# Margin of Error

**Category:** metrics  
**Short Description:** Maximum expected difference between sample estimate and true value. A measure of the precision of a sample estimate.  
**Last Updated:** 2024-03-15

## Definition

Margin of error represents the maximum expected difference between a sample-based estimate and the true population value, given a specific confidence level. In advertising, it helps quantify the reliability of metrics and determines required sample sizes for meaningful testing.

## Formula

**Formula:** `Margin of Error = Critical Value × Standard Error`

Half the width of the confidence interval — how far your sample estimate could sit from the true value at a given confidence level; it shrinks as the sample grows.

## Calculation

**Formula:** `Critical Value × Standard Error`

**Explanation:** For advertising metrics, the critical value depends on desired confidence level (typically 1.96 for 95%), and standard error accounts for sample size and variance. Larger sample sizes generally lead to narrower, more reliable intervals.

### Components

- **Critical Value**: The value based on the desired confidence level
- **Standard Error**: The measure of sample estimate precision

## Examples

- CTR of 2.5% with ±0.3% margin of error at 95% confidence
- Conversion rate estimate requiring ±1% margin of error needs 10,000 impressions
- ROAS projection accuracy within ±15% for budget forecasting

## Related Terms

### Similar Terms

- **[Confidence Interval](/resources/glossary/metrics/confidence-interval)**: Margin of error defines the width of confidence intervals

### Component Terms

- **[Statistical Significance](/resources/glossary/metrics/statistical-significance)**: Helps determine when differences exceed margin of error
- **[Sample Size](/resources/glossary/metrics/sample-size)**: Larger samples reduce margin of error for more precise estimates

## Featured in topic hubs

- [Experimentation & Statistics](/resources/topics/experimentation)