Engineering Data ScienceStatisticsML

Senior Data Scientist

Statistical modeling, A/B testing, causal inference, and advanced analytics.

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You

We want to A/B test removing the coupon code field from checkout. Baseline conversion is 3.2%. We need 95% confidence. How do I size the experiment?

Agent

Sample Size Calculation:

from scipy.stats import norm
import math

def sample_size_per_variant(p_baseline, mde, alpha=0.05, power=0.80):
    """Calculate required n per variant for a two-proportion z-test."""
    p_treatment = p_baseline * (1 + mde)
    p_avg = (p_baseline + p_treatment) / 2
    
    z_alpha = norm.ppf(1 - alpha / 2)  # two-tailed
    z_beta = norm.ppf(power)
    
    n = (z_alpha + z_beta)**2 * (p_baseline*(1-p_baseline) + p_treatment*(1-p_treatment)) / (p_treatment - p_baseline)**2
    return math.ceil(n)

# Your numbers:
n = sample_size_per_variant(p_baseline=0.032, mde=0.10)  # detect 10% relative lift
# → ~8,300 users per variant = 16,600 total

At what traffic volume does this complete?

  • 1,000 checkouts/day → 17 days
  • 5,000 checkouts/day → 4 days

Key decisions before you launch:

  1. MDE choice matters more than alpha: A 10% relative lift on 3.2% = detecting 3.52% vs 3.2% — is that a meaningful business outcome? If not, set MDE to 5% (doubles sample size).
  2. Randomization unit: Randomize by user_id, not session — a user seeing both variants inflates false positives
  3. Guardrail metrics: Track add_to_cart rate and revenue_per_visitor alongside conversion — removing the coupon field could hurt AOV even if it lifts conversion

Analysis (post-experiment):

from scipy.stats import chi2_contingency
contingency = [[control_converted, control_not], [treat_converted, treat_not]]
chi2, p_value, _, _ = chi2_contingency(contingency)

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