Ab Testing

# 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

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.

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## 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%) | 119,000 | 238,000 |
| 10% (5% → 5.5%) | 30,000 | 60,000 |
| 20% (5% → 6%) | 7,500 | 15,000 |
| 50% (5% → 7.5%) | 1,200 | 2,400 |
| 100% (5% → 10%) | 300 | 600 |

### 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 Gu