def minimum_size_statsmodels(self, power=0.80):
return NormalIndPower().solve_power(
effect_size=proportion_effectsize(self.p_alt, self.p_null),
alpha=self.alpha,
power=power,
alternative="larger",
)
def fn(control, test):
if _is_proportion(control, test):
effect_size = proportion_effectsize(np.mean(control), np.mean(test))
func = zt_ind_solve_power
else:
effect_size = _effect_size_nonprop(control, test)
func = tt_ind_solve_power
return func(effect_size=effect_size,
nobs1=len(control),
alpha=0.05,
ratio=len(test) / len(control),
alternative='two-sided')
def test_proportion_effect_size():
# example from blog
es = smprop.proportion_effectsize(0.5, 0.4)
assert_almost_equal(es, 0.2013579207903309, decimal=13)
def test_proportion_effect_size():
# example from blog
es = smprop.proportion_effectsize(0.5, 0.4)
assert_almost_equal(es, 0.2013579207903309, decimal=13)
def get_effect_size(df1, df2):
""" Get the effect size """
p1 = np.mean(df1)
p2 = np.mean(df2)
print("Effect size: {}".format(round(proportion_effectsize(p1, p2), 4)))
from statsmodels.stats.proportion import proportion_effectsize proportion_effectsize(0.6, 0.5) from statsmodels.stats.power import zt_ind_solve_power zt_ind_solve_power(effect_size=0.2, alpha=0.05, power=0.8)
alpha : Type-I error rate
beta : Type-II error rate
Output value:
n : Number of samples required for each group to obtain desired power
"""
# Get necessary z-scores and standard deviations (@ 1 obs per group)
z_null = stats.norm.ppf(1 - alpha)
z_alt = stats.norm.ppf(beta)
sd_null = np.sqrt(2 * p_null * (1 - p_null))
sd_alt = np.sqrt((p_null * (1 - p_null) + (p_alt * (1 - p_alt))))
p_diff = p_alt - p_null
n = ((z_null * sd_null - z_alt * sd_alt) / p_diff)**2
return np.ceil(n)
experiment_size(0.1, 0.12)
# Alternative Approaches
# example of using statsmodels for sample size calculation
from statsmodels.stats.power import NormalIndPower
from statsmodels.stats.proportion import proportion_effectsize
# leave out the "nobs" parameter to solve for it
NormalIndPower().solve_power(effect_size=proportion_effectsize(.12, .1),
alpha=.05,
power=0.8,
alternative='larger')
expected) = proportions_chisquare(count=[success_A, success_B],
nobs=[visits_per_group, visits_per_group])
print("chi2: %f \t p_value: %f" % (chi2, chi2_p_value))
## Examine the output of the chi2_contingency function.
## If the target p_value is 0.05, what is your conclusion? Do you accept or reject H0?
## Note that this test only tells you whether A & B have different conversion rates, not
## which is larger. In this case, since A & B had the same number of visits, this is easy to
## determine. However, if you only showed B to 10% of your visitors, you may want to use a
## one-sided test instead.
## Your team also wants to know the "power" of the above results. Since they want to
## know if H1 is true, what is the possiblity that we accept H0 when H1 is true?
## The power can be obtained using the GofChisquarePower.solve_power function
effect_size = proportion_effectsize(prop1=conversion_rate_A,
prop2=conversion_rate_B)
proportion_test_power = NormalIndPower().solve_power(effect_size=effect_size,
nobs1=visits_per_group,
alpha=0.05)
###################################################################################
## 2. AB Test of Means
## Scenario:
## Your team's manager asks you about dwell time differences between versions A and B
## Question: Is the customers' time spent on page different between version A
## and B of the website?
###################################################################################
## Load the data
## Remember to set your working directory to the bootcamp base folder
dwell_time_A = pd.read_csv('Datasets/Dwell_Time/Dwell_Time_VersionA.csv')
dwell_time_B = pd.read_csv('Datasets/Dwell_Time/Dwell_Time_VersionB.csv')
(chi2, chi2_p_value, expected) = proportions_chisquare(count=[success_A, success_B],
nobs=[visits_per_group, visits_per_group])
print("chi2: %f \t p_value: %f" % (chi2, chi2_p_value))
## Examine the output of the chi2_contingency function.
## If the target p_value is 0.05, what is your conclusion? Do you accept or reject H0?
## Note that this test only tells you whether A & B have different conversion rates, not
## which is larger. In this case, since A & B had the same number of visits, this is easy to
## determine. However, if you only showed B to 10% of your visitors, you may want to use a
## one-sided test instead.
## Your team also wants to know the "power" of the above results. Since they want to
## know if H1 is true, what is the possiblity that we accept H0 when H1 is true?
## The power can be obtained using the GofChisquarePower.solve_power function
effect_size = proportion_effectsize(prop1=conversion_rate_A, prop2=conversion_rate_B)
proportion_test_power = NormalIndPower().solve_power(effect_size=effect_size, nobs1=visits_per_group, alpha=0.05)
###################################################################################
## 2. AB Test of Means
## Scenario:
## Your team's manager asks you about dwell time differences between versions A and B
## Question: Is the customers' time spent on page different between version A
## and B of the website?
###################################################################################
## Load the data
## Remember to set your working directory to the bootcamp base folder
dwell_time_A = pd.read_csv('Datasets/Dwell_Time/Dwell_Time_VersionA.csv')
dwell_time_B = pd.read_csv('Datasets/Dwell_Time/Dwell_Time_VersionB.csv')
## Visualize the data
print('{0:0.3f}'.format(pval))
#2 Tail T test
# Assign the prices of each group
asus = laptops[laptops['Company'] == 'Asus']['Price']
toshiba = laptops[laptops['Company'] == 'Toshiba']['Price']
# Run the t-test
from scipy.stats import ttest_ind
tstat, pval = ttest_ind(asus, toshiba)
print('{0:0.3f}'.format(pval))
#CALCULATING SAMPLE SIZE
# Standardize the effect size
from statsmodels.stats.proportion import proportion_effectsize
std_effect = proportion_effectsize(.20, .25)
# Assign and print the needed sample size
from statsmodels.stats.power import zt_ind_solve_power
sample_size = zt_ind_solve_power(effect_size=std_effect,
nobs1=None,
alpha=.05,
power=0.8)
print(sample_size)
sample_sizes = np.array(range(5, 100))
effect_sizes = np.array([0.2, 0.5, 0.8])
# Create results object for t-test analysis
from statsmodels.stats.power import TTestIndPower
results = TTestIndPower()
# z-test..
stat, pval = proportions_ztest(count, nobs, alternative="larger")
print('{0:0.3f}'.format(pval))
# t-test..
from scipy.stats import ttest_ind
# tstat, pval = ttest_ind(asus, toshiba) # ..comparing 2 price series
# power analysis
# ---
# power and sample size (how to calculate required sample size)
# -> power analysis!
# elements: effect size, significance level, power, sample size all lead
# to a larger sample size
from statsmodels.stats.proportion import proportion_effectsize
std_effect = proportion_effectsize(0.2, 0.25)
# derive the required sample size..
from statsmodels.stats.power import zt_ind_solve_power
sample_size = zt_ind_solve_power(effect_size=std_effect,
nobs1=None,
alpha=0.05,
power=0.95)
print(sample_size)
# relationship between power and sample size..
sample_sizes = np.array(range(5, 100))
effect_sizes = np.array([0.2, 0.5, 0.8])
# esults object for t-test analysis..
from statsmodels.stats.power import TTestIndPower
results = TTestIndPower()
# plot of power analysis..
results.plot_power(dep_var='nobs', nobs=sample_sizes, effect_size=effect_sizes)
