What does "Risk" mean?

Definition of Risk in the context of A/B testing (online controlled experiments).

What is Risk?

In A/B testing risk is the probability associated with a negative event, and event with negative expected value. In particular, we are concerned with the risk of arriving at a wrong conclusion. We can measure this risk by performing an A/B test where the risk of committing a type I error or a type II error are controlled via the error probability guarantees of the procedure we use (usually a significance test). The two types of risk are denoted alpha and beta.

A different kind of framing risk is through an uncertainty related to an estimate. A common method to convey that is the construction of confidence intervals. Yet another approach to assessing risk is to calculate the severity related to any claim about a parameter of interest.

Risk takes a slightly different meaning during a risk-reward analysis where the risk function is calculated based on a prior distribution. Based on that prior we can estimated the risk-adjusted loses we can incur both during and after an A/B test. The difference between a pre-test risk-adjusted loss and the type I error is that the latter is a conservative bound based on the most extreme value of the null hypothesis and does not consider any information external to the test while the former incorporates different types of information and also incorporates loses due to type II errors. Also, the risk-adjusted loss is counterfactual and based entirely on a loss function while the type I error is entirely factual.

It is important to understand that limiting risk always comes at the cost of limited gains (reward).

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