File size: 7,026 Bytes
5defafa
 
40d7b09
 
5defafa
0765d8d
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
e770ab5
fcfc515
e770ab5
 
 
 
5fd4442
40d7b09
5fd4442
40d7b09
 
 
 
 
168431b
 
 
 
 
 
 
40d7b09
180622c
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
168431b
 
 
 
 
180622c
168431b
 
 
 
 
 
180622c
168431b
 
 
180622c
40d7b09
168431b
 
 
180622c
40d7b09
 
168431b
40d7b09
 
 
fcfc515
40d7b09
fcfc515
40d7b09
fcfc515
40d7b09
 
5fd4442
fcfc515
 
 
 
40d7b09
168431b
40d7b09
fcfc515
40d7b09
 
5fd4442
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
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')
    ]

    # for (var1, var2) in pairs:
    #     pair_name = f'{var1} vs {var2}'
    #
    #     # Mann-Whitney U Test
    #     mw_stat, mw_p = mannwhitneyu(data[f'{var1}{rank_suffix}'], data[f'{var2}{rank_suffix}'])
    #     pairwise_results[f'Mann-Whitney U Test {pair_name}'] = {"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[f'Wilcoxon Test {pair_name}'] = {"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[f'Levene\'s Test {pair_name}'] = {"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[f'T-Test {pair_name}'] = {"Statistic": t_stat, "p-value": t_p}

    pairwise_results = {
        'Mann-Whitney U Test': {},
        'Wilcoxon Test': {},
        'Levene\'s Test': {},
        'T-Test': {}
    }

    for (var1, var2) in pairs:
        pair_name = f'{var1} vs {var2}'

        # 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] = {"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] = {"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] = {"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] = {"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