Lab 04: Consumer Behavior & A/B Test Design¶

# ab_sample_size.py
from scipy.stats import norm
import math

def sample_size_per_group(p1, p2, alpha=0.05, power=0.80):
    """
    p1: baseline conversion rate
    p2: target conversion rate
    Returns: required sample size per group
    """
    z_alpha = norm.ppf(1 - alpha/2)  # two-tailed
    z_beta  = norm.ppf(power)

    p_bar = (p1 + p2) / 2
    n = (z_alpha * math.sqrt(2 * p_bar * (1 - p_bar)) +
         z_beta  * math.sqrt(p1*(1-p1) + p2*(1-p2)))**2 / (p2-p1)**2

    return math.ceil(n)

p1 = 0.023  # baseline
p2 = 0.0253 # target (10% relative improvement)

n = sample_size_per_group(p1, p2)
print(f"Required sample size: {n:,} per group ({n*2:,} total)")
print(f"At 50,000 daily checkout visitors, test duration: {math.ceil(n*2/50000)} days")

# Simulate test results
import random
random.seed(42)

control = sum(random.random() < p1 for _ in range(n))
variant = sum(random.random() < p2 for _ in range(n))

print(f"\nSimulated Results:")
print(f"Control:  {control}/{n} conversions ({control/n:.3%})")
print(f"Variant:  {variant}/{n} conversions ({variant/n:.3%})")

# Chi-square test
from scipy.stats import chi2_contingency
table = [[control, n-control], [variant, n-variant]]
chi2, p_val, _, _ = chi2_contingency(table)
print(f"Chi-square: {chi2:.3f}, p-value: {p_val:.4f}")
print(f"Result: {'SIGNIFICANT ✓' if p_val < 0.05 else 'NOT significant ✗'}")

# clv_calculator.py

def calculate_clv(aov, purchase_freq, gross_margin, churn_rate, discount_rate=0.10):
    """
    Simple CLV: (AOV × Purchase Frequency × Gross Margin) / Churn Rate
    DCF CLV: accounts for time value of money
    """
    # Simple CLV
    simple_clv = (aov * purchase_freq * gross_margin) / churn_rate

    # Discounted CLV (3-year horizon)
    dcf_clv = 0
    for year in range(1, 4):
        annual_value = aov * purchase_freq * gross_margin * ((1 - churn_rate) ** (year-1))
        dcf_clv += annual_value / ((1 + discount_rate) ** year)

    return simple_clv, dcf_clv

print("=== E-Commerce CLV Calculator ===\n")

# Scenario 1: Fashion retailer
print("Scenario 1: Online Fashion Retailer")
s_clv, d_clv = calculate_clv(aov=85, purchase_freq=3.2, gross_margin=0.55, churn_rate=0.40)
print(f"  AOV: $85 | Frequency: 3.2x/yr | Margin: 55% | Churn: 40%")
print(f"  Simple CLV: ${s_clv:.2f}")
print(f"  3-Year DCF CLV: ${d_clv:.2f}")
print(f"  Max CAC (at 3:1 ratio): ${d_clv/3:.2f}\n")

# Scenario 2: Subscription box
print("Scenario 2: Monthly Subscription Box")
s_clv, d_clv = calculate_clv(aov=45, purchase_freq=12, gross_margin=0.35, churn_rate=0.08)
print(f"  AOV: $45 | Frequency: 12x/yr | Margin: 35% | Churn: 8%")
print(f"  Simple CLV: ${s_clv:.2f}")
print(f"  3-Year DCF CLV: ${d_clv:.2f}")
print(f"  Max CAC (at 3:1 ratio): ${d_clv/3:.2f}\n")

# Scenario 3: YOUR scenario (fill in)
print("Scenario 3: [Your Business]")
# TODO: Replace with your own e-commerce business scenario
your_aov = float(input("Average Order Value ($): "))
your_freq = float(input("Purchase frequency (times/year): "))
your_margin = float(input("Gross margin (0-1): "))
your_churn = float(input("Annual churn rate (0-1): "))
s_clv, d_clv = calculate_clv(your_aov, your_freq, your_margin, your_churn)
print(f"  Simple CLV: ${s_clv:.2f}")
print(f"  3-Year DCF CLV: ${d_clv:.2f}")
print(f"  Breakeven CAC: ${d_clv:.2f}")
print(f"  Max CAC (at 3:1 LTV:CAC ratio): ${d_clv/3:.2f}")