## What is Alpha-Spending?

Aliases: *alpha-spending function*

Alpha-spending is an approach of distributing (spending) the type I error (denoted alpha) over the duration of a sequential A/B test. Alpha-spending makes it possible to perform sequential testing while maintaining the overall error probability of the procedure. The ability to perform sequential monitoring of the data and to make decisions in case of significant departures from the minimum effect of interest it was planned for is a desirable quality as it allows for faster decision making.

Usually an error-spending function is employed which is an increasing function of the proportion of the maximum sample size of the experiment. An alpha-spending function calculates the cumulative type I error spent up until the time of a observation and thus governs the allocation of alpha at that particular point in time. Notable examples of such functions include O'Brien-Fleming type, Pocock-type, Kim & DeMets power functions and the Shih, Hwang & De Cani function.

From the point of generalizability and acquiring representative samples a spending function should be convex: starting to spend slowly in the early stages of a test, then spending more rapidly around mid-way through and finally slowing down spending towards the end. This way only very extreme outcomes would result in the test being terminated very early with a low sample size that might have some external validity issues.

An AGILE A/B test is an example for a testing method that includes both Alpha- and Beta-Spending functions.

## Articles on Alpha-Spending

- Error Spending in Sequential Testing Explained
- Improving ROI in A/B Testing: the AGILE AB Testing Approach
- Efficient AB Testing with the AGILE Statistical Method

Like this glossary entry? For an in-depth and comprehensive reading on A/B testing stats, check out the book "Statistical Methods in Online A/B Testing" by the author of this glossary, Georgi Georgiev.