# Sample Size Guide
Reference for calculating sample sizes and test duration.

- Contents
- Sample Size Fundamentals (required inputs, what these mean)

## Sample Size Quick Reference Tables

Duration Calculator (formula, examples, minimum duration rules, maximum duration guidelines)

## Online Calculators

### Adjusting for Multiple Variants

### Common Sample Size Mistakes

When Sample Size Requirements Are Too High

## Sequential Testing

### Quick Decision Framework

### Sample Size Fundamentals

### Required Inputs

Baseline conversion rate: Your current rate
Minimum detectable effect (MDE): Smallest change worth detecting
Statistical significance level: Usually 95% (α = 0.05)
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:

- Increase MDE: Accept only detecting larger effects (20%+ lift)
- Lower confidence: Use 90% instead of 95% (risky, document it)
- Reduce variants: Test only the most promising variant
- Combine traffic: Test across multiple similar pages
- Test upstream: Test earlier in funnel where traffic is higher
- Don't test: Make decision based on qualitative data instead
- 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 anyway
