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Power is the probability that an experiment will flag a real change as statistically significant. The conventional threshold for rejecting the null hypothesis is 5%. We reject the null hypothesis if p-value is very low. An A/B test seeks to measures a statistic for control and treatment, and calculates the probability that the difference would be as extreme as the observed difference under the null hypothesis. Null hypothesis is the hypothesis that the treatment has no effect.

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Since an experimenter can instrument the code to trigger an experiment at practically any place in the app, pre-calculating variances for each metric at each possible trigger point is unrealistic. These sub-populations frequently have different values for important metrics than does the overall Twitter population (this is intuitive: people who tap the “New Tweet” icon are a-priori more likely to send a Tweet than those who do not!). However, as described in an earlier post, Twitter experiments use “trigger analysis” - only subsets of users who trigger specific features are included in an experiment.

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Targeted Experiments: When observing an experiment, a naive estimate of variance of a metric would be calculating the metric across the full population, and recording the observed variance.

Variance of such metrics can’t be calculated directly from the metric value, and isn’t something an experimenter is likely to have at hand. “Average number of Tweets people ‘like’” is a non-binary metric.

For example “proportion of people who ‘like’ a Tweet” is a binary metric, a user either hits the ‘like’ button at some point, or she does not. Non-binary metrics: Many metrics we track are not ones that can be described in terms of CTR.None of these were straightforward to incorporate into our experiment creation workflow, for two reasons: They tend to either explicitly ask the experimenter the sample mean and standard deviation (in addition to overall population size) or they address “click through rate” (CTR) or “conversion” - binary-valued metrics (either 1 or 0) for which variance is easy to calculate given the ratio of 1s to 0s. There are many different experiment sizing and power calculation tools available online. To address this problem, we created a special tool to provide guidance for experimenters on sizing their experiment appropriately, and to alert them when experiments are likely to be underpowered. However, if we pick too small a bucket, we might not be able to observe a real change, which will affect our decision-making and/or slow down iteration while we re-run the experiment with larger buckets.

Thus, if 1% of the traffic is sufficient to measure effect of changes, we would prefer to use only 1%. Also, if experimental treatments change as we iterate on designs and approaches, we might confuse a lot of users.Īdditionally, if all experiments ran at a 50/50 split, our users could wind up in multiple experiments simultaneously, making it difficult to reason what anyone should be experiencing at any given time. New features have risk, and we want to limit risk exposure. If all we cared about was how reliably and quickly we could observe a change, we would run all tests at a 50/50 split, which is not always advisable. This post describes how Twitter’s A/B testing framework, DDG, addresses one of the most common questions we hear from experimenters, product managers, and engineers: how many users do we need to sample in order to run an informative experiment?įrom a statistical standpoint, the larger the buckets, the better.

#STATISTICAL POWER FORMULA HOW TO#

In previous posts, we discussed how to detect potentially biased experiments, and explored the implications of using multiple control groups.

Bucket size estimation for A/B experiments

Statistical power formula