Experiment methodology
A/B testing (also known as bucket testing, split-run testing, or split testing) is a user experience research method. A/B tests consist of a randomized experiment that usually involves two variants (A and B), although the concept can be also extended to multiple variants of the same variable. It includes application of statistical hypothesis testing or "two-sample hypothesis testing" as used in the field of statistics. A/B testing is a way to compare multiple versions of a single variable, for example by testing a subject's response to variant A against variant B, and determining which of the variants is more effective.
Multivariate testing or multinomial testing is similar to A/B testing, but may test more than two versions at the same time or use more controls. Simple A/B tests are not valid for observational, quasi-experimental or other non-experimental situations—commonplace with survey data, offline data, and other, more complex phenomena.
Definition.
"A/B testing" is a shorthand for a simple randomized controlled experiment, in which a number of samples (e.g. A and B) of a single vector-variable are compared.
A/B tests are widely considered the simplest form of controlled experiment, especially when they only involve two variants. However, by adding more variants to the test, its complexity grows. 
The following example illustrates an A/B test with a single variable:
Suppose a company has a customer database of 2,000 people and decides to create an email campaign with a discount code in order to generate sales through its website. The company creates two versions of the email with different call to action (the part of the copy which encourages customers to do something — in the case of a sales campaign, make a purchase) and identifying promotional code.
The company then monitors which campaign has the higher success rate by analyzing the use of the promotional codes. The email using the code A1 has a 5% response rate (50 of the 1,000 people emailed used the code to buy a product), and the email using the code B1 has a 3% response rate (30 of the recipients used the code to buy a product). The company therefore determines that in this instance, the first Call To Action is more effective and will use it in future sales. A more nuanced approach would involve applying statistical testing to determine if the differences in response rates between A1 and B1 were statistically significant (that is, highly likely that the differences are real, repeatable, and not due to random chance).
In the example above, the purpose of the test is to determine which is the more effective way to encourage customers to make a purchase. If, however, the aim of the test had been to see which email would generate the higher click-rate—that is, the number of people who actually click onto the website after receiving the email—then the results might have been different.
For example, even though more of the customers receiving the code B1 accessed the website, because the Call To Action didn't state the end-date of the promotion many of them may feel no urgency to make an immediate purchase. Consequently, if the purpose of the test had been simply to see which email would bring more traffic to the website, then the email containing code B1 might well have been more successful. An A/B test should have a defined outcome that is measurable such as number of sales made, click-rate conversion, or number of people signing up/registering.
Common test statistics.
Two-sample hypothesis tests are appropriate for comparing the two samples where the samples are divided by the two control cases in the experiment. Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation. Student's t-tests are appropriate for comparing means under relaxed conditions when less is assumed. Welch's t test assumes the least and is therefore the most commonly used test in a two-sample hypothesis test where the mean of a metric is to be optimized. While the mean of the variable to be optimized is the most common choice of estimator, others are regularly used.
For a comparison of two binomial distributions such as a click-through rate one would use Fisher's exact test.
Segmentation and targeting.
A/B tests most commonly apply the same variant (e.g., user interface element) with equal probability to all users. However, in some circumstances, responses to variants may be heterogeneous. That is, while a variant A might have a higher response rate overall, variant B may have an even higher response rate within a specific segment of the customer base.
For instance, in the above example, the breakdown of the response rates by gender could have been:
In this case, we can see that while variant A had a higher response rate overall, variant B actually had a higher response rate with men.
As a result, the company might select a segmented strategy as a result of the A/B test, sending variant B to men and variant A to women in the future. In this example, a segmented strategy would yield an increase in expected response rates from formula_1 to formula_2 – constituting a 30% increase.
If segmented results are expected from the A/B test, the test should be properly designed at the outset to be evenly distributed across key customer attributes, such as gender. That is, the test should both (a) contain a representative sample of men vs. women, and (b) assign men and women randomly to each “variant” (variant A vs. variant B). Failure to do so could lead to experiment bias and inaccurate conclusions to be drawn from the test.
This segmentation and targeting approach can be further generalized to include multiple customer attributes rather than a single customer attribute—for example, customers' age "and" gender—to identify more nuanced patterns that may exist in the test results.
Tradeoffs.
Positives.
The results of A/B tests are simple to interpret and use to get a clear idea of what users prefer, since it is directly testing one option over another. It is based on real user behavior, so the data can be very helpful especially when determining what works better between two options. 
A/B tests can also provide answers to highly specific design questions. One example of this is Google's A/B testing with hyperlink colors. In order to optimize revenue, they tested dozens of different hyperlink hues to see which color the users tend to click more on.
Negatives.
A/B tests are sensitive to variance; they require a large sample size in order to reduce standard error and produce a statistically significant result. In applications where active users are abundant, such as popular online social media platforms, obtaining a large sample size is trivial. In other cases, large sample sizes are obtained by increasing the experiment enrollment period. However, using a technique coined by Microsoft as Controlled-experiment Using Pre-Experiment Data (CUPED), variance from before the experiment start can be taken into account so that fewer samples are required to produce a statistically significant result.
Due to its nature as an experiment, running an A/B test introduces the risk of wasted time and resources if the test produces unwanted results, such as negative or no impact to business metrics.
In December 2018, representatives with experience in large-scale A/B testing from thirteen different organizations (Airbnb, Amazon, Booking.com, Facebook, Google, LinkedIn, Lyft, Microsoft, Netflix, Twitter, Uber, and Stanford University) summarized the top challenges in a SIGKDD Explorations paper.
The challenges can be grouped into four areas: Analysis, Engineering and Culture, Deviations from Traditional A/B tests, and Data quality.
History.
It is difficult to definitively establish when A/B testing was first used. The first randomized double-blind trial, to assess the effectiveness of a homeopathic drug, occurred in 1835. Experimentation with advertising campaigns, which has been compared to modern A/B testing, began in the early twentieth century. The advertising pioneer Claude Hopkins used promotional coupons to test the effectiveness of his campaigns. However, this process, which Hopkins described in his Scientific Advertising, did not incorporate concepts such as statistical significance and the null hypothesis, which are used in statistical hypothesis testing. Modern statistical methods for assessing the significance of sample data were developed separately in the same period. This work was done in 1908 by William Sealy Gosset when he altered the Z-test to create Student's t-test.
With the growth of the internet, new ways to sample populations have become available. Google engineers ran their first A/B test in the year 2000 in an attempt to determine what the optimum number of results to display on its search engine results page would be. The first test was unsuccessful due to glitches that resulted from slow loading times. Later A/B testing research would be more advanced, but the foundation and underlying principles generally remain the same, and in 2011, 11 years after Google's first test, Google ran over 7,000 different A/B tests.
In 2012, a Microsoft employee working on the search engine Microsoft Bing created an experiment to test different ways of displaying advertising headlines. Within hours, the alternative format produced a revenue increase of 12% with no impact on user-experience metrics. Today, major software companies such as Microsoft and Google each conduct over 10,000 A/B tests annually.
A/B testing has been claimed by some to be a change in philosophy and business-strategy in certain niches, though the approach is identical to a between-subjects design, which is commonly used in a variety of research traditions. A/B testing as a philosophy of web development brings the field into line with a broader movement toward evidence-based practice.
Many companies now use the "designed experiment" approach to making marketing decisions, with the expectation that relevant sample results can improve positive conversion results. It is an increasingly common practice as the tools and expertise grow in this area.
Applications.
A/B testing in online social media.
A/B tests have been used by large social media sites like LinkedIn, Facebook, and Instagram to understand user engagement and satisfaction of online features, such as a new feature or product. A/B tests have also been used to conduct complex experiments on subjects such as network effects when users are offline, how online services affect user actions, and how users influence one another.
A/B testing for e-commerce.
On an e-commerce website, the purchase funnel is typically a good candidate for A/B testing, since even marginal-decreases in drop-off rates can represent a significant gain in sales. Significant improvements can be sometimes seen through testing elements like copy text, layouts, images and colors, but not always. In these tests, users only see one of two versions, since the goal is to discover which of the two versions is preferable.
A/B testing for product pricing.
A/B testing can be used to determine the right price for the product, as this is perhaps one of the most difficult tasks when a new product or service is launched. A/B testing (especially valid for digital goods) is an excellent way to find out which price-point and offering maximize the total revenue.
Political A/B testing.
A/B tests have also been used by political campaigns. In 2007, Barack Obama's presidential campaign used A/B testing as a way to garner online attraction and understand what voters wanted to see from the presidential candidate. For example, Obama's team tested four distinct buttons on their website that led users to sign up for newsletters. Additionally, the team used six different accompanying images to draw in users. Through A/B testing, staffers were able to determine how to effectively draw in voters and garner additional interest.
HTTP Routing and API feature testing.
A/B testing is very common when deploying a newer version of an API. For real-time user experience testing, an HTTP Reverse proxy is configured in such a way that, "N"% of the HTTP traffic goes into the newer version of the backend instance, while the remaining "100-N"% of HTTP traffic hits the (stable) older version of the backend HTTP application service. This is usually done for limiting the exposure of customers to a newer backend instance such that, if there is a bug on the newer version, only "N"% of the total user agents or clients get affected while others get routed to a stable backend, which is a common ingress control mechanism.
References.
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