ab-testing

name	ab-testing
description	Design and analyze A/B tests and controlled experiments for data-driven decisions. Use for: experiment design, hypothesis formulation, sample size calculation, statistical significance testing, multivariate testing, test implementation, results analysis, avoiding common pitfalls, sequential testing, and experimentation platforms.

A/B Testing

Design and analyze controlled experiments to make data-driven decisions about product changes and optimizations.

Overview

A/B testing (split testing) is a rigorous method for comparing two or more variants to determine which performs better on a defined metric. This skill covers statistical foundations, experimental design principles, implementation strategies, and analysis techniques for running effective experiments.

A/B Testing Fundamentals

Core Concepts

Control (A): Current version or baseline Variant (B): New version being tested Randomization: Users randomly assigned to control or variant Metric: Quantifiable measure of success (conversion rate, revenue, engagement) Statistical Significance: Confidence that difference is not due to chance

When to Use A/B Testing

Good Use Cases:

• Testing website/app design changes
• Optimizing email subject lines or content
• Comparing pricing strategies
• Evaluating feature changes
• Testing marketing messages

Not Suitable For:

• Low-traffic pages (insufficient sample size)
• Long-term strategic decisions
• Understanding "why" (use qualitative research)
• Testing many changes simultaneously (use multivariate testing)

Experimental Design

Hypothesis Formulation

Good Hypothesis:

• Specific: "Changing button color from blue to green will increase click-through rate"
• Measurable: Clear metric (CTR)
• Relevant: Tied to business goal
• Falsifiable: Can be proven wrong

Bad Hypothesis:

• Vague: "New design will be better"
• Unmeasurable: "Users will like it more"
• Multiple changes: "New layout, colors, and copy will improve conversions"

Sample Size Calculation

Required Inputs:

• Baseline Conversion Rate: Current metric value
• Minimum Detectable Effect (MDE): Smallest change worth detecting
• Statistical Significance (α): Typically 0.05 (95% confidence)
• Statistical Power (1-β): Typically 0.80 (80% power)

Formula (simplified for proportions):

n = 16 * σ² / (MDE)²

Where:
σ² = p(1-p) for proportions
p = baseline conversion rate
MDE = minimum detectable effect

Example:

• Baseline: 10% conversion rate
• MDE: 2% (relative 20% improvement)
• Significance: 0.05
• Power: 0.80
• Required sample size: ~3,900 per variant

Test Duration

Factors:

• Traffic volume
• Required sample size
• Day-of-week effects (run full weeks)
• Seasonality
• Minimum: 1-2 weeks recommended

Avoid:

• Stopping test early when results look good (peeking problem)
• Running too long (external factors may interfere)

Statistical Analysis

Hypothesis Testing

Null Hypothesis (H₀): No difference between variants Alternative Hypothesis (H₁): Difference exists between variants

P-Value: Probability of observing results if null hypothesis is true

• p < 0.05: Reject null, difference is statistically significant
• p ≥ 0.05: Fail to reject null, no significant difference

Confidence Intervals

95% Confidence Interval: Range where true value likely falls

• If intervals don't overlap, difference is likely significant
• Provides effect size estimate, not just yes/no

Example:

• Control CTR: 10% (95% CI: 9.5% - 10.5%)
• Variant CTR: 12% (95% CI: 11.4% - 12.6%)
• Conclusion: Significant improvement

Statistical Tests

Two-Sample Z-Test (proportions):

from statsmodels.stats.proportion import proportions_ztest

# Control: 1000 conversions out of 10000 visitors
# Variant: 1200 conversions out of 10000 visitors
count = [1000, 1200]
nobs = [10000, 10000]

z_stat, p_value = proportions_ztest(count, nobs)
print(f"P-value: {p_value}")

T-Test (continuous metrics like revenue):

from scipy.stats import ttest_ind

control_revenue = [10, 15, 20, ...]  # Revenue per user
variant_revenue = [12, 18, 22, ...]

t_stat, p_value = ttest_ind(control_revenue, variant_revenue)
print(f"P-value: {p_value}")

Chi-Square Test (categorical outcomes):

from scipy.stats import chi2_contingency

# Observed frequencies
observed = [[900, 9100],   # Control: 900 conversions, 9100 non-conversions
            [1100, 8900]]  # Variant: 1100 conversions, 8900 non-conversions

chi2, p_value, dof, expected = chi2_contingency(observed)
print(f"P-value: {p_value}")

Common Pitfalls and Solutions

Multiple Comparisons Problem

Problem: Testing multiple variants increases false positive rate Solution: Bonferroni correction (divide α by number of comparisons)

• Testing 3 variants: Use α = 0.05/3 = 0.0167

Peeking Problem

Problem: Checking results repeatedly and stopping when significant Solution:

• Pre-determine sample size and duration
• Use sequential testing methods (e.g., always-valid p-values)
• Implement stopping rules

Novelty Effect

Problem: Users react to change itself, not the actual improvement Solution:

• Run test longer (2-4 weeks)
• Analyze new vs returning users separately
• Look for sustained effect over time

Selection Bias

Problem: Non-random assignment or different user populations Solution:

• Ensure proper randomization
• Check for balance in user characteristics
• Use stratified randomization if needed

Insufficient Sample Size

Problem: Test ends before reaching statistical power Solution:

• Calculate required sample size before starting
• Wait for sufficient data
• Consider increasing traffic or MDE

Advanced Techniques

Multivariate Testing (MVT)

Test multiple elements simultaneously:

• Example: Test 2 headlines × 2 images × 2 CTAs = 8 combinations
• Pros: Test interactions between elements
• Cons: Requires much larger sample size

Sequential Testing

Continuously monitor test with valid stopping rules:

• Bayesian A/B Testing: Update beliefs as data arrives
• Always-Valid P-Values: Allow peeking without inflation
• Multi-Armed Bandits: Dynamically allocate traffic to better variant

Stratified Sampling

Ensure balance across important segments:

• Randomize within strata (e.g., mobile vs desktop)
• Improves precision and power
• Reduces variance

CUPED (Controlled-Experiment Using Pre-Experiment Data)

Use pre-experiment data to reduce variance:

• Measure metric before experiment
• Adjust post-experiment metric for pre-experiment value
• Reduces required sample size by 30-50%

Implementation

Randomization

User-Level: Consistent experience for each user Session-Level: Different experience each session Page-Level: Different experience each page view

Hash-Based Assignment:

import hashlib

def assign_variant(user_id, experiment_id, num_variants=2):
    hash_input = f"{user_id}_{experiment_id}"
    hash_value = int(hashlib.md5(hash_input.encode()).hexdigest(), 16)
    return hash_value % num_variants

Tracking

Events to Track:

• Exposure: User saw variant
• Conversion: User completed goal action
• Metadata: Timestamp, user properties, context

Example Schema:

{
  "user_id": "12345",
  "experiment_id": "homepage_redesign",
  "variant": "B",
  "timestamp": "2026-03-15T10:30:00Z",
  "converted": true,
  "revenue": 49.99
}

Platforms

Open Source:

• GrowthBook: Feature flagging and experimentation
• Unleash: Feature toggle system
• Statsig: Experimentation platform

Commercial:

• Optimizely: Enterprise A/B testing
• VWO: Conversion optimization platform
• Google Optimize: Free A/B testing (integrated with Analytics)
• Adobe Target: Personalization and testing

Analysis and Reporting

Metrics to Report

Primary Metric: Main success criterion Secondary Metrics: Supporting metrics Guardrail Metrics: Ensure no negative impact (page load time, error rate)

Example Report:

Experiment: Homepage CTA Button Color
Duration: March 1-14, 2026 (2 weeks)
Sample Size: 50,000 per variant

Primary Metric: Click-Through Rate
- Control (Blue): 10.2% (95% CI: 9.9% - 10.5%)
- Variant (Green): 11.8% (95% CI: 11.5% - 12.1%)
- Lift: +15.7% (p < 0.001)

Secondary Metrics:
- Conversion Rate: +8.3% (p = 0.02)
- Revenue per User: +5.2% (p = 0.15, not significant)

Guardrail Metrics:
- Page Load Time: No change (p = 0.82)
- Bounce Rate: No change (p = 0.45)

Recommendation: Ship variant (green button)

Segmentation Analysis

Analyze results by segment:

• Device type (mobile, desktop, tablet)
• User type (new, returning)
• Geography
• Traffic source

Simpson's Paradox: Overall result may differ from segment results

Best Practices

Before Testing

• Define clear hypothesis and success metrics
• Calculate required sample size
• Set up proper tracking
• Document experiment design
• Get stakeholder alignment

During Testing

• Don't peek at results (or use sequential methods)
• Monitor for technical issues
• Ensure balanced traffic allocation
• Run for predetermined duration

After Testing

• Analyze primary and secondary metrics
• Check for segment differences
• Document learnings
• Communicate results clearly
• Implement winning variant or iterate

Using the Reference Files

When to Read Each Reference

/references/statistical-methods.md — Read when calculating sample sizes, choosing statistical tests, or understanding p-values and confidence intervals.

/references/experiment-design-patterns.md — Read when designing complex experiments, implementing multivariate tests, or using advanced techniques like CUPED.

/references/common-mistakes.md — Read when troubleshooting experiments, avoiding pitfalls, or understanding why results may be misleading.