If youĭid STATS101, you are probably ok with this assumption, but those of you who did STATS102 are noĭoubt objecting. We are assuming the distribution of test statistic is normally distributed, with known variance.Row of the appropriate table below, if it exceeds it you may stop the experiment. Z = p a - p b 1 n a p a ( 1 - p a ) + 1 n b p b ( 1 - p b ). The simplest case of A/B testing is when each observation for each user is a numerical value, suchĪs a count of activity that day, the sales total, or some other usage statistic. To the threshold, and optionally stop the test if the score exceeds the threshold given in the lookup table. For each test during the course of experiment, compute the z-score.For the O’brien-Fleming approach it will be the sequence. For example, for the Pocock approach, α = 0. Thresholds for each of the tests you will run. Lookup on the tables below, or calculate using the ldbounds or GroupSeq R packages, the z-score.Fix the maximum length of your experiment, and the number of times you wish to run the statistical test.I’ve duplicated a few of these tables below for ease of reference.įunction, from those discussed below. Of course, libraries are available for computing these boundaries in several languages. Several standard allocations are commonly used in the research literature. The error spending approach has a lot of flexibility, as the error chances can be distributed arbitrarily between the days. The big advantage of this approach is that is a natural extension of the usual frequentist testing Using dynamic programming, we can then determine a sequence of thresholds, one per day, that we can use with the Say we want to run the test daily for a 30 day experiment. Test’s false-positive chance at every step so that the total false-positive rate is below the threshold Since we can compute these probabilities, we can also adjust the Is normally distributed, it is possible to compute the false-positive probabilities at each stage exactly They key idea of “Group Sequential” testing is that under the usual assumption that our test statistic Giving a very high 12% false positive rate! ![]() Rate (According to a simple numerical simulation) if you stop the experiment on the first p<0.05 result youįigure 2: Paths terminated when they cross the boundary on the next step. Looking at the results each day for a 10ĭay experiment with say 1000 data points per day will give you about an accumulated 17% false positive It’s obviously not an additional 5% each time as the test statistics are highly correlated,īut it turns out that the false positives accumulate very rapidly. On each subsequent test, you have a non-zero additional probability ![]() The intervention had no effect but it looks like it did). On the very first step you have a 5% chance of a false positive (i.e. Say you make a p=0.05 statistical test at each step. If the results look positiveĪnd you may decide to stop the experiment, particularly if it looks like the intervention is giving very bad The key problem is this: Whenever you look at the data (whether you run a formal statistical test or justĮyeball it) you are making a decision about the effectiveness of the intervention. What's wrong with just testing as you go? At the bottom of this post I give tables and references so you can use group sequential They call the setting “Group Sequentialĭesigns”. It turns out that easy to use, practical solutions have been worked outīy clinical statistician decades ago, in papers with many thousands of citations. Iĭiscuss a few of these misguided approaches below. Most discussions of A/B testing do recognize this problem, however the solutions they suggest are simply wrong. Doing so WILL lead to false-positive rates way above 5%, usually on the order of This: If you're going to look at the results of your experiment as it runs, you can not just repeatedly apply a 5% significance level t-test. It’s amazing the amount of confusion on how to run a simple A/B test seen on the internet.
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