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############################################################
#                                                          #
#         Virtual Laboratory of Statistics in Python       #
#                                                          #
#            Enumerative Data Models (18.08.2017)          #
#                                                          #                
#         Complutense University of Madrid, Spain          #
#                                                          #
#   THIS SCRIPT IS PROVIDED BY THE AUTHORS "AS IS" AND     #
#   CAN BE USED BY ANYONE FOR THE PURPOSES OF EDUCATION    #
#   AND RESEARCH.                                          #
#                                                          #
############################################################

import scipy.stats as s
import numpy as np
from statsmodels.stats.proportion import proportions_ztest

# ONE PROPORTION
x = 69
n = 96
H0 = 0.8
# alternative : string in [‘two-sided’, ‘smaller’, ‘larger’]
HA = 'smaller'
z,p = proportions_ztest(x, n, H0, HA)
print()
print(' z-stat. one proportion = {z} \n p-value = {p}'.format(z=z,p=p))
print()

# TWO PROPORTIONS
n1 = 1000
x1 = 702
n2 = 1000
x2 = 198
H0 = 0.0
# alternative : string in [‘two-sided’, ‘smaller’, ‘larger’]
HA='two-sided'
x12 = np.array([x1,x2])
n12 = np.array([n1, n2])
z,p = proportions_ztest(x12, n12, H0, HA)
print()
print(' z-stat. two proportions = {z} \n p-value = {p}'.format(z=z,p=p))
print()

# CHI-SQUARE TEST

# 2x2 - CONTINGENCE TABLE 
data_observed = np.array([[8,22], [12,6]])
chi2_result,p_value,df_value,table_expected=s.chi2_contingency(data_observed)
print()
confidence_level = 0.95
crit_value = s.chi2.ppf(q = confidence_level, df=df_value)
print()
oddsratio, p_value_f = s.fisher_exact(data_observed)
print ('Contingency table 2x2')
print ('====================================')
print ('chi2:', chi2_result)
print ('p-value:', p_value)
print ('df = ', df_value)
print('Critical value: ',crit_value)
print()
print()
print('        Fisher exact test:')
print()
print(' Oddsratio: ',oddsratio,' p-value: ',p_value_f)
print()
print ('              Table')
print ('Obs.: ')
print(data_observed)
print ('Exp.: ')
print(table_expected)
print ('====================================')
print()
print()

# INDEPENDENCE TEST - CONTINGENCE TABLE
data_observed = np.array([[8,22,16,12,19], [24,6,2,12,7]])
chi2_result,p_value,df_value,table_expected=s.chi2_contingency(data_observed)
print()
confidence_level = 0.95
crit_value = s.chi2.ppf(q = confidence_level, df=df_value)
print()
print ('Contingency table')
print ('====================================')
print ('chi2:', chi2_result)
print ('p-value:', p_value)
print ('df = ', df_value)
print('Critical value: ',crit_value)
print()
print ('              Table')
print ('Obs.: ')
print (data_observed)
print ('Exp.: ')
print (table_expected)
print ('====================================')
print()
print()