SQL

How to Calculate Confidence Intervals in SQL

10th May `14, 08:27 AM in SQL

Imagine you have a small online business. This month 200 users signed up on your website, and 10…

BDMS
Guest Contributor
 

Imagine you have a small online business. This month 200 users signed up on your website, and 10 of them bought your $800 service. Great! You’ve made $8k of income. How much should you expect to make this year?

The straightforward answer is $8k * 12 = $96k. But how confident should you be? Will your conversion rate always be so close to 5%? You could pad the estimate ±20% for safety, guessing at $77k to $115k. If $77k would cover all your expenses, should you feel secure?

This is a question of binomial probability. Using our favorite binomial confidence interval calculator, the 95% confidence interval for your conversion rate is about 2.5% to 9%.

With a confidence interval that wide, you should expect to make somewhere between $48k and $172k. Yikes! You could end up with half of your simple guess, and that’s if your business doesn’t change.

These confidence intervals are very informative, but turning to a calculator for every metric is tedious. If you’ve got hundreds of metrics across dozens of dashboards, it’s downright unsustainable.

Fortunately, the math for calculating confidence interval is simple to implement:

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