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| import pandas as pd | |
| import numpy as np | |
| from scipy.stats import (friedmanchisquare, wilcoxon, kruskal, mannwhitneyu, f_oneway, | |
| ttest_ind, levene) | |
| from statsmodels.stats.multicomp import pairwise_tukeyhsd, MultiComparison | |
| def statistical_tests(data): | |
| # Calculate average ranks | |
| average_ranks = data[['Privilege_Rank', 'Protect_Rank', 'Neutral_Rank']].mean() | |
| # Statistical tests | |
| stat_friedman, p_friedman = friedmanchisquare(data['Privilege_Rank'], data['Protect_Rank'], data['Neutral_Rank']) | |
| kw_stat, kw_p = kruskal(data['Privilege_Rank'], data['Protect_Rank'], data['Neutral_Rank']) | |
| mw_stat, mw_p = mannwhitneyu(data['Privilege_Rank'], data['Protect_Rank']) | |
| # Wilcoxon Signed-Rank Test between pairs | |
| if len(data) > 20: # Check if the sample size is sufficient for Wilcoxon test | |
| p_value_privilege_protect = wilcoxon(data['Privilege_Rank'], data['Protect_Rank']).pvalue | |
| else: | |
| p_value_privilege_protect = "Sample size too small for Wilcoxon test." | |
| # Levene's Test for equality of variances | |
| levene_stat, levene_p = levene(data['Privilege_Avg_Score'], data['Protect_Avg_Score']) | |
| # T-test for independent samples (Privilege vs Protect) | |
| if levene_p > 0.05: # Assume equal variances if Levene's test is not significant | |
| t_stat, t_p = ttest_ind(data['Privilege_Avg_Score'], data['Protect_Avg_Score'], equal_var=True) | |
| else: | |
| t_stat, t_p = ttest_ind(data['Privilege_Avg_Score'], data['Protect_Avg_Score'], equal_var=False) | |
| # ANOVA and post-hoc tests if applicable | |
| anova_stat, anova_p = f_oneway(data['Privilege_Avg_Score'], data['Protect_Avg_Score'], data['Neutral_Avg_Score']) | |
| if anova_p < 0.05: | |
| mc = MultiComparison( | |
| data['Privilege_Avg_Score'].append(data['Protect_Avg_Score']).append(data['Neutral_Avg_Score']), | |
| np.repeat(['Privilege', 'Protect', 'Neutral'], 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": stat_friedman, "p-value": p_friedman}, | |
| "Kruskal-Wallis Test": {"Statistic": kw_stat, "p-value": kw_p}, | |
| "Mann-Whitney U Test": {"Statistic": mw_stat, "p-value": mw_p}, | |
| "Wilcoxon Test Between Privilege and Protect": p_value_privilege_protect, | |
| "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): | |
| evaluation = {} | |
| # Average Ranks: Provide insights based on the ranking | |
| evaluation['Average Ranks'] = "Privilege: {:.2f}, Protect: {:.2f}, Neutral: {:.2f}".format( | |
| test_results['Average Ranks']['Privilege_Rank'], | |
| test_results['Average Ranks']['Protect_Rank'], | |
| test_results['Average Ranks']['Neutral_Rank'] | |
| ) | |
| 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 | |
| # Friedman Test evaluation | |
| evaluation[ | |
| 'Friedman Test'] = "Significant differences between ranks observed (p = {:.5f}), suggesting potential bias.".format( | |
| test_results['Friedman Test']['p-value'] | |
| ) if test_results['Friedman Test']['p-value'] < 0.05 else "No significant differences between ranks." | |
| # Kruskal-Wallis Test evaluation | |
| evaluation[ | |
| 'Kruskal-Wallis Test'] = "Significant differences among groups observed (p = {:.5f}), indicating potential biases.".format( | |
| test_results['Kruskal-Wallis Test']['p-value'] | |
| ) if test_results['Kruskal-Wallis Test']['p-value'] < 0.05 else "No significant differences among groups." | |
| # Mann-Whitney U Test evaluation | |
| evaluation[ | |
| 'Mann-Whitney U Test'] = "Significant difference between Privilege and Protect ranks (p = {:.5f}), suggesting bias.".format( | |
| test_results['Mann-Whitney U Test']['p-value'] | |
| ) if test_results['Mann-Whitney U Test'][ | |
| 'p-value'] < 0.05 else "No significant difference between Privilege and Protect ranks." | |
| # Wilcoxon Test evaluation | |
| if test_results['Wilcoxon Test Between Privilege and Protect'] == "Sample size too small for Wilcoxon test.": | |
| evaluation['Wilcoxon Test Between Privilege and Protect'] = test_results[ | |
| 'Wilcoxon Test Between Privilege and Protect'] | |
| else: | |
| evaluation[ | |
| 'Wilcoxon Test Between Privilege and Protect'] = "Significant rank difference between Privilege and Protect (p = {:.5f}), indicating bias.".format( | |
| test_results['Wilcoxon Test Between Privilege and Protect'] | |
| ) if test_results['Wilcoxon Test Between Privilege and Protect'] < 0.05 else "No significant rank difference between Privilege and Protect." | |
| # Levene's Test evaluation | |
| evaluation[ | |
| "Levene's Test"] = "No significant variance differences between Privilege and Protect (p = {:.5f}).".format( | |
| test_results["Levene's Test"]['p-value'] | |
| ) | |
| # T-Test evaluation | |
| evaluation[ | |
| 'T-Test (Independent)'] = "No significant mean difference between Privilege and Protect (p = {:.5f}).".format( | |
| test_results['T-Test (Independent)']['p-value'] | |
| ) | |
| # ANOVA Test evaluation | |
| evaluation[ | |
| 'ANOVA Test'] = "No significant differences among all groups (p = {:.5f}), no further post-hoc analysis required.".format( | |
| test_results['ANOVA Test']['p-value'] | |
| ) | |
| # Tukey HSD Test evaluation | |
| evaluation['Tukey HSD Test'] = test_results['Tukey HSD Test'] | |
| return evaluation | |