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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, 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
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