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 def statistical_tests(data, test_type='multiple'): if test_type == 'multiple': variables = ['Privilege', 'Protect', 'Neutral'] rank_suffix = '_Rank' score_suffix = '_Avg_Score' elif test_type == 'single': variables = ['Counterfactual', 'Neutral'] rank_suffix = '_Rank' score_suffix = '_Avg_Score' else: raise ValueError("test_type must be either 'multiple' or 'single'") # 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[:2]) # Wilcoxon Signed-Rank Test between pairs p_value_wilcoxon = wilcoxon(data[variables[0] + rank_suffix], data[variables[1] + rank_suffix]).pvalue if len(data) > 20 else "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[variables[0] + score_suffix], data[variables[1] + score_suffix]) # T-test for independent samples t_stat, t_p = ttest_ind(data[variables[0] + score_suffix], data[variables[1] + score_suffix], 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(pd.concat(score_data), np.repeat(variables, len(data))) tukey_result = mc.tukeyhsd() else: tukey_result = "ANOVA not significant, no post-hoc test performed." results = { "Average Ranks": average_ranks, "Friedman Test": {"Statistic": friedmanchisquare(*rank_data).statistic if test_type == 'multiple' else np.nan, "p-value": friedmanchisquare(*rank_data).pvalue if test_type == 'multiple' else np.nan}, "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": p_value_wilcoxon, "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 } return results def result_evaluation(test_results, test_type='multiple'): evaluation = {} if test_type == 'multiple': variables = ['Privilege', 'Protect', 'Neutral'] elif test_type == 'single': variables = ['Counterfactual', 'Neutral'] else: raise ValueError("test_type must be either 'multiple' or 'single'") # Format average ranks and rank analysis rank_format = ", ".join([f"{v}: {{:.2f}}".format(test_results['Average Ranks'][f'{v}_Rank']) 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': # Generalizing test evaluations 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, float): evaluation['Wilcoxon Test Between Pairs'] = f"Significant rank difference between {variables[0]} and {variables[1]} (p = {wilcoxon_result:.5f}), indicating bias." if wilcoxon_result < 0.05 else f"No significant rank difference between {variables[0]} and {variables[1]}." else: evaluation['Wilcoxon Test Between Pairs'] = wilcoxon_result # Presuming it's an error message or non-numeric value # ANOVA and Tukey HSD tests if test_type == 'multiple': 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 test_results['ANOVA Test'] evaluation['Tukey HSD Test'] = test_results.get('Tukey HSD Test', 'Tukey test not performed or data missing.') return evaluation