## What is Average Revenue Per User?

Aliases: *ARPU*

Average Revenue per user (ARPU) is simply the arithmetic mean of the revenue per user across a set of users restricted by a time period and/or a specific section or funnel of a website, app or other software. As with any average, it is calculated by dividing the total revenue by the number of users that entered the funnel that generated the revenue: ARPU = Revenue / Users.

The average revenue per user is often the metric closest to the business bottom-line that conversion rate optimization specialist can hope to have at hand as is thus often used as a primary KPI in online controlled experiments. However, due to the complexities related to estimating its standard deviation (due to ARPU being a non-binomial metric) and the inherently significant decrease in the required sample size (thus decrease in test duration) a conversion rate would be selected as the primary KPI while ARPU will be treated as a secondary KPI or as a co-primary KPI but with a non-inferiority test instead of a superiority test.

For example, an experiment can be defined with a main goal to increase the purchas rate of on e-commerce store since the intervention at hand is not expected to lead to lower average order value. Keeping the average revenue per user as a co-primary KPI with a satisfactory non-inferiority margin allows one to perform the test in a shorter time-span while also checking the assumption about the effect on AOV. This approach would also allow easier use of sequential testing methods such as conducting an AGILE A/B test.

Being a non-binomial metric and the often committed mistake of mistaking the RPU distribution (which is usually highly skewed) with the distribution of the statistic of interest (ARPU) prompts some people to search for non-parametric tests such as the Mann-Whitney-Wilcoxon rank-sum test which they believe are required due to a perceived issue with the normality assumption behind classic parametric tests. However, no such complications are necessary since the statistic of interest is in fact the average revenue per user and being an arithmetic mean it follows the Central Limit Theorem (CLT) and thus has a normal distribution. Worries about the normality assumption as thus unwarranted, especially with the sample sizes typical in A/B testing. Furthermore, if one is still testing the same thing (difference in means) then the MWW test is only a substitute for a proper t or z test if the assumptions of the latter two are met...