How confident are you that that you have a good conversion rate? How confident are you that the change to your site increased your conversion rate? Luckily for us, 16^{th} century math geeks already figured all this out; all you need to do is apply it.

## Confidence Intervals

You may have seen a poll in the newspaper use a plus-minus symbol (±). Example: 1 % of people love maths ±1%.

Your local paper didn’t ask everybody so can’t be sure, so instead have a confidence interval. This example means that they can be confident that between 0% and 2% of people love maths.

## Confidence Levels

Confidence intervals can vary depending on how `confident` you want to be on the results. This is based on deviations. Generally we use a confidence level of 95% which is translated to 1.91 deviations. 95% of a population is within 1.96 deviations from the mean.

### Confidence level deviations

99% = 2.575

95% = 1.96

90% = 1.645

## Calculating your confidence interval

**Warning:** At this point you will need a basic understanding of statistics. If you’re in the 99% ± 1% of people who hate maths you should look away now, if you haven’t already.

To calculate your confidence interval (*ci*) you’ll need the following:

- number of visits (
*v*) - number of conversions (
*c*) - your confidence level (
*cl*)

1) First you need to calculate your conversion rate (*m*)

*m = c / v*

2) Now you have everything you need you can calculate the conversion interval

*ci = cl * ( sqrt( m * (1-m) ) / v ) )*

## Example 1

Widgets.com has **10 visits **and** **made **2 sales **and we want to be** 95% **(1.91 deviations)** **confident of the conversion** **rate.

The conversion rate is 0.2 ( or 20% ) * = 2 sales / 10 visits*

The confidence interval is = **0.0764 **(or 7.64%) = *1.91 * ( sqrt( 0.2 * ( 1 - 0.2 ) ) / 10 )*

So we can be 95% sure the conversion rate is 20% ± 7.64%

**OR **we can be 95% sure that the conversion rate is between 12.36% and 27.64%

## Example 2

Widgets.com has **1000 visits **and** **made **15 sales **and we want to be** 95% **(1.91 deviations)** **confident of the conversion** **rate.

The conversion rate is **0.015** (or 1.5%) * = 15 sales / 1000 visits*

The confidence interval is = **0.000232 **(or 0.0232%) = *1.91 * ( sqrt( 0.015 * ( 1 - 0.015) ) / 1000 )*

So we can be 95% sure that the conversion rate is 1.5% ± 0.0232%

**OR **we can be 95% sure conversion rate is between 1.4768% and 1.5232%

## In Summary

You should check any changes you make when make an update to your website, but you also need to be confident that your conversion rate is accurate enough for you to say that change was positive. If you’re not checking your conversion rate confidence it could be the difference between going forward, and going backward.