17th March 2011

# Conversion Rate Confidence

David Walsh

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, 16th 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 they 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

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) youll need the following:

• number of visits (v)
• number of conversions (c)

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.

## How We Can Help

Need a bit of work on your conversion rate? Then get in touch with us by calling 0161 402 3170 or use our nifty contact form and our conversion rate optimisation (CRO) experts will be happy to provide a free consultation on how you can improve your site.