# Confidence Interval

**Category:** metrics  
**Short Description:** Range of values likely to contain the true population parameter.  
**Last Updated:** 2024-03-15

## Definition

A confidence interval provides a range of values that likely contains the true value of a metric, given a certain confidence level. In digital advertising, it helps marketers understand the reliability of their performance measurements and make more informed decisions about campaign optimization. Wider intervals suggest more uncertainty, while narrower intervals indicate more precise estimates of true performance.

## Formula

**Formula:** `CI = Point Estimate ± (Critical Value × Standard Error)`

The range your true value most likely falls in — the observed estimate plus or minus a margin that widens with higher confidence and shrinks with larger samples.

## Calculation

**Formula:** `CI = Point Estimate ± (Critical Value × Standard Error)`

**Explanation:** For advertising metrics, the point estimate is the observed value (e.g., CTR, conversion rate), 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

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

## Examples

- 95% confidence that true campaign ROAS is between 2.1 and 2.4, informing budget decisions
- Conversion rate of 3% ± 0.5% at 90% confidence for a new audience segment
- CTR confidence interval narrowing from ±1% to ±0.2% as impressions increase

## Related Terms

### Similar Terms

- **[Statistical Significance](/resources/glossary/metrics/statistical-significance)**: While statistical significance confirms differences, confidence intervals quantify uncertainty
- **[Margin of Error](/resources/glossary/metrics/margin-of-error)**: Expresses uncertainty range in more accessible format for stakeholders
- **[Creative Testing](/resources/glossary/creative/creative-testing)**: Confidence intervals guide minimum test durations and sample sizes

### Component Terms

- **[Standard Deviation](/resources/glossary/metrics/standard-deviation)**: Determines interval width based on metric volatility

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