# Sample Size Calculations in Ruby

I really love the abba tool. It’s great. So is R. So are Zed Shaw’s rants on statistics.

What really sucks is the complete lack of basic statis libraries in Ruby. After spending more time than I’d like to admit going over some reference implementations in R, I added both sample size and confidence interval calculations to ABAnalyzer. Here are some excerpts from the docs.

## Sample Size Calculations

Let’s say you want to determine how large your sample size needs to be for an A/B test. Let’s say your baseline is 10%, and you want to be able to determine if there’s at least a 10% relative lift (1% absolute) to 11%. Let’s assume you want a power of 0.8 and a significance level of 0.05 (that is, an 80% chance of that you’ll fail to recognize a difference when there is one, and a 5% chance of a false negative).

This means that you will need at least 14,751 people in each group sample. You can see this same example with R at on the 37 signals blog.

## Confidence Intervals

You can also get a confidence interval. Let’s say you have the results of a test where there were 711 successes out of 4000 trials. To get a 95% confidence interval of the “true” value of the conversion rate, use:

This means (roughly) that if you ran this experiment over and over, 95% of the time the resulting proportion would be between 17% and 19%.

You can also determine what the relative confidence intervals would be. Let’s say that your old conversion rate was 13%, and you wanted to know what sort of relative lift you could get.

This means (roughly) that if you ran this experiment over and over, 95% of the time the resulting proportion would be a relative lift of between 28% and 46%. Go buy yourself a beer!