# Statistical Test for dollar losses in A/B test where losses depend on sales

I'm trying to analyze the results of an A/B test, specifically around losses. We had two groups, who had bought something, and then were put into our A/B test to minimize potential losses from their purchases. So our treatment did not affect their purchase volume, but potentially the subsequent losses.

Say we have two groups: A: losses = $500, purchases =$1500 B: losses = $520, purchases =$1550

The loss amount is partly dependent on our treatment (we did something to try to reduce losses), but also on the purchases (if people buy more, they are more likely to have losses, just because of greater volume).

So if I do a t-test on the losses, I'm ignoring the effect of the purchase amounts. However, if I do a proportions test, I am 'fooling' the test into thinking I had (500, 520) successes and (1500, 1550) trials, which is not really the case.

What's the right approach here? Thank you!!

• What's a loss? If individual $i$ makes a purchase, is there some probability that the purchase is a loss? Is an independent observation essentially a purchase? Oct 24 '16 at 10:36
• Each observation is a purchase yes. Say if Buyer A makes one purchase of $100. That would count as one observation, with a value of$100. Then there is a possibility, if what was bought is faulty, that this purchase will turn into a loss (which could be of \$100 or less in the case of a partial refund). It's a loss because we don't get the item back. Does this help? Oct 24 '16 at 10:40