Articles on Statistics

Articles on statistics written for marketers, user experience specialists, and web analysists in mind. Digging deep into statistics for online experiments (a.k.a. online A/B tests) and the methodological issues and approaches for solving them.

The Perils of Using Google Analytics User Counts in A/B Testing

Google Analytics User Data in AB Testing

(Updated Sep 2022 to include updated information about Google Analytics 4) Many analysts, marketers, product managers, UX and CRO professionals nowadays rely on user counts provided by Google Analytics, Adobe Analytics, or similar tools, in order to perform various statistical analyses. Such analyses may involve the statistical hypothesis tests and estimations part of A/B testing, […] Read more…

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The Effect of Using Cardinality Estimates Like HyperLogLog in Statistical Analyses

This article will examine the effects of using the HyperLogLog++ (HLL++) cardinality estimation algorithm in applications where its output serves as input for statistical calculations. A prominent example of such a scenario can be found in online controlled experiments (online A/B tests) where key performance measures are often based on the number of unique users, […] Read more…

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Error Spending in Sequential Testing Explained

Sequential Hypothesis Testing with Efficacy and Futility Bound

Sequential analysis of experimental data from A/B tests has been quite prominent in recent years due to the myriad of Bayesian solutions offered by big industry players. However, this type of sequential analysis is not sequential testing proper as these solutions have generally abandoned the idea of testing and therefore error control, substituting it for […] Read more…

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Frequentist vs Bayesian Inference

Frequentist vs Bayesian Inference

In this article I’m revisiting* the topic of frequentist vs Bayesian inference with specific focus on online A/B testing as usual. The present discussion easily generalizes to any area where we need to measure uncertainty while using data to guide decision-making and/or business risk management. In particular, I will discuss each of the following five […] Read more…

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Underpowered A/B Tests – Confusions, Myths, and Reality

Underpowered A/B Tests

In recent years a lot more CRO & A/B testing practitioners have started paying more attention to the statistical power of their online experiments, at least based on my observations. While this a positive development for which I hope I had contributed somewhat, it comes with the inevitable confusions and misunderstandings surrounding a complex concept […] Read more…

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The Perils of Poor Data Visualization in CRO & A/B Testing

As any UX & CRO expert should now, the way we present information matters a lot both in terms of how well it is understood and in terms of the probability that it will lead to the desired action. A/B testing calculators and other tools of the trade are no exception and here I will […] Read more…

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Does Your A/B Test Pass the Sample Ratio Mismatch Check?

Sample Ratio Mismatch AB Testing

Most, if not all successful online businesses nowadays rely on one or more systems for conducting A/B tests in order to inform business decisions ranging from simple website or advertising campaign interventions to complex product and business model changes. While testing might have become a prerequisite for releasing the tiniest of changes, one type of […] Read more…

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Statistical Methods in Online A/B Testing – the book

Book Cover Statistical Methods Online A/B Testing

The long wait is finally over! “Statistical Methods in Online A/B Testing” can now be found as a paperback and an e-book on your preferred Amazon store. Note that the Kindle edition is available for $2.99 or equivalent if you’ve already purchased the paperback (through Kindle Matchbook). The book is a comprehensive guide to statistics […] Read more…

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A/B Testing with a Small Sample Size

AB Testing Small Business

The question “How to test if my website has a small number of users” comes up frequently when I chat to people about statistics in A/B testing, online and offline alike. There are different opinions on the topic ranging from altering the significance threshold, statistical power or the minimum effect of interest all the way […] Read more…

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