R: Modelling a Conversion Rate with a Binomial Distribution
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Join For FreeAs 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.
Published at DZone with permission of Mark Needham, DZone MVB. See the original article here.
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