## Delta method for ratio metrics

Statsig uses the delta method when calculating the variance for variables that have a numerator and denominator.

The variance of ratio and mean metrics depends on the numerator and denominator variables, which are typically correlated. For example, consider a *clicks per session* metric. The number of clicks and the number of sessions are two sets of observations from the same group of users, so they aren't independent of each other. To account for this correlation, Statsig obtains the variance of a ratio metric *R* using the delta method:

{% figure %}
![Delta method variance formula](/images/snippets/stats-methods/delta-method/167956015-cc3f9fca-2c4d-410c-bff1-3f13dd16d105.png)
{% /figure %}

where the variance of the numerator and denominator means are computed as described for count metrics, and the covariance is

{% figure %}
![Covariance calculation formula](/images/snippets/stats-methods/delta-method/167956127-c17017ef-07b2-4f76-88c4-00539eec50a7.png)
{% /figure %}

## Delta method for relative lifts

Statsig may also use the delta method when calculating the confidence interval for relative lifts. The other methodology is [Fieller Intervals](/experiments/statistical-methods/methodologies/fieller-intervals). The delta method is a heuristic for Fieller Intervals that converges with a large population.