
Ab Test Setup
- 538 installs
- 23.5k repo stars
- Updated July 17, 2026
- alirezarezvani/claude-skills
ab-test-setup is a Claude Code skill that designs statistically defensible A/B and split-test plans with hypothesis, single-variable control, and sample-size guidance for developers who validate UI, copy, or onboarding c
About
A/B Test Setup is a marketing experimentation skill that walks developers through planning and designing A/B, split, and multivariate tests with statistical discipline. It triggers on language like A/B test, variant copy, hypothesis, conversion experiment, and statistical significance. The agent acts as an experimentation coach: clarify what you are improving, baseline conversion and traffic, tooling and timeline, then shape a test that can produce actionable winners—not open-ended tinkering. It aligns with product marketing context when a repo already has `.claude/product-marketing-context.md`. Core principles cover hypotheses, one change per test, and rigor around sample size and early stopping. Use it before you ship UI or copy changes you intend to measure, and pair with analytics-tracking when you need event or funnel implementation. Intermediate complexity reflects traffic math and tooling choices without requiring a dedicated data science team.
- Forces a specific hypothesis and single-variable tests so results are interpretable
- Runs an initial assessment for context, baseline conversion, traffic, and constraints before design
- Reads `.claude/product-marketing-context.md` when present to avoid redundant questions
- Emphasizes pre-set sample size and not peeking early for statistical rigor
- Hands off implementation tracking to analytics-tracking when instrumentation is needed
Ab Test Setup by the numbers
- 538 all-time installs (skills.sh)
- Ranked #723 of 1,879 Marketing & SEO skills by installs in the Skillselion catalog
- Security screen: HIGH risk (skills.sh audit)
- Data as of Jul 31, 2026 (Skillselion catalog sync)
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| Installs | 538 |
|---|---|
| repo stars | ★ 23.5k |
| Security audit | 2 / 3 scanners passed |
| Last updated | July 17, 2026 |
| Repository | alirezarezvani/claude-skills ↗ |
How do you design a statistically valid A/B test?
Install this when you need a statistically defensible A/B or split-test plan—hypothesis, one variable, sample size—before changing copy, pricing UI, or onboarding flows.
Who is it for?
Developers or product engineers planning conversion experiments on onboarding, pricing UI, or landing-page copy before writing tracking code.
Skip if: Teams needing analytics pipeline implementation alone or multivariate tests without bandwidth to isolate one variable at a time.
When should I use this skill?
The user mentions A/B test, split test, experiment, variant copy, statistical significance, or conversion experiment planning.
What you get
A documented hypothesis, single-variable experiment design, sample-size estimate, and statistical significance criteria ready for implementation.
- Experiment hypothesis document
- Sample-size estimate
- Single-variable test plan
By the numbers
- Skill version 1.0.0 under MIT license
- Metadata category: marketing, updated 2026-03-06
Files
A/B Test Setup
You are an expert in experimentation and A/B testing. Your goal is to help design tests that produce statistically valid, actionable results.
Initial Assessment
Check for product marketing context first: If .claude/product-marketing-context.md exists, read it before asking questions. Use that context and only ask for information not already covered or specific to this task.
Before designing a test, understand:
1. Test Context - What are you trying to improve? What change are you considering? 2. Current State - Baseline conversion rate? Current traffic volume? 3. Constraints - Technical complexity? Timeline? Tools available?
---
Core Principles
1. Start with a Hypothesis
- Not just "let's see what happens"
- Specific prediction of outcome
- Based on reasoning or data
2. Test One Thing
- Single variable per test
- Otherwise you don't know what worked
3. Statistical Rigor
- Pre-determine sample size
- Don't peek and stop early
- Commit to the methodology
4. Measure What Matters
- Primary metric tied to business value
- Secondary metrics for context
- Guardrail metrics to prevent harm
---
Hypothesis Framework
Structure
Because [observation/data],
we believe [change]
will cause [expected outcome]
for [audience].
We'll know this is true when [metrics].Example
Weak: "Changing the button color might increase clicks."
Strong: "Because users report difficulty finding the CTA (per heatmaps and feedback), we believe making the button larger and using contrasting color will increase CTA clicks by 15%+ for new visitors. We'll measure click-through rate from page view to signup start."
---
Test Types
| Type | Description | Traffic Needed |
|---|---|---|
| A/B | Two versions, single change | Moderate |
| A/B/n | Multiple variants | Higher |
| MVT | Multiple changes in combinations | Very high |
| Split URL | Different URLs for variants | Moderate |
---
Sample Size
Calculate It (bundled tool)
Use this skill's own calculator — don't eyeball it:
python3 scripts/sample_size_calculator.py --baseline 0.05 --mde 0.20 # human-readable
python3 scripts/sample_size_calculator.py --baseline 0.05 --mde 0.20 --json # for pipelines
python3 scripts/sample_size_calculator.py --baseline 0.05 --mde 0.20 --daily-traffic 2000 # adds test-duration estimatePaste sample_size_per_variation and the duration estimate directly into the test plan's "Sample size + duration" row before any test is approved to run.
Quick Reference
Generated by sample_size_calculator.py (two-proportion z-test, α=0.05 two-tailed, 80% power; relative MDE):
| Baseline | 10% Lift | 20% Lift | 50% Lift |
|---|---|---|---|
| 1% | 163k/variant | 43k/variant | 7.7k/variant |
| 3% | 53k/variant | 14k/variant | 2.5k/variant |
| 5% | 31k/variant | 8.2k/variant | 1.5k/variant |
| 10% | 15k/variant | 3.8k/variant | 683/variant |
Cross-check calculators (should agree with the script within rounding):
For detailed sample size tables and duration calculations: See references/sample-size-guide.md
---
Metrics Selection
Primary Metric
- Single metric that matters most
- Directly tied to hypothesis
- What you'll use to call the test
Secondary Metrics
- Support primary metric interpretation
- Explain why/how the change worked
Guardrail Metrics
- Things that shouldn't get worse
- Stop test if significantly negative
Example: Pricing Page Test
- Primary: Plan selection rate
- Secondary: Time on page, plan distribution
- Guardrail: Support tickets, refund rate
---
Designing Variants
What to Vary
| Category | Examples |
|---|---|
| Headlines/Copy | Message angle, value prop, specificity, tone |
| Visual Design | Layout, color, images, hierarchy |
| CTA | Button copy, size, placement, number |
| Content | Information included, order, amount, social proof |
Best Practices
- Single, meaningful change
- Bold enough to make a difference
- True to the hypothesis
---
Traffic Allocation
| Approach | Split | When to Use |
|---|---|---|
| Standard | 50/50 | Default for A/B |
| Conservative | 90/10, 80/20 | Limit risk of bad variant |
| Ramping | Start small, increase | Technical risk mitigation |
Considerations:
- Consistency: Users see same variant on return
- Balanced exposure across time of day/week
---
Implementation
Client-Side
- JavaScript modifies page after load
- Quick to implement, can cause flicker
- Tools: PostHog, Optimizely, VWO
Server-Side
- Variant determined before render
- No flicker, requires dev work
- Tools: PostHog, LaunchDarkly, Split
---
Running the Test
Pre-Launch Checklist
- [ ] Hypothesis documented
- [ ] Primary metric defined
- [ ] Sample size calculated
- [ ] Variants implemented correctly
- [ ] Tracking verified
- [ ] QA completed on all variants
During the Test
DO:
- Monitor for technical issues
- Check segment quality
- Document external factors
DON'T:
- Peek at results and stop early
- Make changes to variants
- Add traffic from new sources
The Peeking Problem
Looking at results before reaching sample size and stopping early leads to false positives and wrong decisions. Pre-commit to sample size and trust the process.
---
Analyzing Results
Statistical Significance
- 95% confidence = p-value < 0.05
- Means <5% chance result is random
- Not a guarantee—just a threshold
Analysis Checklist
1. Reach sample size? If not, result is preliminary 2. Statistically significant? Check confidence intervals 3. Effect size meaningful? Compare to MDE, project impact 4. Secondary metrics consistent? Support the primary? 5. Guardrail concerns? Anything get worse? 6. Segment differences? Mobile vs. desktop? New vs. returning?
Interpreting Results
| Result | Conclusion |
|---|---|
| Significant winner | Implement variant |
| Significant loser | Keep control, learn why |
| No significant difference | Need more traffic or bolder test |
| Mixed signals | Dig deeper, maybe segment |
---
Documentation
Document every test with:
- Hypothesis
- Variants (with screenshots)
- Results (sample, metrics, significance)
- Decision and learnings
For templates: See references/test-templates.md
---
Common Mistakes
Test Design
- Testing too small a change (undetectable)
- Testing too many things (can't isolate)
- No clear hypothesis
Execution
- Stopping early
- Changing things mid-test
- Not checking implementation
Analysis
- Ignoring confidence intervals
- Cherry-picking segments
- Over-interpreting inconclusive results
---
Task-Specific Questions
1. What's your current conversion rate? 2. How much traffic does this page get? 3. What change are you considering and why? 4. What's the smallest improvement worth detecting? 5. What tools do you have for testing? 6. Have you tested this area before?
---
Proactive Triggers
Proactively offer A/B test design when:
1. Conversion rate mentioned — User shares a conversion rate and asks how to improve it; suggest designing a test rather than guessing at solutions. 2. Copy or design decision is unclear — When two variants of a headline, CTA, or layout are being debated, propose testing instead of opinionating. 3. Campaign underperformance — User reports a landing page or email performing below expectations; offer a structured test plan. 4. Pricing page discussion — Any mention of pricing page changes should trigger an offer to design a pricing test with guardrail metrics. 5. Post-launch review — After a feature or campaign goes live, propose follow-up experiments to optimize the result.
---
Output Artifacts
| Artifact | Format | Description |
|---|---|---|
| Experiment Brief | Markdown doc | Hypothesis, variants, metrics, sample size, duration, owner |
| Sample Size Calculator Input | Table | Baseline rate, MDE, confidence level, power |
| Pre-Launch QA Checklist | Checklist | Implementation, tracking, variant rendering verification |
| Results Analysis Report | Markdown doc | Statistical significance, effect size, segment breakdown, decision |
| Test Backlog | Prioritized list | Ranked experiments by expected impact and feasibility |
---
Communication
All outputs should meet the quality standard: clear hypothesis, pre-registered metrics, and documented decisions. Avoid presenting inconclusive results as wins. Every test should produce a learning, even if the variant loses. Reference marketing-context for product and audience framing before designing experiments.
---
Related Skills
- page-cro — USE when you need ideas for what to test; NOT when you already have a hypothesis and just need test design.
- analytics-tracking — USE to set up measurement infrastructure before running tests; NOT as a substitute for defining primary metrics upfront.
- campaign-analytics — USE after tests conclude to fold results into broader campaign attribution; NOT during the test itself.
- pricing-strategy — USE when test results affect pricing decisions; NOT to replace a controlled test with pure strategic reasoning.
- marketing-context — USE as foundation before any test design to ensure hypotheses align with ICP and positioning; always load first.
Sample Size Guide
Reference for calculating sample sizes and test duration.
Sample Size Fundamentals
Required Inputs
1. Baseline conversion rate: Your current rate 2. Minimum detectable effect (MDE): Smallest change worth detecting 3. Statistical significance level: Usually 95% (α = 0.05) 4. Statistical power: Usually 80% (β = 0.20)
What These Mean
Baseline conversion rate: If your page converts at 5%, that's your baseline.
MDE (Minimum Detectable Effect): The smallest improvement you care about detecting. Set this based on:
- Business impact (is a 5% lift meaningful?)
- Implementation cost (worth the effort?)
- Realistic expectations (what have past tests shown?)
Statistical significance (95%): Means there's less than 5% chance the observed difference is due to random chance.
Statistical power (80%): Means if there's a real effect of size MDE, you have 80% chance of detecting it.
---
Sample Size Quick Reference Tables
Conversion Rate: 1%
| Lift to Detect | Sample per Variant | Total Sample |
|---|---|---|
| 5% (1% → 1.05%) | 1,500,000 | 3,000,000 |
| 10% (1% → 1.1%) | 380,000 | 760,000 |
| 20% (1% → 1.2%) | 97,000 | 194,000 |
| 50% (1% → 1.5%) | 16,000 | 32,000 |
| 100% (1% → 2%) | 4,200 | 8,400 |
Conversion Rate: 3%
| Lift to Detect | Sample per Variant | Total Sample |
|---|---|---|
| 5% (3% → 3.15%) | 480,000 | 960,000 |
| 10% (3% → 3.3%) | 120,000 | 240,000 |
| 20% (3% → 3.6%) | 31,000 | 62,000 |
| 50% (3% → 4.5%) | 5,200 | 10,400 |
| 100% (3% → 6%) | 1,400 | 2,800 |
Conversion Rate: 5%
| Lift to Detect | Sample per Variant | Total Sample |
|---|---|---|
| 5% (5% → 5.25%) | 280,000 | 560,000 |
| 10% (5% → 5.5%) | 72,000 | 144,000 |
| 20% (5% → 6%) | 18,000 | 36,000 |
| 50% (5% → 7.5%) | 3,100 | 6,200 |
| 100% (5% → 10%) | 810 | 1,620 |
Conversion Rate: 10%
| Lift to Detect | Sample per Variant | Total Sample |
|---|---|---|
| 5% (10% → 10.5%) | 130,000 | 260,000 |
| 10% (10% → 11%) | 34,000 | 68,000 |
| 20% (10% → 12%) | 8,700 | 17,400 |
| 50% (10% → 15%) | 1,500 | 3,000 |
| 100% (10% → 20%) | 400 | 800 |
Conversion Rate: 20%
| Lift to Detect | Sample per Variant | Total Sample |
|---|---|---|
| 5% (20% → 21%) | 60,000 | 120,000 |
| 10% (20% → 22%) | 16,000 | 32,000 |
| 20% (20% → 24%) | 4,000 | 8,000 |
| 50% (20% → 30%) | 700 | 1,400 |
| 100% (20% → 40%) | 200 | 400 |
---
Duration Calculator
Formula
Duration (days) = (Sample per variant × Number of variants) / (Daily traffic × % exposed)Examples
Scenario 1: High-traffic page
- Need: 10,000 per variant (2 variants = 20,000 total)
- Daily traffic: 5,000 visitors
- 100% exposed to test
- Duration: 20,000 / 5,000 = 4 days
Scenario 2: Medium-traffic page
- Need: 30,000 per variant (60,000 total)
- Daily traffic: 2,000 visitors
- 100% exposed
- Duration: 60,000 / 2,000 = 30 days
Scenario 3: Low-traffic with partial exposure
- Need: 15,000 per variant (30,000 total)
- Daily traffic: 500 visitors
- 50% exposed to test
- Effective daily: 250
- Duration: 30,000 / 250 = 120 days (too long!)
Minimum Duration Rules
Even with sufficient sample size, run tests for at least:
- 1 full week: To capture day-of-week variation
- 2 business cycles: If B2B (weekday vs. weekend patterns)
- Through paydays: If e-commerce (beginning/end of month)
Maximum Duration Guidelines
Avoid running tests longer than 4-8 weeks:
- Novelty effects wear off
- External factors intervene
- Opportunity cost of other tests
---
Online Calculators
Recommended Tools
Evan Miller's Calculator https://www.evanmiller.org/ab-testing/sample-size.html
- Simple interface
- Bookmark-worthy
Optimizely's Calculator https://www.optimizely.com/sample-size-calculator/
- Business-friendly language
- Duration estimates
AB Test Guide Calculator https://www.abtestguide.com/calc/
- Includes Bayesian option
- Multiple test types
VWO Duration Calculator https://vwo.com/tools/ab-test-duration-calculator/
- Duration-focused
- Good for planning
---
Adjusting for Multiple Variants
With more than 2 variants (A/B/n tests), you need more sample:
| Variants | Multiplier |
|---|---|
| 2 (A/B) | 1x |
| 3 (A/B/C) | ~1.5x |
| 4 (A/B/C/D) | ~2x |
| 5+ | Consider reducing variants |
Why? More comparisons increase chance of false positives. You're comparing:
- A vs B
- A vs C
- B vs C (sometimes)
Apply Bonferroni correction or use tools that handle this automatically.
---
Common Sample Size Mistakes
1. Underpowered tests
Problem: Not enough sample to detect realistic effects Fix: Be realistic about MDE, get more traffic, or don't test
2. Overpowered tests
Problem: Waiting for sample size when you already have significance Fix: This is actually fine—you committed to sample size, honor it
3. Wrong baseline rate
Problem: Using wrong conversion rate for calculation Fix: Use the specific metric and page, not site-wide averages
4. Ignoring segments
Problem: Calculating for full traffic, then analyzing segments Fix: If you plan segment analysis, calculate sample for smallest segment
5. Testing too many things
Problem: Dividing traffic too many ways Fix: Prioritize ruthlessly, run fewer concurrent tests
---
When Sample Size Requirements Are Too High
Options when you can't get enough traffic:
1. Increase MDE: Accept only detecting larger effects (20%+ lift) 2. Lower confidence: Use 90% instead of 95% (risky, document it) 3. Reduce variants: Test only the most promising variant 4. Combine traffic: Test across multiple similar pages 5. Test upstream: Test earlier in funnel where traffic is higher 6. Don't test: Make decision based on qualitative data instead 7. Longer test: Accept longer duration (weeks/months)
---
Sequential Testing
If you must check results before reaching sample size:
What is it?
Statistical method that adjusts for multiple looks at data.
When to use
- High-risk changes
- Need to stop bad variants early
- Time-sensitive decisions
Tools that support it
- Optimizely (Stats Accelerator)
- VWO (SmartStats)
- PostHog (Bayesian approach)
Tradeoff
- More flexibility to stop early
- Slightly larger sample size requirement
- More complex analysis
---
Quick Decision Framework
Can I run this test?
Daily traffic to page: _____
Baseline conversion rate: _____
MDE I care about: _____
Sample needed per variant: _____ (from tables above)
Days to run: Sample / Daily traffic = _____
If days > 60: Consider alternatives
If days > 30: Acceptable for high-impact tests
If days < 14: Likely feasible
If days < 7: Easy to run, consider running longer anywayA/B Test Templates Reference
Templates for planning, documenting, and analyzing experiments.
Test Plan Template
# A/B Test: [Name]
## Overview
- **Owner**: [Name]
- **Test ID**: [ID in testing tool]
- **Page/Feature**: [What's being tested]
- **Planned dates**: [Start] - [End]
## Hypothesis
Because [observation/data],
we believe [change]
will cause [expected outcome]
for [audience].
We'll know this is true when [metrics].
## Test Design
| Element | Details |
|---------|---------|
| Test type | A/B / A/B/n / MVT |
| Duration | X weeks |
| Sample size | X per variant |
| Traffic allocation | 50/50 |
| Tool | [Tool name] |
| Implementation | Client-side / Server-side |
## Variants
### Control (A)
[Screenshot]
- Current experience
- [Key details about current state]
### Variant (B)
[Screenshot or mockup]
- [Specific change #1]
- [Specific change #2]
- Rationale: [Why we think this will win]
## Metrics
### Primary
- **Metric**: [metric name]
- **Definition**: [how it's calculated]
- **Current baseline**: [X%]
- **Minimum detectable effect**: [X%]
### Secondary
- [Metric 1]: [what it tells us]
- [Metric 2]: [what it tells us]
- [Metric 3]: [what it tells us]
### Guardrails
- [Metric that shouldn't get worse]
- [Another safety metric]
## Segment Analysis Plan
- Mobile vs. desktop
- New vs. returning visitors
- Traffic source
- [Other relevant segments]
## Success Criteria
- Winner: [Primary metric improves by X% with 95% confidence]
- Loser: [Primary metric decreases significantly]
- Inconclusive: [What we'll do if no significant result]
## Pre-Launch Checklist
- [ ] Hypothesis documented and reviewed
- [ ] Primary metric defined and trackable
- [ ] Sample size calculated
- [ ] Test duration estimated
- [ ] Variants implemented correctly
- [ ] Tracking verified in all variants
- [ ] QA completed on all variants
- [ ] Stakeholders informed
- [ ] Calendar hold for analysis date---
Results Documentation Template
# A/B Test Results: [Name]
## Summary
| Element | Value |
|---------|-------|
| Test ID | [ID] |
| Dates | [Start] - [End] |
| Duration | X days |
| Result | Winner / Loser / Inconclusive |
| Decision | [What we're doing] |
## Hypothesis (Reminder)
[Copy from test plan]
## Results
### Sample Size
| Variant | Target | Actual | % of target |
|---------|--------|--------|-------------|
| Control | X | Y | Z% |
| Variant | X | Y | Z% |
### Primary Metric: [Metric Name]
| Variant | Value | 95% CI | vs. Control |
|---------|-------|--------|-------------|
| Control | X% | [X%, Y%] | — |
| Variant | X% | [X%, Y%] | +X% |
**Statistical significance**: p = X.XX (95% = sig / not sig)
**Practical significance**: [Is this lift meaningful for the business?]
### Secondary Metrics
| Metric | Control | Variant | Change | Significant? |
|--------|---------|---------|--------|--------------|
| [Metric 1] | X | Y | +Z% | Yes/No |
| [Metric 2] | X | Y | +Z% | Yes/No |
### Guardrail Metrics
| Metric | Control | Variant | Change | Concern? |
|--------|---------|---------|--------|----------|
| [Metric 1] | X | Y | +Z% | Yes/No |
### Segment Analysis
**Mobile vs. Desktop**
| Segment | Control | Variant | Lift |
|---------|---------|---------|------|
| Mobile | X% | Y% | +Z% |
| Desktop | X% | Y% | +Z% |
**New vs. Returning**
| Segment | Control | Variant | Lift |
|---------|---------|---------|------|
| New | X% | Y% | +Z% |
| Returning | X% | Y% | +Z% |
## Interpretation
### What happened?
[Explanation of results in plain language]
### Why do we think this happened?
[Analysis and reasoning]
### Caveats
[Any limitations, external factors, or concerns]
## Decision
**Winner**: [Control / Variant]
**Action**: [Implement variant / Keep control / Re-test]
**Timeline**: [When changes will be implemented]
## Learnings
### What we learned
- [Key insight 1]
- [Key insight 2]
### What to test next
- [Follow-up test idea 1]
- [Follow-up test idea 2]
### Impact
- **Projected lift**: [X% improvement in Y metric]
- **Business impact**: [Revenue, conversions, etc.]---
Test Repository Entry Template
For tracking all tests in a central location:
| Test ID | Name | Page | Dates | Primary Metric | Result | Lift | Link |
|---------|------|------|-------|----------------|--------|------|------|
| 001 | Hero headline test | Homepage | 1/1-1/15 | CTR | Winner | +12% | [Link] |
| 002 | Pricing table layout | Pricing | 1/10-1/31 | Plan selection | Loser | -5% | [Link] |
| 003 | Signup form fields | Signup | 2/1-2/14 | Completion | Inconclusive | +2% | [Link] |---
Quick Test Brief Template
For simple tests that don't need full documentation:
## [Test Name]
**What**: [One sentence description]
**Why**: [One sentence hypothesis]
**Metric**: [Primary metric]
**Duration**: [X weeks]
**Result**: [TBD / Winner / Loser / Inconclusive]
**Learnings**: [Key takeaway]---
Stakeholder Update Template
## A/B Test Update: [Name]
**Status**: Running / Complete
**Days remaining**: X (or complete)
**Current sample**: X% of target
### Preliminary observations
[What we're seeing - without making decisions yet]
### Next steps
[What happens next]
### Timeline
- [Date]: Analysis complete
- [Date]: Decision and recommendation
- [Date]: Implementation (if winner)---
Experiment Prioritization Scorecard
For deciding which tests to run:
| Factor | Weight | Test A | Test B | Test C |
|---|---|---|---|---|
| Potential impact | 30% | |||
| Confidence in hypothesis | 25% | |||
| Ease of implementation | 20% | |||
| Risk if wrong | 15% | |||
| Strategic alignment | 10% | |||
| Total |
Scoring: 1-5 (5 = best)
---
Hypothesis Bank Template
For collecting test ideas:
| ID | Page/Area | Observation | Hypothesis | Potential Impact | Status |
|----|-----------|-------------|------------|------------------|--------|
| H1 | Homepage | Low scroll depth | Shorter hero will increase scroll | High | Testing |
| H2 | Pricing | Users compare plans | Comparison table will help | Medium | Backlog |
| H3 | Signup | Drop-off at email | Social login will increase completion | Medium | Backlog |#!/usr/bin/env python3
"""
sample_size_calculator.py — A/B Test Sample Size Calculator
100% stdlib, no pip installs required.
Usage:
python3 sample_size_calculator.py # demo mode
python3 sample_size_calculator.py --baseline 0.05 --mde 0.20
python3 sample_size_calculator.py --baseline 0.05 --mde 0.20 --daily-traffic 500
python3 sample_size_calculator.py --baseline 0.05 --mde 0.20 --json
"""
import argparse
import json
import math
import sys
# ---------------------------------------------------------------------------
# Z-score approximation (scipy-free, Beasley-Springer-Moro algorithm)
# ---------------------------------------------------------------------------
def _norm_ppf(p: float) -> float:
"""Percent-point function (inverse CDF) of the standard normal.
Uses rational approximation — accurate to ~1e-9.
Reference: Abramowitz & Stegun 26.2.17 / Peter Acklam's algorithm.
"""
if p <= 0 or p >= 1:
raise ValueError(f"p must be in (0, 1), got {p}")
# Coefficients for rational approximation
a = [-3.969683028665376e+01, 2.209460984245205e+02,
-2.759285104469687e+02, 1.383577518672690e+02,
-3.066479806614716e+01, 2.506628277459239e+00]
b = [-5.447609879822406e+01, 1.615858368580409e+02,
-1.556989798598866e+02, 6.680131188771972e+01,
-1.328068155288572e+01]
c = [-7.784894002430293e-03, -3.223964580411365e-01,
-2.400758277161838e+00, -2.549732539343734e+00,
4.374664141464968e+00, 2.938163982698783e+00]
d = [7.784695709041462e-03, 3.224671290700398e-01,
2.445134137142996e+00, 3.754408661907416e+00]
p_low = 0.02425
p_high = 1 - p_low
if p < p_low:
q = math.sqrt(-2 * math.log(p))
return (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) / \
((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
elif p <= p_high:
q = p - 0.5
r = q * q
return (((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r+a[5])*q / \
(((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r+1)
else:
q = math.sqrt(-2 * math.log(1 - p))
return -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) / \
((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
# ---------------------------------------------------------------------------
# Core calculation
# ---------------------------------------------------------------------------
def calculate_sample_size(
baseline: float,
mde: float,
alpha: float = 0.05,
power: float = 0.80,
) -> dict:
"""
Two-proportion z-test sample size formula (two-tailed).
n = (Z_alpha/2 + Z_beta)^2 * (p1*(1-p1) + p2*(1-p2)) / (p2 - p1)^2
Args:
baseline : baseline conversion rate (e.g. 0.05 for 5%)
mde : minimum detectable effect as relative lift (e.g. 0.20 for +20%)
alpha : significance level (Type I error rate), default 0.05
power : statistical power (1 - Type II error rate), default 0.80
Returns dict with all intermediate values and results.
"""
p1 = baseline
p2 = baseline * (1 + mde) # expected conversion with treatment
if not (0 < p1 < 1):
raise ValueError(f"baseline must be in (0,1), got {p1}")
if not (0 < p2 < 1):
raise ValueError(
f"baseline * (1 + mde) = {p2:.4f} is outside (0,1). "
"Reduce mde or increase baseline."
)
z_alpha = _norm_ppf(1 - alpha / 2) # two-tailed
z_beta = _norm_ppf(power)
pooled_var = p1 * (1 - p1) + p2 * (1 - p2)
effect_sq = (p2 - p1) ** 2
n_raw = ((z_alpha + z_beta) ** 2 * pooled_var) / effect_sq
n = math.ceil(n_raw)
return {
"inputs": {
"baseline_conversion_rate": p1,
"minimum_detectable_effect_relative": mde,
"expected_variant_conversion_rate": round(p2, 6),
"significance_level_alpha": alpha,
"statistical_power": power,
},
"z_scores": {
"z_alpha_2": round(z_alpha, 4),
"z_beta": round(z_beta, 4),
},
"results": {
"sample_size_per_variation": n,
"total_sample_size": n * 2,
"absolute_lift": round(p2 - p1, 6),
"relative_lift_pct": round(mde * 100, 2),
},
"formula": (
"n = (Z_α/2 + Z_β)² × (p1(1−p1) + p2(1−p2)) / (p2−p1)² "
"[two-proportion z-test, two-tailed]"
),
"assumptions": [
"Two-tailed test (detecting lift in either direction)",
"Independent samples (no within-subject correlation)",
"Fixed horizon (not sequential / always-valid)",
"Binomial outcome (conversion yes/no)",
"No novelty effect correction applied",
],
}
def add_duration(result: dict, daily_traffic: int) -> dict:
"""Append estimated test duration given total daily traffic (both variants)."""
n_total = result["results"]["total_sample_size"]
days = math.ceil(n_total / daily_traffic)
weeks = round(days / 7, 1)
result["duration"] = {
"daily_traffic_both_variants": daily_traffic,
"estimated_days": days,
"estimated_weeks": weeks,
"note": (
"Assumes traffic is evenly split 50/50 between control and variant. "
"Add ~10–20% buffer for weekday/weekend variance."
),
}
return result
# ---------------------------------------------------------------------------
# Scoring helper (0-100)
# ---------------------------------------------------------------------------
def score_test_design(result: dict) -> dict:
"""Heuristic quality score for the A/B test design."""
score = 100
reasons = []
inputs = result["inputs"]
# Penalise very low baseline (unreliable estimates)
if inputs["baseline_conversion_rate"] < 0.01:
score -= 15
reasons.append("Baseline <1%: high variance, consider aggregating more data first.")
# Penalise tiny MDE (will need enormous sample)
mde = inputs["minimum_detectable_effect_relative"]
if mde < 0.05:
score -= 20
reasons.append("MDE <5%: very small effect, experiment may take months.")
elif mde < 0.10:
score -= 10
reasons.append("MDE <10%: moderately small effect size.")
# Penalise overly aggressive alpha
if inputs["significance_level_alpha"] > 0.10:
score -= 15
reasons.append("α >10%: high false-positive risk.")
# Penalise low power
if inputs["statistical_power"] < 0.80:
score -= 20
reasons.append("Power <80%: elevated risk of missing real effects (Type II error).")
# Duration penalty (if available)
dur = result.get("duration")
if dur:
days = dur["estimated_days"]
if days > 90:
score -= 20
reasons.append(f"Test duration {days}d >90 days: novelty/seasonal effects likely.")
elif days > 30:
score -= 10
reasons.append(f"Test duration {days}d >30 days: monitor for external confounders.")
score = max(0, score)
return {
"design_quality_score": score,
"score_interpretation": _score_label(score),
"issues": reasons if reasons else ["No major design issues detected."],
}
def _score_label(s: int) -> str:
if s >= 90: return "Excellent"
if s >= 75: return "Good"
if s >= 60: return "Fair"
if s >= 40: return "Poor"
return "Critical"
# ---------------------------------------------------------------------------
# Pretty-print
# ---------------------------------------------------------------------------
def pretty_print(result: dict, score: dict) -> None:
inp = result["inputs"]
res = result["results"]
zs = result["z_scores"]
print("\n" + "=" * 60)
print(" A/B TEST SAMPLE SIZE CALCULATOR")
print("=" * 60)
print("\n📥 INPUTS")
print(f" Baseline conversion rate : {inp['baseline_conversion_rate']*100:.2f}%")
print(f" Variant conversion rate : {inp['expected_variant_conversion_rate']*100:.2f}%")
print(f" Minimum detectable effect: {inp['minimum_detectable_effect_relative']*100:.1f}% relative "
f"(+{res['absolute_lift']*100:.3f}pp absolute)")
print(f" Significance level (α) : {inp['significance_level_alpha']}")
print(f" Statistical power : {inp['statistical_power']*100:.0f}%")
print("\n📐 FORMULA")
print(f" {result['formula']}")
print(f" Z_α/2 = {zs['z_alpha_2']} Z_β = {zs['z_beta']}")
print("\n📊 RESULTS")
print(f" ✅ Sample size per variation : {res['sample_size_per_variation']:,}")
print(f" ✅ Total sample size (both) : {res['total_sample_size']:,}")
if "duration" in result:
d = result["duration"]
print(f"\n⏱️ DURATION ESTIMATE (traffic: {d['daily_traffic_both_variants']:,}/day)")
print(f" Estimated test duration : {d['estimated_days']} days (~{d['estimated_weeks']} weeks)")
print(f" Note: {d['note']}")
print("\n💡 ASSUMPTIONS")
for a in result["assumptions"]:
print(f" • {a}")
print(f"\n🎯 DESIGN QUALITY SCORE: {score['design_quality_score']}/100 ({score['score_interpretation']})")
for issue in score["issues"]:
print(f" ⚠ {issue}")
print()
# ---------------------------------------------------------------------------
# CLI
# ---------------------------------------------------------------------------
def parse_args():
parser = argparse.ArgumentParser(
description="Calculate required sample size for an A/B test (stdlib only).",
formatter_class=argparse.RawDescriptionHelpFormatter,
epilog=__doc__,
)
parser.add_argument("--baseline", type=float, default=None,
help="Baseline conversion rate (e.g. 0.05 for 5%%)")
parser.add_argument("--mde", type=float, default=None,
help="Minimum detectable effect as relative lift (e.g. 0.20 for +20%%)")
parser.add_argument("--alpha", type=float, default=0.05,
help="Significance level α (default: 0.05)")
parser.add_argument("--power", type=float, default=0.80,
help="Statistical power 1-β (default: 0.80)")
parser.add_argument("--daily-traffic", type=int, default=None,
help="Total daily visitors across both variants (for duration estimate)")
parser.add_argument("--json", action="store_true",
help="Output results as JSON")
return parser.parse_args()
DEMO_SCENARIOS = [
{"label": "E-commerce checkout (low baseline)",
"baseline": 0.03, "mde": 0.20, "alpha": 0.05, "power": 0.80, "daily_traffic": 800},
{"label": "SaaS free-trial signup (medium baseline)",
"baseline": 0.08, "mde": 0.15, "alpha": 0.05, "power": 0.80, "daily_traffic": 2000},
{"label": "Button CTA (high baseline)",
"baseline": 0.25, "mde": 0.10, "alpha": 0.05, "power": 0.80, "daily_traffic": 5000},
]
def main():
args = parse_args()
demo_mode = (args.baseline is None and args.mde is None)
if demo_mode:
print("🔬 DEMO MODE — running 3 sample scenarios\n")
all_results = []
for sc in DEMO_SCENARIOS:
res = calculate_sample_size(sc["baseline"], sc["mde"], sc["alpha"], sc["power"])
res = add_duration(res, sc["daily_traffic"])
sc_score = score_test_design(res)
res["scenario"] = sc["label"]
res["score"] = sc_score
all_results.append(res)
if not args.json:
print(f"\n{'─'*60}")
print(f"SCENARIO: {sc['label']}")
pretty_print(res, sc_score)
if args.json:
print(json.dumps(all_results, indent=2))
return
# Single calculation mode
if args.baseline is None or args.mde is None:
print("Error: --baseline and --mde are required (or omit both for demo mode).", file=sys.stderr)
sys.exit(1)
result = calculate_sample_size(args.baseline, args.mde, args.alpha, args.power)
if args.daily_traffic:
result = add_duration(result, args.daily_traffic)
sc_score = score_test_design(result)
result["score"] = sc_score
if args.json:
print(json.dumps(result, indent=2))
else:
pretty_print(result, sc_score)
if __name__ == "__main__":
main()
Related skills
How it compares
Use ab-test-setup for experiment design; pair with analytics-tracking when the task is event instrumentation rather than hypothesis planning.
FAQ
What does ab-test-setup produce before implementation?
ab-test-setup produces a hypothesis, a single-variable experiment design, sample-size guidance, and statistical significance criteria so developers avoid under-powered A/B or split tests on copy, pricing UI, or onboarding.
Does ab-test-setup implement analytics tracking?
ab-test-setup focuses on experiment design and points tracking implementation to the separate analytics-tracking skill in alirezarezvani/claude-skills, keeping planning distinct from instrumentation work.
Is Ab Test Setup safe to install?
skills.sh reports 2 of 3 security scanners passed. Review the Security Audits panel on this page before installing in production.