I'm confused about if t-test can only test means (sum / sample size), or if it can test sums as well (not normalizing for sample size).
Below is a passage from a trusted book.
Note that even though we want to increase overall revenue, we do not recommend using the sum of revenue itself, as it depends on the number of users in each variant. Even if the variants are allocated with equal traffic, the actual number of users may vary due to chance. We recommend that key metrics be normalized by the actual sample sizes, making revenue-per-user a good metric.
What test would test for differences in sum of revenue?
Edit: Data involved would be two series of unequal length. One observation would be a unique user placing a unique order.
For instance, control group has sales data in USD [12, 11, 9, 20] for a sum of 52 USD; and treatment group has sales data [19, 10, 8] for a total of 37 USD.