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I'm working on an analysis project that is really pushing the limits of my statistics knowledge and I'd love some advice! The project involves measuring the outcome from a pricing test in which one group of customers is shown a higher price than others. This leads to lower conversion in the test group (fewer people buy the product), but more revenue per purchase. I can measure which one is more successful by simply measuring which group generates more total revenue, but I'm stuck on how to test this data for statistical significance.

My current approach is to build a dataset that includes the revenue for each individual customer that views a price. If they buy the product, they create revenue of a certain amount. If they don't buy the product, they create zero revenue. Here are two sample datasets:

control <- (0, 0, 15, 0, 25, 0, 17, 0, 0, 12, 0)

test <- (0, 0, 0, 0, 30, 0, 19, 0, 0, 20, 0)

In this example, control had a higher conversion rate, but test generated more revenue per user. I want a test that can help me understand whether test or control are likely to generate more total revenue (or if I don't have enough data to say either way). So far I've tried running a simple t-test on the two datasets, since I was hoping that I had enough data points to not worry about the data not being normally distributed. I've also been looking at the Wilcoxon Test, but I'm having a hard time understanding it!

Sorry if this is a basic question, but any advice at all would be super helpful!

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  • $\begingroup$ Go for a nonparametric permutation test instead of a t-test. $\endgroup$
    – Ggjj11
    Commented Jul 16, 2023 at 8:04

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I would look into something like a censored regression, hurdle or two-part model, where you are postulating that there are two different processes at work: (a) one that determines whether or not someone decides to pay, and (b) one that determines how much.

The hurdle model is typically used for count data, and I'm not super familiar with censored regression and two-part models, but here are some leads:

https://cran.r-project.org/web/packages/censReg/vignettes/censReg.pdf

http://seananderson.ca/2014/05/18/gamma-hurdle.html

https://www.researchgate.net/post/Are_there_generalizations_of_zero-inflated_negative_binomial_and_hurdle_modeling_that_address_continuous_ie_non-count_variables

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    $\begingroup$ Semiparametric regression (e.g., ordinal models such as the proportional odds model which generalizes the Wilcoxon test) will handle arbitrary clumping at zero. Examples using ordinal models for analyzing continuous Y may be found here and here. $\endgroup$
    – Frank Harrell
    Commented Aug 16, 2023 at 11:40

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