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.

A/B Testing Statistics – A Concise Guide for Non-Statisticians

AB Testing Statistics

Navigating the maze of A/B testing statistics can be challenging. This is especially true for those new to statistics and probability. One reason is the obscure terminology popping up in every other sentence. Another is that the writings can be vague, conflicting, incomplete, or simply wrong, depending on the source. Articles sprinkled with advanced math, […] Read more…

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P-values and Confidence Intervals Explained

P-values and confidence intervals explained

Hundreds if not thousands of books have been written about both p-values and confidence intervals (CIs) – two of the most widely used statistics in online controlled experiments. Yet, these concepts remain elusive to many otherwise well-trained researchers, including A/B testing practitioners. Misconceptions and misinterpretations abound despite great efforts from statistics educators and experimentation evangelists. […] Read more…

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Improve your A/B tests with 9 lessons from the COVID-19 vaccine trials

Lessons for Online AB Testing from the COVID Vaccine Trials

A full year has passed since results from the first clinical trials of COVID-19 vaccines became available. Vast swaths of follow-up observational data are now in circulation which enables some conclusions about the strengths and weaknesses of those trials. Since modern medical trials are among the most rigorous and scrutinized experiments they can serve as […] Read more…

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The new standard for planning and analyzing A/B tests is here

A/B testing statistics done right

The first major overhaul of Analytics Toolkit since its release in early 2014 has finally arrived and it brings with it solutions to many of the hard questions facing practitioners when planning and analyzing A/B tests. Conducting statistically rigorous tests while achieving the best return on investment go hand in hand in the new Toolkit. […] Read more…

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Bayesian Probability and Nonsensical Bayesian Statistics in A/B Testing

Bayesian Probability and Bayesian Statistics in AB Testing

Many adherents of Bayesian methods put forth claims of superiority of Bayesian statistics and inference over the established frequentist approach based mainly on the supposedly intuitive nature of the Bayesian approach. Rational thinking or even human reasoning in general is Bayesian by nature according to some of them. Others argue that proper decision-making is inherently […] Read more…

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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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