Let’s take a quick look at a very important and common experimental problem: checking if the difference in success rates of two Binomial experiments is statistically significant. This can arise in A/B testing situations such as online advertising, sales, and manufacturing.
We already share a free video course on a Bayesian treatment of planning and evaluating A/B tests (including a free Shiny application). Let’s now take a look at the should be simple task of simply building a summary statistic that includes a classic frequentist significance.
Continue reading Quick Significance Calculations for A/B Tests in R
Win-Vector LLC has been offering a couple of online video courses on the topics of data science and A/B testing (both using R). These are high quality courses and well worth the money and time needed to work through them closely (with all materials distributed on GitHub).
Our current distributor is Udemy, which has just announced a unilateral change in pricing policy (March 2, 2016). This note is about the current status of these courses. Continue reading Win-Vector video courses: price/status changes
As a “thank you” to our blog, mailing list, and Twitter followers (@WinVectorLLC) we at Win-Vector LLC have decided to re-release our formerly fee-based A/B testing video course as a free (advertisement supported) video course here on Youtube.
The course emphasizes how to design A/B tests using prior “guestimates” of effect sizes (often you have these from prior campaigns, or somebody claims an effect size and it is merely your job to confirm it). It is fairly technical, and the emphasis is Bayesian- where we are trying to get an actual estimate of the distribution unknown true expected payoff rate of the various campaigns (the so-called posteriors). We show how to design and evaluate a sales campaigns for a product at two different price points.
The solution is coded in R and Nina Zumel has contributed an updated Shiny user interface demonstrating the technique (for more on Shiny, please see here). The code for the calculation methods and older shiny app are shared here. Continue reading Free video course: applied Bayesian A/B testing in R
We here at Win-Vector LLC been working through an ad-hoc series about A/B testing combining elements of both operations research and statistical points of view.
Our most recent article was a dynamic programming solution to the A/B test problem. Explicitly solving such dynamic programs gets long and tedious, so you are well served by finding and introducing clever invariants to track (something better than just raw win-rates). That clever idea is called “sequential analysis” and was introduced by Abraham Wald (somebody we have written about before). If you have ever heard of a test plan such as “first process to get more than 30 wins ahead of the other is the one we choose” you have seen methods derived from Wald’s sequential analysis technique.
Wald’s famous airplane armor problem
A corrected version of the detailed article is now here.
A corrected version of this article is now here.
Our last article on A/B testing described the scope of the realistic circumstances of A/B testing in practice and gave links to different standard solutions. In this article we will be take an idealized specific situation allowing us to show a particularly beautiful solution to one very special type of A/B test.
For this article we are assigning two different advertising message to our potential customers. The first message, called “A”, we have been using a long time, and we have a very good estimate at what rate it generates sales (we are going to assume all sales are for exactly $1, so all we are trying to estimate rates or probabilities). We have a new proposed advertising message, called “B”, and we wish to know does B convert traffic to sales at a higher rate than A?
We are assuming:
- We know exact rate of A events.
- We know exactly how long we are going to be in this business (how many potential customers we will ever attempt to message, or the total number of events we will ever process).
- The goal is to maximize expected revenue over the lifetime of the project.
As we wrote in our previous article: in practice you usually do not know the answers to the above questions. There is always uncertainty in the value of the A-group, you never know how long you are going to run the business (in terms of events or in terms of time, and you would also want to time-discount any far future revenue), and often you value things other than revenue (valuing knowing if B is greater than A, or even maximizing risk adjusted returns instead of gross returns). This represents severe idealization of the A/B testing problem, one that will let us solve the problem exactly using fairly simple R code. The solution comes from the theory of binomial option pricing (which is in turn related to Pascal’s triangle).
Yang Hui (ca. 1238–1298) (Pascal’s) triangle, as depicted by the Chinese using rod numerals.
For this “statistics as it should be” (in partnership with Revolution Analytics) article let us work the problem (using R) pretending things are this simple. Continue reading A dynamic programming solution to A/B test design
Why does planning something as simple as an A/B test always end up feeling so complicated?
An A/B test is a very simple controlled experiment where one group is subject to a new treatment (often group “B”) and the other group (often group “A”) is considered a control group. The classic example is attempting to compare defect rates of two production processes (the current process, and perhaps a new machine).
Illustration: Boris Artzybasheff
(photo James Vaughan, some rights reserved)
In our time an A/B test typically compares the conversion to sales rate of different web-traffic sources or different web-advertising creatives (like industrial defects, a low rate process). An A/B test uses a randomized “at the same time” test design to help mitigate the impact of any possible interfering or omitted variables
. So you do not run “A” on Monday and then “B” on Tuesday, but instead continuously route a fraction of your customers to each treatment. Roughly a complete “test design” is: how much traffic to route to A, how much traffic to route to B, and how to chose A versus B after the results are available.
A/B testing is one of the simplest controlled experimental design problems possible (and one of the simplest examples of a Markov decision process). And that is part of the problem: it is likely the first time a person will need to truly worry about:
- Design of experiments
- Defining utility
- Priors or beliefs
- Efficiency of inference
All of these are technical terms we will touch on in this article. However, we argue the biggest sticking point of A/B testing is: it requires a lot more communication between the business partner (sponsoring the test) and the analyst (designing and implementing the test) than a statistician or data scientist would care to admit. In this first article of a new series called “statistics as it should be” (in partnership with Revolution Analytics) we will discuss some of the essential issues in planning A/B tests. Continue reading Why does designing a simple A/B test seem so complicated?
The June 4, 2015 Wikipedia entry on A/B Testing claims Google data scientists were the origin of the term “A/B test”:
Google data scientists ran their first A/B test at the turn of the millennium to determine the optimum number of results to display on a search engine results page. While this was the origin of the term, very similar methods had been used by marketers long before “A/B test” was coined. Common terms used before the internet era were “split test” and “bucket test”.
It is very unlikely Google data scientists were the first to use the informal shorthand “A/B test.” Test groups have been routinely called “A” and “B” at least as early as the 1940s. So it would be natural for any working group to informally call their test comparing abstract groups “A” and “B” an “A/B test” from time to time. Statisticians are famous for using the names of variables (merely chosen by convention) as formal names of procedures (p-values, t-tests, and many more).
Even if other terms were dominant in earlier writing, it is likely A/B test was used in speech. And writings of our time are sufficiently informal (or like speech) that they should be compared to earlier speech, not just earlier formal writing.
That being said, a quick search yields some examples of previous use. We list but a few below. Continue reading I do not believe Google invented the term A/B test