Importing the python packages
In [ ]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.stats as stats
from scipy.stats import ttest_1samp
from scipy.stats import ttest_ind
from scipy.stats import ttest_rel
from scipy.stats import chisquare
from scipy.stats import chi2
from scipy.stats import chi2_contingency
from scipy.stats import f_oneway
from scipy.stats import kruskal
from scipy.stats import shapiro
from scipy.stats import levene
from scipy.stats import kstest
Importing the data set
In [ ]:
!gdown https://drive.google.com/uc?id=1fMo4Y25KsVtTWcsjZ3wGsiUjBEO9Wcn6
Downloading... From: https://drive.google.com/uc?id=1fMo4Y25KsVtTWcsjZ3wGsiUjBEO9Wcn6 To: /content/walmart_data.csv 100% 23.0M/23.0M [00:00<00:00, 103MB/s]
In [ ]:
df = pd.read_csv('walmart_data.csv')
Preliminary checking
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df.shape
Out[ ]:
(550068, 10)
In [ ]:
df.sample(5)
Out[ ]:
| User_ID | Product_ID | Gender | Age | Occupation | City_Category | Stay_In_Current_City_Years | Marital_Status | Product_Category | Purchase | |
|---|---|---|---|---|---|---|---|---|---|---|
| 219556 | 1003841 | P00182242 | M | 46-50 | 18 | A | 4+ | 0 | 1 | 11782 |
| 85229 | 1001164 | P00110842 | F | 26-35 | 19 | A | 1 | 1 | 1 | 11699 |
| 426469 | 1005659 | P00117442 | M | 26-35 | 0 | C | 3 | 1 | 5 | 8678 |
| 308625 | 1005555 | P00057542 | M | 0-17 | 10 | B | 2 | 0 | 3 | 8319 |
| 354073 | 1000549 | P00202042 | M | 26-35 | 6 | A | 3 | 0 | 8 | 7849 |
In [ ]:
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 550068 entries, 0 to 550067 Data columns (total 10 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 User_ID 550068 non-null int64 1 Product_ID 550068 non-null object 2 Gender 550068 non-null object 3 Age 550068 non-null object 4 Occupation 550068 non-null int64 5 City_Category 550068 non-null object 6 Stay_In_Current_City_Years 550068 non-null object 7 Marital_Status 550068 non-null int64 8 Product_Category 550068 non-null int64 9 Purchase 550068 non-null int64 dtypes: int64(5), object(5) memory usage: 42.0+ MB
In [ ]:
df.describe()
Out[ ]:
| User_ID | Occupation | Marital_Status | Product_Category | Purchase | |
|---|---|---|---|---|---|
| count | 5.500680e+05 | 550068.000000 | 550068.000000 | 550068.000000 | 550068.000000 |
| mean | 1.003029e+06 | 8.076707 | 0.409653 | 5.404270 | 9263.968713 |
| std | 1.727592e+03 | 6.522660 | 0.491770 | 3.936211 | 5023.065394 |
| min | 1.000001e+06 | 0.000000 | 0.000000 | 1.000000 | 12.000000 |
| 25% | 1.001516e+06 | 2.000000 | 0.000000 | 1.000000 | 5823.000000 |
| 50% | 1.003077e+06 | 7.000000 | 0.000000 | 5.000000 | 8047.000000 |
| 75% | 1.004478e+06 | 14.000000 | 1.000000 | 8.000000 | 12054.000000 |
| max | 1.006040e+06 | 20.000000 | 1.000000 | 20.000000 | 23961.000000 |
In [ ]:
df.describe(include = "object")
Out[ ]:
| Product_ID | Gender | Age | City_Category | Stay_In_Current_City_Years | |
|---|---|---|---|---|---|
| count | 550068 | 550068 | 550068 | 550068 | 550068 |
| unique | 3631 | 2 | 7 | 3 | 5 |
| top | P00265242 | M | 26-35 | B | 1 |
| freq | 1880 | 414259 | 219587 | 231173 | 193821 |
In [ ]:
df.value_counts()
Out[ ]:
| count | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| User_ID | Product_ID | Gender | Age | Occupation | City_Category | Stay_In_Current_City_Years | Marital_Status | Product_Category | Purchase | |
| 1000001 | P00000142 | F | 0-17 | 10 | A | 2 | 0 | 3 | 13650 | 1 |
| 1004007 | P00105342 | M | 36-45 | 12 | A | 1 | 1 | 1 | 11668 | 1 |
| P00115942 | M | 36-45 | 12 | A | 1 | 1 | 8 | 9800 | 1 | |
| P00115142 | M | 36-45 | 12 | A | 1 | 1 | 1 | 11633 | 1 | |
| P00114942 | M | 36-45 | 12 | A | 1 | 1 | 1 | 19148 | 1 | |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 1001973 | P00265242 | M | 26-35 | 1 | A | 0 | 0 | 5 | 8659 | 1 |
| P00226342 | M | 26-35 | 1 | A | 0 | 0 | 11 | 6112 | 1 | |
| P00198042 | M | 26-35 | 1 | A | 0 | 0 | 11 | 5915 | 1 | |
| P00129842 | M | 26-35 | 1 | A | 0 | 0 | 6 | 16101 | 1 | |
| 1006040 | P00349442 | M | 26-35 | 6 | B | 2 | 0 | 6 | 16389 | 1 |
550068 rows × 1 columns
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df['Product_ID'].nunique()
Out[ ]:
3631
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df['Product_ID'].value_counts()
Out[ ]:
| count | |
|---|---|
| Product_ID | |
| P00265242 | 1880 |
| P00025442 | 1615 |
| P00110742 | 1612 |
| P00112142 | 1562 |
| P00057642 | 1470 |
| ... | ... |
| P00314842 | 1 |
| P00298842 | 1 |
| P00231642 | 1 |
| P00204442 | 1 |
| P00066342 | 1 |
3631 rows × 1 columns
In [ ]:
df['Age'].value_counts()
Out[ ]:
| count | |
|---|---|
| Age | |
| 26-35 | 219587 |
| 36-45 | 110013 |
| 18-25 | 99660 |
| 46-50 | 45701 |
| 51-55 | 38501 |
| 55+ | 21504 |
| 0-17 | 15102 |
In [ ]:
df['Gender'].value_counts()
Out[ ]:
| count | |
|---|---|
| Gender | |
| M | 414259 |
| F | 135809 |
In [ ]:
df['User_ID'].nunique()
Out[ ]:
5891
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df['Occupation'].nunique()
Out[ ]:
21
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df['City_Category'].nunique()
Out[ ]:
3
In [ ]:
df['Stay_In_Current_City_Years'].value_counts()
Out[ ]:
| count | |
|---|---|
| Stay_In_Current_City_Years | |
| 1 | 193821 |
| 2 | 101838 |
| 3 | 95285 |
| 4+ | 84726 |
| 0 | 74398 |
In [ ]:
df['Marital_Status'].value_counts()
Out[ ]:
| count | |
|---|---|
| Marital_Status | |
| 0 | 324731 |
| 1 | 225337 |
In [ ]:
df['Product_Category'].nunique()
Out[ ]:
20
Preliminary Analysis
Changing the numerical columns "Marital_Status", "Occupation" and "Product_Category" to categorcial columns
In [ ]:
df['Marital_Status'] = df['Marital_Status'].astype("category")
df['Product_Category'] = df['Product_Category'].astype("category")
df['Occupation'] = df['Occupation'].astype("category")
In [ ]:
sns.pairplot(df)
plt.show()
NULL values and Outliers
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df.isnull().sum()
Out[ ]:
| 0 | |
|---|---|
| User_ID | 0 |
| Product_ID | 0 |
| Gender | 0 |
| Age | 0 |
| Occupation | 0 |
| City_Category | 0 |
| Stay_In_Current_City_Years | 0 |
| Marital_Status | 0 |
| Product_Category | 0 |
| Purchase | 0 |
There are no missing or null values.
Identifying Outliers
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plt.figure(figsize=(10, 6))
sns.boxplot(data = df, y = "Purchase")
plt.show()
Cliping the data between 5th and 95th percentile
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lower_bound = df['Purchase'].quantile(0.05)
upper_bound = df['Purchase'].quantile(0.95)
df['Purchase_clipped'] = np.clip(df['Purchase'], lower_bound, upper_bound)
In [ ]:
df1 = df.drop('Purchase', axis = 1)
df1 = df1.rename(columns = {'Purchase_clipped': 'Purchase'})
In [ ]:
plt.figure(figsize=(10, 6))
sns.boxplot(data = df1, y = "Purchase")
plt.show()
Data exploration
Tracking the amount spent per transaction of all the 50 million female customers, and all the 50 million male customers, calculate the average, and conclude the results.
In [ ]:
sns.boxplot(data = df1, x = "Gender", y = "Purchase")
mean_values = df1.groupby('Gender')['Purchase'].mean()
for gender in mean_values.index:
plt.annotate(f'Mean: {mean_values[gender]:.2f}',
xy=(gender, mean_values[gender]),
xytext=(gender, mean_values[gender] + 5),
ha='center', va='bottom', color='black', fontweight='bold')
plt.show()
Finding: The average amount spent by male customers are slightly higher than the female customers
The interval within which the average spending of 50 million male and female customers may lie
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female_spending = df1[df1['Gender'] == 'F']['Purchase']
male_spending = df1[df1['Gender'] == 'M']['Purchase']
sample_mean_f = np.mean(female_spending)
sample_mean_m = np.mean(male_spending)
sample_std_f = np.std(female_spending, ddof=1)
sample_std_m = np.std(female_spending, ddof=1)
sample_size_f = len(female_spending)
sample_size_m = len(male_spending)
standard_error_f = sample_std_f / np.sqrt(sample_size_f)
standard_error_m = sample_std_m / np.sqrt(sample_size_m)
confidence_level_1 = 0.90
confidence_level_2 = 0.95
confidence_level_3 = 0.99
degrees_of_freedom_f = sample_size_f - 1
degrees_of_freedom_m = sample_size_m - 1
t_value_f_1 = stats.t.ppf(1 - (1 - confidence_level_1) / 2, degrees_of_freedom_f)
t_value_m_1 = stats.t.ppf(1 - (1 - confidence_level_1) / 2, degrees_of_freedom_m)
t_value_f_2 = stats.t.ppf(1 - (1 - confidence_level_2) / 2, degrees_of_freedom_f)
t_value_m_2 = stats.t.ppf(1 - (1 - confidence_level_2) / 2, degrees_of_freedom_m)
t_value_f_3 = stats.t.ppf(1 - (1 - confidence_level_3) / 2, degrees_of_freedom_f)
t_value_m_3 = stats.t.ppf(1 - (1 - confidence_level_3) / 2, degrees_of_freedom_m)
margin_of_error_f_1 = t_value_f_1 * standard_error_f
margin_of_error_m_1 = t_value_m_1 * standard_error_m
margin_of_error_f_2 = t_value_f_2 * standard_error_f
margin_of_error_m_2 = t_value_m_2 * standard_error_m
margin_of_error_f_3 = t_value_f_3 * standard_error_f
margin_of_error_m_3 = t_value_m_3 * standard_error_m
confidence_interval_f_1 = (sample_mean_f - margin_of_error_f_1, sample_mean_f + margin_of_error_f_1)
confidence_interval_m_1 = (sample_mean_m - margin_of_error_m_1, sample_mean_m + margin_of_error_m_1)
confidence_interval_f_2 = (sample_mean_f - margin_of_error_f_2, sample_mean_f + margin_of_error_f_2)
confidence_interval_m_2 = (sample_mean_m - margin_of_error_m_2, sample_mean_m + margin_of_error_m_2)
confidence_interval_f_3 = (sample_mean_f - margin_of_error_f_3, sample_mean_f + margin_of_error_f_3)
confidence_interval_m_3 = (sample_mean_m - margin_of_error_m_3, sample_mean_m + margin_of_error_m_3)
print(f"The {confidence_level_1*100}% confidence interval for the male population mean is: {confidence_interval_m_1} and female population mean is: {confidence_interval_f_1}")
print(f"The {confidence_level_2*100}% confidence interval for the male population mean is: {confidence_interval_m_2} and female population mean is: {confidence_interval_f_2}")
print(f"The {confidence_level_3*100}% confidence interval for the male population mean is: {confidence_interval_m_3} and female population mean is: {confidence_interval_f_3}")
The 90.0% confidence interval for the male population mean is: (9415.49295967642, 9438.989033472793) and female population mean is: (8716.022078632317, 8757.058453585725) The 95.0% confidence interval for the male population mean is: (9413.242337595677, 9441.239655553536) and female population mean is: (8712.091286628549, 8760.989245589493) The 99.0% confidence interval for the male population mean is: (9408.843609132742, 9445.63838401647) and female population mean is: (8704.40869525922, 8768.671836958822)
Use the Central limit theorem to compute the interval. Change the sample size to observe the distribution of the mean of the expenses by female and male customers.
In [ ]:
def simulate_sampling(data, num_samples, sample_size):
sample_means = []
for _ in range(num_samples):
sample = np.random.choice(data, size=sample_size, replace=False)
sample_mean = np.mean(sample)
sample_means.append(sample_mean)
return np.array(sample_means)
#My PC unable to execute for the higher values
#num_samples = df1.shape[0]
#sample_sizes = [300, 3000, 30000]
#So I took lower values
num_samples = 5000
sample_sizes = [30, 300, 3000]
In [ ]:
for sample_size in sample_sizes:
female_sample_means = simulate_sampling(female_spending, num_samples, sample_size)
male_sample_means = simulate_sampling(male_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(female_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Female Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(male_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Male Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
female_mean = np.mean(female_sample_means)
female_se = np.std(female_sample_means) / np.sqrt(sample_size)
female_ci = stats.norm.interval(0.90, loc=female_mean, scale=female_se)
male_mean = np.mean(male_sample_means)
male_se = np.std(male_sample_means) / np.sqrt(sample_size)
male_ci = stats.norm.interval(0.90, loc=male_mean, scale=male_se)
print(f'90% Confidence Interval for Female (Sample Size = {sample_size}): {female_ci}')
print(f'90% Confidence Interval for Male (Sample Size = {sample_size}): {male_ci}\n')
90% Confidence Interval for Female (Sample Size = 30): (8480.031842889337, 8991.046690443993) 90% Confidence Interval for Male (Sample Size = 30): (9148.3364986633, 9687.591208003365)
90% Confidence Interval for Female (Sample Size = 300): (8711.475095267024, 8761.93189939964) 90% Confidence Interval for Male (Sample Size = 300): (9398.929162081715, 9453.559721918284)
90% Confidence Interval for Female (Sample Size = 3000): (8734.787925490225, 8739.786386909775) 90% Confidence Interval for Male (Sample Size = 3000): (9424.77712915229, 9430.137304581045)
In [ ]:
for sample_size in sample_sizes:
female_sample_means = simulate_sampling(female_spending, num_samples, sample_size)
male_sample_means = simulate_sampling(male_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(female_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Female Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(male_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Male Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
female_mean = np.mean(female_sample_means)
female_se = np.std(female_sample_means) / np.sqrt(sample_size)
female_ci = stats.norm.interval(0.95, loc=female_mean, scale=female_se)
male_mean = np.mean(male_sample_means)
male_se = np.std(male_sample_means) / np.sqrt(sample_size)
male_ci = stats.norm.interval(0.95, loc=male_mean, scale=male_se)
print(f'95% Confidence Interval for Female (Sample Size = {sample_size}): {female_ci}')
print(f'95% Confidence Interval for Male (Sample Size = {sample_size}): {male_ci}\n')
95% Confidence Interval for Female (Sample Size = 30): (8441.511410646679, 9037.625416019986) 95% Confidence Interval for Male (Sample Size = 30): (9105.844192432965, 9753.991940900365)
95% Confidence Interval for Female (Sample Size = 300): (8705.974390153826, 8766.105849846173) 95% Confidence Interval for Male (Sample Size = 300): (9393.379587833406, 9458.286376166594)
95% Confidence Interval for Female (Sample Size = 3000): (8733.468386258623, 8739.412305874708) 95% Confidence Interval for Male (Sample Size = 3000): (9422.45985337089, 9428.784093295775)
In [ ]:
for sample_size in sample_sizes:
female_sample_means = simulate_sampling(female_spending, num_samples, sample_size)
male_sample_means = simulate_sampling(male_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(female_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Female Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(male_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Male Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
female_mean = np.mean(female_sample_means)
female_se = np.std(female_sample_means) / np.sqrt(sample_size)
female_ci = stats.norm.interval(0.95, loc=female_mean, scale=female_se)
male_mean = np.mean(male_sample_means)
male_se = np.std(male_sample_means) / np.sqrt(sample_size)
male_ci = stats.norm.interval(0.99, loc=male_mean, scale=male_se)
print(f'99% Confidence Interval for Female (Sample Size = {sample_size}): {female_ci}')
print(f'99% Confidence Interval for Male (Sample Size = {sample_size}): {male_ci}\n')
99% Confidence Interval for Female (Sample Size = 30): (8444.110962957091, 9038.385063709573) 99% Confidence Interval for Male (Sample Size = 30): (9018.917228836463, 9852.611704496869)
99% Confidence Interval for Female (Sample Size = 300): (8703.35108799944, 8763.944176000561) 99% Confidence Interval for Male (Sample Size = 300): (9388.071421524905, 9474.15172914176)
99% Confidence Interval for Female (Sample Size = 3000): (8730.889566910286, 8736.855668956381) 99% Confidence Interval for Male (Sample Size = 3000): (9420.68577656256, 9429.104112637442)
Distribution of Sample Means: As the sample size increases, the distribution of the sample means becomes narrower and more normally distributed, confirming the Central Limit Theorem.
Confidence Interval: As the sample size increases, the confidence interval becomes narrower, indicating a more precise estimate of the population mean.
Conclude the results and check if the confidence intervals of average male and female spends are overlapping or not overlapping. How can Walmart leverage this conclusion to make changes or improvements?
From the above analysis, it is clear that the confidence intervals for the male and female customers are not over lapping.
It indicates that there is a statistically significant difference in spending patterns between the genders.
Walmart can infer that male and female customers have distinct spending behaviors. This can guide targeted marketing strategies, such as personalized promotions or product offerings tailored to each gender.
Walmart can develop gender-specific marketing strategies. For example, if females spend more on certain categories, Walmart can promote those products more aggressively towards female customers.
Walmart could adjust its product assortment based on the spending tendencies of each gender. For example, increasing inventory in categories where female customers spend more, or introducing more products that are popular with male customers.
Walmart might consider dynamic pricing, offering discounts or promotions on products that are more appealing to one gender to drive sales.
Walmart could consider gender-based store layouts or online experiences, making it easier for each gender to find and purchase products they are more likely to spend on.
Married vs Unmarried
In [ ]:
married_spending = df1[df1['Marital_Status'] == 1]['Purchase']
unmarried_spending = df1[df1['Marital_Status'] == 0]['Purchase']
for sample_size in sample_sizes:
married_sample_means = simulate_sampling(married_spending, num_samples, sample_size)
unmarried_sample_means = simulate_sampling(unmarried_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(married_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Married Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(unmarried_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Unmarried Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
married_mean = np.mean(married_sample_means)
married_se = np.std(married_sample_means) / np.sqrt(sample_size)
married_ci = stats.norm.interval(0.90, loc=married_mean, scale=married_se)
unmarried_mean = np.mean(unmarried_sample_means)
unmarried_se = np.std(unmarried_sample_means) / np.sqrt(sample_size)
unmarried_ci = stats.norm.interval(0.90, loc=unmarried_mean, scale=unmarried_se)
print(f'90% Confidence Interval for Married (Sample Size = {sample_size}): {married_ci}')
print(f'90% Confidence Interval for Unmarried (Sample Size = {sample_size}): {unmarried_ci}\n')
90% Confidence Interval for Married (Sample Size = 30): (8972.799099357788, 9507.275273975549) 90% Confidence Interval for Unmarried (Sample Size = 30): (9016.850882164203, 9546.933917835799)
90% Confidence Interval for Married (Sample Size = 300): (9223.69367071199, 9276.504786621343) 90% Confidence Interval for Unmarried (Sample Size = 300): (9227.382390850815, 9282.306421149186)
90% Confidence Interval for Married (Sample Size = 3000): (9248.812973449672, 9254.01616655033) 90% Confidence Interval for Unmarried (Sample Size = 3000): (9256.782889190263, 9262.013548276404)
In [ ]:
for sample_size in sample_sizes:
married_sample_means = simulate_sampling(married_spending, num_samples, sample_size)
unmarried_sample_means = simulate_sampling(unmarried_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(married_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Married Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(unmarried_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Unmarried Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
married_mean = np.mean(married_sample_means)
married_se = np.std(married_sample_means) / np.sqrt(sample_size)
married_ci = stats.norm.interval(0.90, loc=married_mean, scale=married_se)
unmarried_mean = np.mean(unmarried_sample_means)
unmarried_se = np.std(unmarried_sample_means) / np.sqrt(sample_size)
unmarried_ci = stats.norm.interval(0.95, loc=unmarried_mean, scale=unmarried_se)
print(f'95% Confidence Interval for Married (Sample Size = {sample_size}): {married_ci}')
print(f'95% Confidence Interval for Unmarried (Sample Size = {sample_size}): {unmarried_ci}\n')
95% Confidence Interval for Married (Sample Size = 30): (8996.077604063985, 9531.840635936014) 95% Confidence Interval for Unmarried (Sample Size = 30): (8925.768056045881, 9553.487183954121)
95% Confidence Interval for Married (Sample Size = 300): (9225.10740129436, 9277.74835470564) 95% Confidence Interval for Unmarried (Sample Size = 300): (9227.908104757928, 9290.893168575407)
95% Confidence Interval for Married (Sample Size = 3000): (9251.255401244956, 9256.507321688377) 95% Confidence Interval for Unmarried (Sample Size = 3000): (9254.375203478237, 9260.821893055097)
In [ ]:
for sample_size in sample_sizes:
married_sample_means = simulate_sampling(married_spending, num_samples, sample_size)
unmarried_sample_means = simulate_sampling(unmarried_spending, num_samples, sample_size)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.hist(married_sample_means, bins=30, color='blue', alpha=0.7)
plt.title(f'Distribution of Married Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.subplot(1, 2, 2)
plt.hist(unmarried_sample_means, bins=30, color='green', alpha=0.7)
plt.title(f'Distribution of Unmarried Sample Means (Sample Size = {sample_size})')
plt.xlabel('Mean of Sample')
plt.ylabel('Frequency')
plt.tight_layout()
plt.show()
married_mean = np.mean(married_sample_means)
married_se = np.std(married_sample_means) / np.sqrt(sample_size)
married_ci = stats.norm.interval(0.90, loc=married_mean, scale=married_se)
unmarried_mean = np.mean(unmarried_sample_means)
unmarried_se = np.std(unmarried_sample_means) / np.sqrt(sample_size)
unmarried_ci = stats.norm.interval(0.99, loc=unmarried_mean, scale=unmarried_se)
print(f'99% Confidence Interval for Married (Sample Size = {sample_size}): {married_ci}')
print(f'99% Confidence Interval for Unmarried (Sample Size = {sample_size}): {unmarried_ci}\n')
99% Confidence Interval for Married (Sample Size = 30): (8976.03379355569, 9511.640339777643) 99% Confidence Interval for Unmarried (Sample Size = 30): (8853.398431501355, 9693.40886183198)
99% Confidence Interval for Married (Sample Size = 300): (9230.885108021537, 9284.24659864513) 99% Confidence Interval for Unmarried (Sample Size = 300): (9218.669368208848, 9302.855289124484)
99% Confidence Interval for Married (Sample Size = 3000): (9250.197546849133, 9255.493704617536) 99% Confidence Interval for Unmarried (Sample Size = 3000): (9254.31466728117, 9262.722706718829)
From the above analysis, the confidence interval for married and unmarried over lapping on each other.
It suggests that there is no strong evidence of a difference in average spending between married and unmarried customers.
Walmart may not need to differentiate marketing strategies based on Marital status, focusing instead on other factors like product type, age group, or geographical location.
Walmart might choose to stock products that are universally appealing, ensuring a balanced inventory that caters to both married and unmarried customers.
Walmart could implement uniform pricing strategies, knowing that both marital status respond similarly to price changes.
Walmart can design store layouts that are neutral (marital status), focusing on ease of access and product visibility for all customers.
Age
In [ ]:
plt.figure(figsize=(15, 9))
sns.boxplot(data = df1, x = "Age", y = "Purchase")
mean_values = df1.groupby('Age')['Purchase'].mean()
for age in mean_values.index:
plt.annotate(f'Mean: {mean_values[age]:.2f}',
xy=(age, mean_values[age]),
xytext=(age, mean_values[age] + 5),
ha='center', va='bottom', color='black', fontweight='bold')
plt.show()
From the above analysis for age, the average spending for all the age groups almost similar.
In [ ]:
sns.kdeplot(data = df1, x = "Purchase", hue = "Age", fill = True)
plt.show()
From the above graph, it is clear that the purchase amount mean is not normally distributed among the different age groups.
In [ ]:
a = df1[df1['Age'] == '0-17']['Purchase']
b = df1[df1['Age'] == '18-25']['Purchase']
c = df1[df1['Age'] == '26-35']['Purchase']
d = df1[df1['Age'] == '36-45']['Purchase']
e = df1[df1['Age'] == '46-50']['Purchase']
f = df1[df1['Age'] == '51-55']['Purchase']
g = df1[df1['Age'] == '55+']['Purchase']
stat, p_value = kruskal(a, b, c, d, e, f, g)
print(f"Kruskal-Wallis Test Statistic: {stat}")
print(f"p-value: {p_value}")
Kruskal-Wallis Test Statistic: 316.4269448324082 p-value: 2.46438599591188e-65
In [ ]:
statistic, pvalue_levene = levene(a, b, c, d, e, f, g)
print('Levene test p-value:', pvalue_levene)
Levene test p-value: 2.4089831185669614e-18
Since the P_value is very less than 0.01 siginifance level, atleast one of the median of the purchase amount is different among the all age groups.
T-test analysis for different age groups
In [ ]:
li = [(a, 'a'), (b, 'b'), (c, 'c'), (d, 'd'), (e, 'e'), (f, 'f'), (g, 'g')]
for i in range(len(li)):
for j in range(i+1, len(li)):
t_stat, p_value = ttest_ind(li[i][0], li[j][0])
print(f"P-value for {li[i][1]} vs {li[j][1]}: {p_value}")
p_values.append(p_value)
if p_value < 0.01:
print(f"Mean for {li[i][1]} vs {li[j][1]} are different")
else:
print(f"Mean for {li[i][1]} vs {li[j][1]} are not different")
P-value for a vs b: 9.24780800277167e-08 Mean for a vs b are different P-value for a vs c: 1.2374433719441918e-13 Mean for a vs c are different P-value for a vs d: 1.2511766028692978e-19 Mean for a vs d are different P-value for a vs e: 5.9154753390416615e-09 Mean for a vs e are different P-value for a vs f: 2.588529750468243e-34 Mean for a vs f are different P-value for a vs g: 5.457409718987201e-14 Mean for a vs g are different P-value for b vs c: 5.745443104774875e-05 Mean for b vs c are different P-value for b vs d: 4.826112763709447e-13 Mean for b vs d are different P-value for b vs e: 0.19955449362883126 Mean for b vs e are not different P-value for b vs f: 4.1169646189717254e-32 Mean for b vs f are different P-value for b vs g: 1.4514865212013256e-05 Mean for b vs g are different P-value for c vs d: 1.0091325892582545e-05 Mean for c vs d are different P-value for c vs e: 0.11206968398444146 Mean for c vs e are not different P-value for c vs f: 5.602787400997221e-24 Mean for c vs f are different P-value for c vs g: 0.015305566991815853 Mean for c vs g are not different P-value for d vs e: 1.0027594932979892e-05 Mean for d vs e are different P-value for d vs f: 2.4398060592744895e-11 Mean for d vs f are different P-value for d vs g: 0.8924745240949798 Mean for d vs g are not different P-value for e vs f: 1.3744431162023413e-20 Mean for e vs f are different P-value for e vs g: 0.0017855800648166704 Mean for e vs g are different P-value for f vs g: 5.643685669707695e-06 Mean for f vs g are different
From the above T-test analysis, the mean of purchase amount spent,
- 18-25 vs 46-50 are not different
- 26-35 vs 46-50 are not different
- 26-35 vs 55+ are not different
- 36-45 vs 55+ are not different
And the rest of the age groups are significantly different.
Insights & Recommendations
The average amount spent by male customers are slightly higher than the female customers.
From the above analysis, it is clear that the confidence intervals for the male and female customers are not over lapping.
It indicates that there is a statistically significant difference in spending patterns between the genders.
Walmart can infer that male and female customers have distinct spending behaviors. This can guide targeted marketing strategies, such as personalized promotions or product offerings tailored to each gender.
Walmart can develop gender-specific marketing strategies. For example, if females spend more on certain categories, Walmart can promote those products more aggressively towards female customers.
Walmart could adjust its product assortment based on the spending tendencies of each gender. For example, increasing inventory in categories where female customers spend more, or introducing more products that are popular with male customers.
Walmart might consider dynamic pricing, offering discounts or promotions on products that are more appealing to one gender to drive sales.
Walmart could consider gender-based store layouts or online experiences, making it easier for each gender to find and purchase products they are more likely to spend on.
From the above analysis, the confidence interval for married and unmarried over lapping on each other.
It suggests that there is no strong evidence of a difference in average spending between married and unmarried customers.
Walmart may not need to differentiate marketing strategies based on Marital status, focusing instead on other factors like product type, age group, or geographical location.
Walmart might choose to stock products that are universally appealing, ensuring a balanced inventory that caters to both married and unmarried customers.
Walmart could implement uniform pricing strategies, knowing that both marital status respond similarly to price changes.
Walmart can design store layouts that are neutral (marital status), focusing on ease of access and product visibility for all customers.
From the above T-test analysis, the mean of purchase amount spent amoung the different age groups, 18-25 vs 46-50 are not different 26-35 vs 46-50 are not different 26-35 vs 55+ are not different 36-45 vs 55+ are not different And the rest of the age groups are significantly different. The age group 0-17 is significantly differs from the age groups. It could be possibly of the kids and teenagers.