Games Howell Test (Multiple Comparisons)

Games_Howell.py

from scipy.stats import f_oneway
a = all_metrics[all_metrics['significance'] == 'insignficant']['post_covid_return'].dropna().values
b = all_metrics[all_metrics['significance'] == 'intrinsic_only']['post_covid_return'].dropna().values
c = all_metrics[all_metrics['significance'] == 'sharpe_only']['post_covid_return'].dropna().values
d = all_metrics[all_metrics['significance'] == 'both']['post_covid_return'].dropna().values

import statsmodels
print(f_oneway(a,b,c,d)) # Signficicant Difference between groups

from itertools import combinations, product
import numpy_indexed as npi
from statsmodels.stats.libqsturng import qsturng, psturng

def games_howell(data=None, dv=None, between=None, effsize='hedges'):
    group_comps = []
    mean_differences = []
    degrees_freedom = []
    t_values = []
    p_values = []
    std_err = []
    up_conf = []
    low_conf = []

    data = data[[dv, between]].reset_index().values
    alpha = 0.05
    k = len(np.unique(data[:,2]))

    group_means = dict(npi.group_by(data[:, 2], data[:, 1], np.mean))
    group_obs = dict(npi.group_by(data[:, 2], data[:, 1], len))
    group_variance = dict(npi.group_by(data[:, 2], data[:, 1], np.var))

    combs = list(combinations(np.unique(data[:, 2]), 2))

    for comb in combs:    
        
        # Mean differences of each group combination
        diff = group_means[comb[1]] - group_means[comb[0]]
        
        # t-value of each group combination
        t_val = np.abs(diff) / np.sqrt((group_variance[comb[0]] / group_obs[comb[0]]) + 
                                    (group_variance[comb[1]] / group_obs[comb[1]]))
        
        # Numerator of the Welch-Satterthwaite equation
        df_num = (group_variance[comb[0]] / group_obs[comb[0]] + group_variance[comb[1]] / group_obs[comb[1]]) ** 2
        
        # Denominator of the Welch-Satterthwaite equation
        df_denom = ((group_variance[comb[0]] / group_obs[comb[0]]) ** 2 / (group_obs[comb[0]] - 1) +
                    (group_variance[comb[1]] / group_obs[comb[1]]) ** 2 / (group_obs[comb[1]] - 1))
        
        # Degrees of freedom
        df = df_num / df_denom
        
        # p-value of the group comparison
        p_val = psturng(t_val * np.sqrt(2), k, df)

        # Standard error of each group combination
        se = np.sqrt(0.5 * (group_variance[comb[0]] / group_obs[comb[0]] + 
                            group_variance[comb[1]] / group_obs[comb[1]]))
        
        # Upper and lower confidence intervals
        upper_conf = diff + qsturng(1 - alpha, k, df)
        lower_conf = diff - qsturng(1 - alpha, k, df)
        
        # Append the computed values to their respective lists.
        mean_differences.append(diff)
        degrees_freedom.append(df)
        t_values.append(t_val)
        p_values.append(p_val)
        std_err.append(se)
        up_conf.append(upper_conf)
        low_conf.append(lower_conf)
        group_comps.append(str(comb[0]) + ' : ' + str(comb[1]))

    result_df = pd.DataFrame({'groups': group_comps,
                          'mean_difference': mean_differences,
                          'std_error': std_err,
                          't_value': t_values,
                          'p_value': p_values,
                          'upper_limit': up_conf,
                          'lower limit': low_conf})
    return result_df

games_howell(all_metrics, dv='post_covid_return', between='significance')