util/evaluation.py

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