def example_compare_two_proportions(number_of_flips, fairness_1=0.5, fairness_2=0.5,
significance_level=0.95):
""" Two-sided test for the null hypothesis that 2 proportions are equal """
results_1, results_2 = [], []
for _ in range(number_of_flips):
results_1.append(flip_a_coin(fairness_1))
results_2.append(flip_a_coin(fairness_2))
# Two-sided test of whether 2 samples are drawn from the same distribution and parameters or not.
ks_statistic, prob = stats.ks_2samp(results_1, results_2)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'Proportions are equal'
else:
return 'Proportions are not equal'
def example_compare_two_coins(number_of_flips, fairness_1=0.5, fairness_2=0.5, significance_level=0.95):
""" Two-sided test for the null hypothesis that 2 coins are equal """
results_1, results_2 = [], []
for _ in range(number_of_flips):
results_1.append(flip_a_coin(fairness_1))
results_2.append(flip_a_coin(fairness_2))
# If equal_var=True: assumes equal population variances.
# If equal_var=False, perform Welch t-test
t_statistic, prob = stats.ttest_ind(results_1, results_2, equal_var=False)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'Coins are equal'
else:
return 'Coins are not equal'
def example_compare_two_proportions(number_of_flips,
fairness_1=0.5,
fairness_2=0.5,
significance_level=0.95):
""" Two-sided test for the null hypothesis that 2 proportions are equal """
results_1, results_2 = [], []
for _ in range(number_of_flips):
results_1.append(flip_a_coin(fairness_1))
results_2.append(flip_a_coin(fairness_2))
# Two-sided test of whether 2 samples are drawn from the same distribution and parameters or not.
ks_statistic, prob = stats.ks_2samp(results_1, results_2)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'Proportions are equal'
else:
return 'Proportions are not equal'
def example_compare_two_coins(number_of_flips,
fairness_1=0.5,
fairness_2=0.5,
significance_level=0.95):
""" Two-sided test for the null hypothesis that 2 coins are equal """
results_1, results_2 = [], []
for _ in range(number_of_flips):
results_1.append(flip_a_coin(fairness_1))
results_2.append(flip_a_coin(fairness_2))
# If equal_var=True: assumes equal population variances.
# If equal_var=False, perform Welch t-test
t_statistic, prob = stats.ttest_ind(results_1, results_2, equal_var=False)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'Coins are equal'
else:
return 'Coins are not equal'
def example_test_coin_fairness(number_of_flips, fairness=0.5, significance_level=0.95):
""" Two-sided test for the null hypothesis that the coin is fair """
results = [flip_a_coin(fairness) for flip in range(number_of_flips)]
# Test if mean of random sample is equal to true mean (here 0.5 - fair coin)
t_statistic, prob = stats.ttest_1samp(results, 0.5)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'The coin is fair'
else:
return 'The coin is unfair'
def example_test_coin_fairness(number_of_flips,
fairness=0.5,
significance_level=0.95):
""" Two-sided test for the null hypothesis that the coin is fair """
results = [flip_a_coin(fairness) for flip in range(number_of_flips)]
# Test if mean of random sample is equal to true mean (here 0.5 - fair coin)
t_statistic, prob = stats.ttest_1samp(results, 0.5)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'The coin is fair'
else:
return 'The coin is unfair'
def example_test_single_proportion(number_of_flips, fairness=0.5, significance_level=0.95):
""" Two-sided test for the null hypothesis that a proportion is equal to 0.5 """
results = [flip_a_coin(fairness) for flip in range(number_of_flips)]
success = sum(results)
failure = len(results) - success
# Exact two-sided test of the null hypothesis that the probability of success
# in a Bernoulli experiment is 0.5 (here, fair coin)
prob = stats.binom_test([success, failure], p=0.5)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'The proportion is equal to target'
else:
return 'The proportion is not equal to target'
def example_test_single_proportion(number_of_flips,
fairness=0.5,
significance_level=0.95):
""" Two-sided test for the null hypothesis that a proportion is equal to 0.5 """
results = [flip_a_coin(fairness) for flip in range(number_of_flips)]
success = sum(results)
failure = len(results) - success
# Exact two-sided test of the null hypothesis that the probability of success
# in a Bernoulli experiment is 0.5 (here, fair coin)
prob = stats.binom_test([success, failure], p=0.5)
# If we observe a large p-value, for example larger than 0.05 or 0.1,
# then we cannot reject the null hypothesis of identical averages
alpha = 1 - significance_level
if prob > alpha:
return 'The proportion is equal to target'
else:
return 'The proportion is not equal to target'
