant differences among all groups (p = {anova_p:.5f}), no further post-hoc analysis required." if anova_p >= 0.05 else f"Significant differences found among groups (p = {anova_p:.5f})." evaluation['Tukey HSD Test'] = test_results.get('Tukey HSD Test', 'Tukey test not performed or data missing.') return evaluation