def apply_t_test(samples, population_mean, alpha=0.05, difference=1.0, desc=""):
"""
Applies a t-test, considering test power also.
:param samples: Samples from simulation.
:param population_mean: Mean on the test dataset.
:param alpha: Type 1 risk: Rejecting null when null is true.
:param difference: Expected difference.
:return: None
"""
t_stat, two_tail_prob = stats.ttest_1samp(samples, population_mean)
logger.info(desc + ": Two-Sample T-test: t-statistic " + str(t_stat) + " p-value " + str(two_tail_prob))
sample_mean = np.mean(samples)
sample_size = len(samples)
sample_std = np.std(samples)
df = sample_size - 1
# FYI: The examples on Discrete-Event Simulation by Jerry Banks were replicated using the following python code.
threshold = stats.t.ppf(1 - alpha / 2, df)
logger.info(desc + ": Critical value of t: " + str(threshold) + " for a level of significance (alpha) " + str(
alpha) + " and degrees of freedom " + str(df))
null_hypothesis = "The mean of the sample (" + str(sample_mean) + ") is equal to the population mean ( " + str(
population_mean) + ")"
reject_null = None
if abs(t_stat) > threshold:
reject_null = True
logger.info(desc + ": We REJECT the null hypothesis: " + null_hypothesis)
else:
reject_null = False
logger.info(desc + ": We CANNOT REJECT the null hypothesis " + null_hypothesis)
effect_size = difference / sample_std
logger.info(desc + ": Effect size for a difference of " + str(difference) + ": " + str(effect_size))
test_power = power.tt_solve_power(effect_size=effect_size, alpha=alpha, nobs=sample_size)
logger.info(desc + ": Test power: " + str(test_power))
return reject_null, test_power
ttest_pow = TTestPower()
print('\nroundtrip - root with respect to all variables')
print('\n calculated, desired')
nobs_p = ttest_pow.solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power)
print('nobs ', nobs_p)
print('effect', ttest_pow.solve_power(effect_size=None, nobs=nobs_p, alpha=alpha, power=power), effect_size)
print('alpha ', ttest_pow.solve_power(effect_size=effect_size, nobs=nobs_p, alpha=None, power=power), alpha)
print('power ', ttest_pow.solve_power(effect_size=effect_size, nobs=nobs_p, alpha=alpha, power=None), power)
print('\nroundtrip - root with respect to all variables')
print('\n calculated, desired')
print('nobs ', tt_solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power), nobs_p)
print('effect', tt_solve_power(effect_size=None, nobs=nobs_p, alpha=alpha, power=power), effect_size)
print('alpha ', tt_solve_power(effect_size=effect_size, nobs=nobs_p, alpha=None, power=power), alpha)
print('power ', tt_solve_power(effect_size=effect_size, nobs=nobs_p, alpha=alpha, power=None), power)
print('\none sided')
nobs_p1 = tt_solve_power(effect_size=effect_size, nobs=None, alpha=alpha, power=power, alternative='larger')
print('nobs ', nobs_p1)
print('effect', tt_solve_power(effect_size=None, nobs=nobs_p1, alpha=alpha, power=power, alternative='larger'), effect_size)
print('alpha ', tt_solve_power(effect_size=effect_size, nobs=nobs_p1, alpha=None, power=power, alternative='larger'), alpha)
print('power ', tt_solve_power(effect_size=effect_size, nobs=nobs_p1, alpha=alpha, power=None, alternative='larger'), power)
#start_ttp = dict(effect_size=0.01, nobs1=10., alpha=0.15, power=0.6)
ttind_solve_power = TTestIndPower().solve_power
#Calculate effect size over a range of hypothetical save percentages compared to average
Effect_Size = (np.arange(93, 100.25, 0.25) - SV_Average) / SV_Deviation
#Set alpha to be constant at 0.05
alpha = 0.05
#Calculate sample size required to achieve specified power over the range of effect sizes calculated above
Sample_80 = []
Sample_85 = []
Sample_90 = []
Sample_95 = []
for effect in Effect_Size:
Sample_80.append(
tt_solve_power(effect_size=effect,
nobs=None,
alpha=alpha,
power=0.8,
alternative='two-sided'))
Sample_85.append(
tt_solve_power(effect_size=effect,
nobs=None,
alpha=alpha,
power=0.85,
alternative='two-sided'))
Sample_90.append(
tt_solve_power(effect_size=effect,
nobs=None,
alpha=alpha,
power=0.9,
alternative='two-sided'))
Sample_95.append(
alpha=None,
power=power), alpha)
print(
'power ',
ttest_pow.solve_power(effect_size=effect_size,
nobs=nobs_p,
alpha=alpha,
power=None), power)
print('\nroundtrip - root with respect to all variables')
print('\n calculated, desired')
print(
'nobs ',
tt_solve_power(effect_size=effect_size,
nobs=None,
alpha=alpha,
power=power), nobs_p)
print(
'effect',
tt_solve_power(effect_size=None, nobs=nobs_p, alpha=alpha,
power=power), effect_size)
print(
'alpha ',
tt_solve_power(effect_size=effect_size,
nobs=nobs_p,
alpha=None,
power=power), alpha)
print(
'power ',
tt_solve_power(effect_size=effect_size,