---
title: Delta Method
description: "How Statsig Warehouse Native uses the delta method to compute variances for ratio metrics and non-linear functions of user-level data."
product: general
token_estimate: 413
---
# Delta Method

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## 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 coming from the same group of users, so they aren't independent of each other. To properly account for this correlation, Statsig obtains the variance of a ratio metric _R_ using the delta method:

![Delta method variance formula](https://docs.statsig.com/images/snippets/stats-methods/delta-method/167956015-cc3f9fca-2c4d-410c-bff1-3f13dd16d105.png)

where Statsig computes the variance of the numerator and denominator means in the same way as detailed above for count metrics, and the covariance is

![Covariance calculation formula](https://docs.statsig.com/images/snippets/stats-methods/delta-method/167956127-c17017ef-07b2-4f76-88c4-00539eec50a7.png)

## Delta method for relative lifts

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