CI & p-Values

# Import essential libraries for statistical calculations
import pandas as pd
import numpy as np
from scipy import stats

# Load the ecommerce dataset
df = pd.read_csv('dataplexa_ecommerce.csv')
print(f"Total rows loaded: {len(df)}")
print(df.head())

# Filter for Electronics category only
electronics = df[df['product_category'] == 'Electronics']
print(f"Electronics orders: {len(electronics)}")

# Calculate sample statistics needed for confidence interval
sample_mean = electronics['revenue'].mean()
sample_std = electronics['revenue'].std()
sample_size = len(electronics)

print(f"Sample mean: ₹{sample_mean:.2f}")
print(f"Sample std: ₹{sample_std:.2f}")
print(f"Sample size: {sample_size}")

# Calculate 95% confidence interval using t-distribution
confidence_level = 0.95
alpha = 1 - confidence_level
degrees_freedom = sample_size - 1

# Get the t-critical value for 95% confidence
t_critical = stats.t.ppf(1 - alpha/2, degrees_freedom)
print(f"t-critical value: {t_critical:.4f}")

# Calculate standard error of the mean
standard_error = sample_std / np.sqrt(sample_size)
print(f"Standard error: ₹{standard_error:.2f}")

# Calculate margin of error
margin_of_error = t_critical * standard_error
print(f"Margin of error: ₹{margin_of_error:.2f}")

# Build the confidence interval
ci_lower = sample_mean - margin_of_error
ci_upper = sample_mean + margin_of_error

print(f"\n95% Confidence Interval for Electronics Revenue:")
print(f"₹{ci_lower:.2f} to ₹{ci_upper:.2f}")

# Extract revenue data for both categories
electronics_revenue = df[df['product_category'] == 'Electronics']['revenue']
clothing_revenue = df[df['product_category'] == 'Clothing']['revenue']

print(f"Electronics: {len(electronics_revenue)} orders, mean ₹{electronics_revenue.mean():.2f}")
print(f"Clothing: {len(clothing_revenue)} orders, mean ₹{clothing_revenue.mean():.2f}")
print(f"Difference: ₹{electronics_revenue.mean() - clothing_revenue.mean():.2f}")

# Perform independent t-test 
# H0: Electronics revenue = Clothing revenue
# H1: Electronics revenue ≠ Clothing revenue
t_stat, p_value = stats.ttest_ind(electronics_revenue, clothing_revenue)

print(f"t-statistic: {t_stat:.4f}")
print(f"p-value: {p_value:.2e}")
print(f"Degrees of freedom: {len(electronics_revenue) + len(clothing_revenue) - 2}")

# Interpret the result
alpha = 0.05
if p_value < alpha:
    print(f"\nResult: REJECT null hypothesis (p < {alpha})")
    print("Electronics revenue is significantly different from Clothing revenue")
else:
    print(f"\nResult: FAIL TO REJECT null hypothesis (p >= {alpha})")
    print("No significant difference found")

# Calculate Cohen's d for effect size
def cohens_d(group1, group2):
    # Calculate means
    mean1, mean2 = group1.mean(), group2.mean()
    
    # Calculate pooled standard deviation
    n1, n2 = len(group1), len(group2)
    pooled_std = np.sqrt(((n1-1)*group1.std()**2 + (n2-1)*group2.std()**2) / (n1+n2-2))
    
    # Cohen's d formula
    d = (mean1 - mean2) / pooled_std
    return d

effect_size = cohens_d(electronics_revenue, clothing_revenue)
print(f"Cohen's d: {effect_size:.4f}")

# Interpret Cohen's d effect size
def interpret_cohens_d(d):
    d = abs(d)  # Take absolute value for magnitude
    if d < 0.2:
        return "Negligible effect"
    elif d < 0.5:
        return "Small effect"
    elif d < 0.8:
        return "Medium effect"
    else:
        return "Large effect"

interpretation = interpret_cohens_d(effect_size)
print(f"Effect size interpretation: {interpretation}")
print(f"Practical meaning: Electronics revenue is {abs(effect_size):.2f} standard deviations higher")

# Business context
revenue_difference = electronics_revenue.mean() - clothing_revenue.mean()
print(f"\nBusiness Impact:")
print(f"• Revenue difference: ₹{revenue_difference:.2f} per order")
print(f"• With 3000+ orders monthly: ₹{revenue_difference * 3000:.0f} extra revenue")

# Compare revenue across ALL product categories
from scipy.stats import f_oneway
from statsmodels.stats.multicomp import pairwise_tukeyhsd

# Get all categories
categories = df['product_category'].unique()
print(f"Categories to compare: {list(categories)}")

# Extract revenue for each category
category_revenues = []
for category in categories:
    revenue = df[df['product_category'] == category]['revenue']
    category_revenues.append(revenue)
    print(f"{category}: {len(revenue)} orders, mean ₹{revenue.mean():.2f}")

# Perform ANOVA test first (overall comparison)
f_stat, p_value_anova = f_oneway(*category_revenues)
print(f"ANOVA Results:")
print(f"F-statistic: {f_stat:.4f}")
print(f"p-value: {p_value_anova:.2e}")

if p_value_anova < 0.05:
    print("\nANOVA significant - at least one category differs")
    print("Proceeding with post-hoc pairwise comparisons...")
else:
    print("\nANOVA not significant - no category differences found")