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The A/B testing problem with Gaussian priors

Eduardo M. Azevedo, David Mao, José Luis Montiel Olea and Amilcar Velez

Journal of Economic Theory, 2023, vol. 210, issue C

Abstract: A risk-neutral firm can perform a randomized experiment (A/B test) to learn about the effects of implementing an idea of unknown quality. The firm's goal is to decide the experiment's sample size and whether or not the idea should be implemented after observing the experiment's outcome. We show that when the distribution for idea quality is Gaussian and there are linear costs of experimentation, there are exact formulae for the firm's optimal implementation decisions, the value of obtaining more data, and optimal experiment sizes. Our formulae—which assume that companies use randomized experiments to help them maximize expected profits—provide a simple alternative to i) the standard rules-of-thumb of power calculations for determining the sample size of an experiment, and also to ii) ad hoc thresholds based on statistical significance to interpret the outcome of an experiment.

Keywords: Statistical Decision Theory; Optimal learning; Experiment design; A/B testing (search for similar items in EconPapers)
JEL-codes: C00 C44 C9 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:210:y:2023:i:c:s002205312300042x

DOI: 10.1016/j.jet.2023.105646

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