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abtest.py
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abtest.py
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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
from statsmodels.stats.proportion import proportions_ztest
from scipy.stats import norm,t
from statsmodels.stats import weightstats
from statsmodels.stats import proportion
import math
from IPython.core.display import HTML
def z_test_ci(mu,std,n=1,sig_level=0.05,tail='two.sided'):
if tail=='two.sided':
sig_level = sig_level/2
left,right = norm.interval(1-sig_level, loc=mu, scale=std)
return (left,right)
def t_test_ci(mu,std,df,sig_level=0.05,tail='two.sided'):
if tail=='two.sided':
sig_level = sig_level/2
left,right = t.interval(1-sig_level,df,loc=mu,scale=std)
return (left,right)
def plot_CI(ax,mu,s,df=1,tail='two.sided',sig_level=0.05,color='grey',test_type='z-test'):
if test_type=='t-test':
left,right = t_test_ci(mu,s,df,sig_level,tail=tail)
else:
left,right = z_test_ci(mu,s,sig_level,tail=tail)
ax.axvline(left, c=color, linestyle='--', alpha=0.5)
ax.axvline(right, c=color, linestyle='--', alpha=0.5)
def plot_norm_dist(ax,mu,std,n=1,with_CI=False,sig_level=0.05,label=None,tail='two.sided',color=None):
x = np.linspace(mu-6*std,mu+6*std,1000)
y = norm(mu,std).pdf(x)
ax.plot(x,y,label=label,c=color)
ax.axvline(mu, c=color, linestyle='--', alpha=0.5)
if with_CI:
plot_CI(ax,mu,std,sig_level=sig_level,tail=tail,test_type='z-test')
def plot_vbar_result(ax,data,mu_dict,delta=0.4):
yspan = len(data)
color = ['#c1daf0','#cccccc']
linecolor = ['#428bca','#555555']
yplaces = [.5+i for i in range(yspan)]
ylabels = list(data.keys())
ax.set_yticks(yplaces,)
ax.set_yticklabels(ylabels,fontsize='xx-large')
ax.set_ylim(0,yspan)
ax.set_facecolor('white')
low,hi = data[ylabels[0]]
for pos,label in zip(yplaces,ylabels):
start,end = data[label]
ax.add_patch(patches.Rectangle((start,pos-delta/2.0),end-start,delta))
if start<low: low = start #loop for min of range
if end>hi: hi= end #loop for max of range
t=0
for i,rec in zip(ylabels,ax.patches):
mu = mu_dict[i]
ax.plot([mu,mu],[rec.get_y(),rec.get_y()+rec.get_height()],
linewidth=3,color= linecolor[t])
rec.set(facecolor =color[t])
ax.text(rec.get_x()+ 0.7*rec.get_width(),
rec.get_y()+ 0.2*rec.get_height(),'{}'.format(round(mu,5)),
ha='center',va='bottom',fontsize = 'x-large')
t+=1
ax.plot((low,hi),(0,0))
return ax
def plot_show_alpha(ax,mu,std,df,sig_level=0.05,tail='two.sided',color='green',test_type='z-test'):
x = np.linspace(mu-8*std,mu+8*std,1000)
if test_type =='t-test':
left,right = t_test_ci(mu,std,df,tail=tail,sig_level=sig_level)
null = t.pdf(x,df,loc=mu,scale=std)
else:
left,right = z_test_ci(mu,std,sig_level=sig_level,tail=tail)
null = norm(mu,std).pdf(x)
if tail=='two.sided':
ax.fill_between(x,0,null,color=color,alpha=0.25,where= (x<left) | (x>right))
elif tail == 'greater':
ax.fill_between(x,0,null,color=color,alpha=0.25,where= (x>right))
elif tail == 'less':
ax.fill_between(x,0,null,color=color,alpha=0.25,where= (x<left))
def setting_table(sig_level,alternative,labelA,labelB,diff_value):
alternative_dict = {'two.sided':'two-sided',
'less':'smaller',
'greater':'larger'}
if diff_value != 0 :
hypothesis_dict = {'two.sided':'μA ≠ μB',
'two-sided':'μA ≠ μB',
'greater': 'μA > μB + {}'.format(diff_value),
'larger' : 'μA > μB + {}'.format(diff_value),
'smaller': 'μA < μB + {}'.format(diff_value),
'less': 'μA < μB + {}'.format(diff_value)
}
else:
hypothesis_dict = {'two.sided':'μA ≠ μB',
'two-sided':'μA ≠ μB',
'greater': 'μA > μB',
'larger' : 'μA > μB',
'smaller': 'μA < μB',
'less': 'μA < μB'
}
setting_table = """<tr><th>Control Group</th><th>Variation Group</th><th>Alternative Hypothesis</th><th>Significance Level</th></tr>
<tr><td>{}</td><td>{}</td><td>{}</td><td>{}</td></tr>""".format(labelA,labelB,hypothesis_dict[alternative],sig_level)
main_table_html = """
<style>table {width: 100%;}
td {text-align: center;}
tr:hover {background-color: #f5f5f5;}
</style>
<center><h3>Test Setting</h3></center>
<table>""" +setting_table+ "</table>"
display(HTML(main_table_html), metadata=dict(isolated=True))
def result_table(pA=1,pB=1,power=1,p=1,tscore=1,sA=1,sB=1,stderr=1,nA=1,nB=1,df=1,sig_level=0.05):
sig = ""
if p<=sig_level:
sig = " (<{})".format(sig_level)
star = "***"
else:
sig = " (>{})".format(sig_level)
star = ""
kpi_table = """<tr><th>μA</th><th>μB</th><th>Uplift</th></tr>
<tr><td>{}</td><td>{}</td><td>{}%{}</td></tr>""".format(round(pA,5),round(pB,5),round((pB-pA)/pA*100,2),star)
n_table = """<tr><th>Sample Size A</th><th>Sample Size B</th></tr>
<tr><td>{}</td><td>{}</td></tr>""".format(nA,nB, round(df,5) if df!=None else 'NaN')
result_table = """<tr><th>p value</h5></th><th>t-Score/z-score</th></tr>
<tr><td>{}</td><td>{}</td></tr>""".format(str(round(p,5)) + sig +star,round(tscore,5))
main_table_html = """
<style>table {width: 100%;}
td {text-align: center;}
tr:hover {background-color: #f5f5f5;}
</style>
<hr>
<center><h3>Test Statistics</h3></center>
<table>""" + kpi_table + result_table + n_table + "</table>"
display(HTML(main_table_html), metadata=dict(isolated=True))
def z_test(data_frame,variant_column,control_label,variant_label,kpi_name,
alternative,diff_value = 0, sig_level=0.05,show_plot=False,show_p_value=False,show_alpha=False
):
"""
Input:
=========
#data_frame: Data frame for your test with each row is an observation.
Example: You want to test average WEIGHT between group "A" and group "control"
the data frame should look like:
+----------+----------------+----------------------+----------------------+
| index | variant_type | weight_gram | height_cm |
|----------+----------------+----------------------+----------------------|
| 1 | A | 100.5 | 50 |
|----------+----------------+----------------------+----------------------+
| 2 | control | 112.9 | 50 |
|----------+----------------+----------------------+----------------------+
| 3 | control | 102.5 | 50 |
|----------+----------------+----------------------+----------------------+
| 4 | A | 132.7 | 50 |
|----------+----------------+----------------------+----------------------+
#variant_column: The column contains the info of which variant the observation falls into
In the above example it should be "variant_type"
#control_label: Value of the control group.
In the above example it should be "control"
#variant_label: Value of the Variant lable.
In the above example it should be "A"
#kpi_name: The column name of the easurement you want to evaluate.
In the above example it should be "weight_gram"
Method:
=========
"""
control = data_frame.query('{} == "{}"'.format(variant_column,control_label))[[kpi_name]]
variant = data_frame.query('{} == "{}"'.format(variant_column,variant_label))[[kpi_name]]
labelA = control_label
labelB = variant_label
meanA = control.mean()[0]
meanB = variant.mean()[0]
nA = control.count()[0]
nB = variant.count()[0]
sA = (control.std()/math.sqrt(nA))[0]
sB = (variant.std()/math.sqrt(nB))[0]
color = ['#428bca','#555555']
stderr = np.sqrt(sA**2+sB**2)
### Report Reading ###
alternative_dict = {'two.sided':'two-sided',
'less':'smaller',
'greater':'larger'}
z,p = [k[0] for k in weightstats.ztest(control, variant, value=diff_value, alternative=alternative)]
#No Binomial Correction
power = 'NaN'
### Plot Title ###
display(HTML("<center><h2>Two Mean Z-Test</h2> <br> for {} and {}</center>".format(labelA,labelB)))
display(HTML("""<hr style="border-top: 2px double #8c8b8b";/> """))
setting_table(sig_level,alternative,labelA,labelB,diff_value)
if show_plot:
## Prepare ploting ###
fig = plt.figure(figsize=(16,4),constrained_layout=True)
spec = fig.add_gridspec(ncols=2,nrows=1,width_ratios=[4,10],height_ratios=[4])
ax1 = fig.add_subplot(spec[0,0])
ax1.set_title("KPI Value and Confidence Interval",fontsize='xx-large')
ax2 = fig.add_subplot(spec[0,1],facecolor='white')
ax2.set_title("Expected Distribution",fontsize='xx-large')
### Plot result ###
mu_dict = {labelA:meanA,labelB:meanB}
data_dict = {labelA:z_test_ci(meanA,sA,nA,sig_level,tail=alternative),
labelB:(z_test_ci(meanB,sB,nB,sig_level,tail=alternative))}
plot_vbar_result(ax1,data_dict,mu_dict)
### Plot Hypothesis ####
display(HTML("<hr><center><h3>Distribution Plot</h3></center>"))
plot_norm_dist(ax2,meanA,sA,nA,label=labelA,with_CI=True,tail=alternative,color=color[0])
plot_norm_dist(ax2,meanB,sB,nB,label=labelB,tail=alternative,color=color[1])
if show_alpha:
plot_show_alpha(ax2,meanA,sA,nA,sig_level=sig_level,tail=alternative,color=color[0],test_type='z-test')
plt.legend(loc='best')
plt.show()
### Plot Table ###
result_table(pA=meanA,pB=meanB,power=power,p=p,tscore=z,sA=sA,sB=sB,
stderr=stderr,nA=nA,nB=nB,df=None,sig_level=sig_level)
display(HTML("<center><i>*** : statistical significant</i></center>"))
display(HTML("""<hr style="border-top: 2px double #8c8b8b";/> """))
def z_proportion_test(data_frame,variant_column,control_label,variant_label,kpi_name,
alternative,diff_value = 0, sig_level=0.05,show_plot=False,show_p_value=False,show_alpha=False
#labelA='Control',labelB='Variation'
):
"""
Input:
=========
#data_frame: Data frame for your test with each row is an observation.
Example: You want to test converstion rate between group "A" and group "control"
the data frame should look like:
+----------+----------------+----------------------+----------------------+
| index | variant_type | converted_1_0 | height_cm |
|----------+----------------+----------------------+----------------------|
| 1 | A | 1 | 50 |
|----------+----------------+----------------------+----------------------+
| 2 | control | 0 | 50 |
|----------+----------------+----------------------+----------------------+
| 3 | control | 0 | 50 |
|----------+----------------+----------------------+----------------------+
| 4 | A | 1 | 50 |
|----------+----------------+----------------------+----------------------+
#variant_column: The column contains the info of which variant the observation falls into
In the above example it should be "variant_type"
#control_label: Value of the control group.
In the above example it should be "control"
#variant_label: Value of the Variant lable.
In the above example it should be "A"
#kpi_name: The column name of the easurement you want to evaluate.
In the above example it should be "converted_1_0"
"""
control = data_frame.query('{} == "{}"'.format(variant_column,control_label))[[kpi_name]]
variant = data_frame.query('{} == "{}"'.format(variant_column,variant_label))[[kpi_name]]
labelA = control_label
labelB = variant_label
cA = control.sum()[0]
cB = variant.sum()[0]
nA = control.count()[0]
nB = variant.count()[0]
pA = (cA/nA)
pB = (cB/nB)
count = [cA,cB]
nobs = [nA,nB]
sA = math.sqrt(pA*(1-pA)/nA)
sB = math.sqrt(pB*(1-pB)/nB)
color = ['#428bca','#555555']
stderr = np.sqrt(sA**2+sB**2)
### Report Reading ###
alternative_dict = {'two.sided':'two-sided',
'less':'smaller',
'greater':'larger'}
z,p = proportion.proportions_ztest(count, nobs, value=diff_value, alternative=alternative)
#No Binomial Correction
power = 'NaN'
### Plot Title ###
display(HTML("<center><h2>Two Proportion Z-Test</h2> <br> for {} and {}</center>".format(labelA,labelB)))
display(HTML("""<hr style="border-top: 2px double #8c8b8b";/> """))
setting_table(sig_level,alternative,labelA,labelB,diff_value)
if show_plot:
## Prepare ploting ###
fig = plt.figure(figsize=(16,4),constrained_layout=True)
spec = fig.add_gridspec(ncols=2,nrows=1,width_ratios=[4,10],height_ratios=[4])
ax1 = fig.add_subplot(spec[0,0])
ax1.set_title("KPI Value and Confidence Interval",fontsize='xx-large')
ax2 = fig.add_subplot(spec[0,1],facecolor='white')
ax2.set_title("Expected Distribution",fontsize='xx-large')
### Plot result ###
mu_dict = {labelA:pA,labelB:pB}
data_dict = {labelA:z_test_ci(pA,sA,nA,sig_level,tail=alternative),
labelB:(z_test_ci(pB,sB,nB,sig_level,tail=alternative))}
plot_vbar_result(ax1,data_dict,mu_dict)
### Plot Hypothesis ####
display(HTML("<hr><center><h3>Distribution Plot</h3></center>"))
plot_norm_dist(ax2,pA,sA,nA,label=labelA,with_CI=True,tail=alternative,color=color[0])
plot_norm_dist(ax2,pB,sB,nB,label=labelB,tail=alternative,color=color[1])
if show_alpha:
plot_show_alpha(ax2,pA,sA,nA,sig_level=sig_level,tail=alternative,color=color[0],test_type='z-test')
plt.legend(loc='best')
plt.show()
### Plot Table ###
result_table(pA=pA,pB=pB,power=power,p=p,tscore=z,sA=sA,sB=sB,
stderr=stderr,nA=nA,nB=nB,df=None,sig_level=sig_level)
display(HTML("<center><i>*** : statistical significant</i></center>"))
display(HTML("""<hr style="border-top: 2px double #8c8b8b";/> """))