R: Modelling a Conversion Rate with a Binomial Distribution

As part of some work Sid and I were doing last week we wanted to simulate the conversion rate for an A/B testing we were planning.

We started with the following function which returns the simulated conversion rate for a given conversion rate of 12%:

generateConversionRates <- function(sampleSize) {
	sample_a <- rbinom(seq(0, sampleSize), 1, 0.12)
	conversion_a <- length(sample_a[sample_a == 1]) / sampleSize
 
	sample_b <- rbinom(seq(0, sampleSize), 1, 0.12)
	conversion_b <- length(sample_b[sample_b == 1]) / sampleSize
 
	c(conversion_a, conversion_b)
}

If we call it:

> generateConversionRates(10000)
[1] 0.1230 0.1207

We have a 12.3% conversion rate on A and a 12.07% conversion rate on B based on 10,000 sample values.

We then wrote the following function to come up with 1000 versions of those conversion rates:

generateSample <- function(sampleSize) {
	lapply(seq(1, 1000), function(x) generateConversionRates(sampleSize))
}

We can call that like this:

> getSample(10000)
[[998]]
[1] 0.1179 0.1216
 
[[999]]
[1] 0.1246 0.1211
 
[[1000]]
[1] 0.1248 0.1234

We were then using these conversion rates to try and work out how many samples we needed to include in an A/B test to have reasonable confidence that it represented the population.

We actually ended up abandoning that exercise but I thought I’d record the code because I thought it was pretty interesting.