BUSINESS STATISTICS: E-NEWS EXPRESS
A/B TESTING
Problem Statement
E-news Express wants to test whether a new landing page improves user engagement and conversions compared to the old page
Objective
1. To perform univariate analysis
2. To perform bivariate analysis
3. To provide insight and business recommendations
#import relevant library
import pandas as pd # for data manipulation
import numpy as np # for numerical analysis
from scipy import stats
import matplotlib.pyplot as plt # for data visulization
import seaborn as sns # for advanced ploting
data = pd.read_csv(r"C:\Users\njugu\Downloads\New folder\abtest.csv")
data.head()## user_id group ... converted language_preferred
## 0 546592 control ... no Spanish
## 1 546468 treatment ... yes English
## 2 546462 treatment ... no Spanish
## 3 546567 control ... no French
## 4 546459 treatment ... yes Spanish
##
## [5 rows x 6 columns]data.tail()## user_id group ... converted language_preferred
## 95 546446 treatment ... no Spanish
## 96 546544 control ... yes English
## 97 546472 treatment ... yes Spanish
## 98 546481 treatment ... yes Spanish
## 99 546483 treatment ... yes English
##
## [5 rows x 6 columns]data.describe()## user_id time_spent_on_the_page
## count 100.000000 100.000000
## mean 546517.000000 5.377800
## std 52.295779 2.378166
## min 546443.000000 0.190000
## 25% 546467.750000 3.880000
## 50% 546492.500000 5.415000
## 75% 546567.250000 7.022500
## max 546592.000000 10.710000data.shape## (100, 6)data.isnull().sum().sort_values(ascending=False)#for missing values## user_id 0
## group 0
## landing_page 0
## time_spent_on_the_page 0
## converted 0
## language_preferred 0
## dtype: int64data.duplicated().sum()#looking for duplicates## np.int64(0)#separating categorical column from numerical colun
numerical = data.select_dtypes(include=["int64", "float64"])
categorical = data.select_dtypes(include=["object", "category"])
numerical.describe()## user_id time_spent_on_the_page
## count 100.000000 100.000000
## mean 546517.000000 5.377800
## std 52.295779 2.378166
## min 546443.000000 0.190000
## 25% 546467.750000 3.880000
## 50% 546492.500000 5.415000
## 75% 546567.250000 7.022500
## max 546592.000000 10.710000categorical.describe()## group landing_page converted language_preferred
## count 100 100 100 100
## unique 2 2 2 3
## top control old yes Spanish
## freq 50 50 54 34PERFORMING UNIVARIATE ANALYSIS FOR NUMERICAL COLUMNS
# SUMMARY STATISTICS FOR NUMERICAL COLUMN
data["time_spent_on_the_page"].describe()## count 100.000000
## mean 5.377800
## std 2.378166
## min 0.190000
## 25% 3.880000
## 50% 5.415000
## 75% 7.022500
## max 10.710000
## Name: time_spent_on_the_page, dtype: float64# plot histogram
plt.figure(figsize=(10,5))
sns.histplot(data["time_spent_on_the_page"], kde=True)
plt.title("A HISTOGRAM OF TIME SPENT ON THE PAGE")
plt.show()
#plot the boxplot
sns.boxplot(data["time_spent_on_the_page"])
plt.title("BOXPLOT OF TIME SPENT ON THE PAGE")
plt.show()
# UNIVARIATE ANALYSIS FOR CATEGORICAL COLUMNS
# ANALYZE USER GROUP
data["group"].value_counts()## group
## control 50
## treatment 50
## Name: count, dtype: int64sns.countplot(x=data['group'])
plt.title("DISTRIBUTION OF USER GROUP")
plt.show()
data["landing_page"].value_counts()## landing_page
## old 50
## new 50
## Name: count, dtype: int64sns.countplot(x=data["landing_page"])
plt.title("DISTRIBUTION OF LANDING PAGES")
plt.show()
data["converted"].value_counts()## converted
## yes 54
## no 46
## Name: count, dtype: int64sns.countplot(x=data["converted"])
plt.title("CONVERSION DISTRIBUTION")
plt.show()
data['language_preferred'].value_counts()## language_preferred
## Spanish 34
## French 34
## English 32
## Name: count, dtype: int64sns.countplot(x=data['language_preferred'])
plt.title("Distribution of Preferred Languages")
plt.show()
BIVARIATE ANALYSIS
Do users spend more time on than on the old page
sns.boxplot(x='landing_page', y='time_spent_on_the_page', data=data)
plt.title("LANDING PAGE VS TIME SPENT")
plt.show()
Null hypothesis : Users spend the same amount of time on old and new pages.
Alternative hypothesis : Users spend more time on the new page
old_page = data[data['landing_page'] == 'old']['time_spent_on_the_page']
new_page = data[data['landing_page'] == 'new']['time_spent_on_the_page']
t_stat, p_value = stats.ttest_ind(new_page, old_page, equal_var=False)
t_stat, p_value## (np.float64(3.7867702694199856), np.float64(0.0002784762450333098))If p < 0.05 → reject H₀ → conclude users spend more time on the new page.
If p ≥ 0.05 → fail to reject H₀ → no significant difference.
we now conclude that users spend more time on new page
Is the conversion rate higher for the new page?
#We count how many users converted vs not converted for each page
pd.crosstab(data['landing_page'], data['converted'])## converted no yes
## landing_page
## new 17 33
## old 29 21H_0: Conversion rate is the same for old and new pages.
H_1: Conversion rate is higher for the new page.
#both variable are categorical we will use chi square test for independence
table = pd.crosstab(data['landing_page'], data['converted'])
chi2, p_value, dof, expected = stats.chi2_contingency(table)
chi2, p_value## (np.float64(4.871175523349437), np.float64(0.02730889175492232))we conclude that users who spend more time on the new page are more likely to be convertad
Are conversion and language preference related?
pd.crosstab(data['language_preferred'], data['converted'])## converted no yes
## language_preferred
## English 11 21
## French 19 15
## Spanish 16 18H_0:Conversion is independent of language.
H_1:Conversion depends on language.
table2 = pd.crosstab(data['language_preferred'], data['converted'])
chi2, p_value, dof, expected = stats.chi2_contingency(table2)
chi2, p_value## (np.float64(3.0930306905370832), np.float64(0.2129888748754345))we conclude that language does not matter in the conversion
Is time spent on the new page the same across different languages?
sns.boxplot(x='language_preferred', y='time_spent_on_the_page', data=data)
plt.title("Time Spent Across Languages")
plt.show()
#### H_0:Mean time spent is the same across languages. #### H_1:some of
the language group spend different time
languages = [group['time_spent_on_the_page'].values
for name, group in data.groupby('language_preferred')]
f_stat, p_value = stats.f_oneway(*languages)
f_stat, p_value## (np.float64(0.1434343922124044), np.float64(0.8665610536012649))