A/B Testing with Machine Learning  A StepbyStep Tutorial
Written by Matt Dancho
With the rise of digital marketing led by tools including Google Analytics, Google Adwords, and Facebook Ads, a key competitive advantage for businesses is using A/B testing to determine effects of digital marketing efforts. Why? In short, small changes can have big effects.
This is why A/B testing is a huge benefit. A/B Testing enables us to determine whether changes in landing pages, popup forms, article titles, and other digital marketing decisions improve conversion rates and ultimately customer purchasing behavior. A successful A/B Testing strategy can lead to massive gains  more satisfied users, more engagement, and more sales  WinWinWin.
A key competitive advantage for businesses is using A/B testing
A major issue with traditional, statisticalinference approaches to A/B Testing is that it only compares 2 variables  an experiment/control to an outcome. The problem is that customer behavior is vastly more complex than this. Customers take different paths, spend different amounts of time on the site, come from different backgrounds (age, gender, interests), and more. This is where Machine Learning excels  generating insights from complex systems.
Article Overview
In this article you will experience how to implement Machine Learning for A/B Testing stepbystep. After reading this post you will:

Understand what A/B Testing is

Understand why Machine Learning is a better approach for performing A/B Testing versus traditional statistical inference (e.g. zscore, ttest)
 Get a StepbyStep Walkthrough for implementing machine learning for A/B Testing in
R
using 3 different algorithms: Linear Regression
 Decision Trees
 XGBoost

Develop a Story for what contributes to the goal of gaining Enrollments
 Get a Learning Recommendation for those that want to learn how to implement machine learning following best practices for any business problem.
1.0 What is A/B Testing?
A/B Testing is a triedandtrue method commonly performed using a traditional statistical inference approach grounded in a hypothesis test (e.g. ttest, zscore, chisquared test). In plain English, 2 tests are run in parallel:

Treatment Group (Group A)  This group is exposed to the new web page, popup form, etc.

Control Group (Group B)  This group experiences no change from the current setup.
The goal of the A/B is then to compare the conversion rates of the two groups using statistical inference.
The problem is that the world is not a vacuum involving only the experiment (treatment vs control group) and effect. The situation is vastly more complex and dynamic. Consider these situations:

Users have different characteristics: Different ages, genders, new vs returning, etc

Users spend different amounts of time on the website: Some hit the page right away, others spend more time on the site

Users are find your website differently: Some come from email or newsletters, others from web searches, others from social media

Users take different paths: Users take actions on the website going to different pages prior to being confronted with the event and goal
Often modeling an A/B test in this vacuum can lead to misunderstanding of the true story.
The world is not a vacuum involving only the changes and effect. The situation is more complex.
This is where Machine Learning can help.
2.0 Why use Machine Learning?
Unlike statistical inference, Machine Learning algorithms enable us to model complex systems that include all of the ongoing events, user features, and more. There are a number of algorithms each with strengths and weaknesses.
An attractive benefit to Machine Learning is that we can combine multiple approaches to gain insights.
Rather than discuss in abstract, we can use an example from Udacityâ€™s A/B Testing Course, but apply the applied Machine Learning techniques from our Business Analysis with R Course to gain better insights into the innerworkings of the system rather than simply comparing an experiment and control group in an A/B Test.
3.0 A/B Test Using Machine Learning: StepByStep Walkthrough
Weâ€™ll implement machine learning to perform the A/B test using the R
statistical programming language, an excellent tool for business professionals seeking to advance their careers by learning Data Science and Machine Learning [Read 6 Reasons to Learn R for Business Next].
For those interested in the traditional statistical inference approach to A/B Testing, we found this article on Kaggle to be of very high quality: A/B Tests With Python
Experiment Name: â€śFree Trialâ€ť Screener
In the experiment, Udacity tested a change where if the student clicked â€śstart free trialâ€ť, they were asked how much time they had available to devote to the course.
If the student indicated 5 or more hours per week, they would be taken through the checkout process as usual. If they indicated fewer than 5 hours per week, a message would appear indicating that Udacity courses usually require a greater time commitment for successful completion.
This screenshot shows what the experiment looks like.
Why Implement the Form?
The goal with this popup was that this might set clearer expectations for students upfront, thus reducing the number of frustrated students who left the free trial because they didnâ€™t have enough time.
However, what Udacity wants to avoid is â€śsignificantlyâ€ť reducing the number of students that continue past the free trial and eventually complete the course.
Project Goal
In this analysis, we will investigate which features are contributing enrollments and determine if there is an impact on enrollments from the new â€śSetting Expectationsâ€ť form.
 The users that experience the form will be denoted as â€śExperiment = 1â€ť
 The control group (users that donâ€™t see the form) will be denoted as â€śExperiment = 0â€ť.
3.1 Get the Data
The data set for this A/B Test can be retrieved from Kaggle Data Sets.
3.2 Libraries
Weâ€™ll need the following libraries for this tutorial. You can install them with install.packages("package_name")
. Weâ€™ll be using:

tidyverse
andtidyquant
: These are the core data manipulation and visualization packages. Weâ€™ll mainly be usingdplyr
for data manipulation,ggplot2
for data visualization, andtidyquant
themes for business reporting. 
parsnip
,rsample
,recipes
, andyardstick
: These are the tidyverse modeling packages. Theparsnip
package is an amazing tool that connects to the main machine learning algorithms. We teachparsnip
indepth (44 lessons, 5 hours of video) in Business Analysis with R, Week 6, Part 2  Machine Learning (Regression). 
rpart
,rpart.plot
, andxgboost
: These are the modeling libraries that weâ€™ll connect to through theparsnip
interface.
3.3 Import the Data
Next, we can import the data using the read_csv()
function. Side Note  We teach Data Import with readr
, odbc
(for data bases) in Week 2 of Business Analysis with R.
3.4 Investigate the Data
We can use the head()
function to see what the first 5 rows of data looks like. The pipe (%>%
) is used to chain functions into complex expressions, a key feature of the tidyverse
.
We have 5 columns consisting of:
 Date: a character formatted Day, Month, and Day of Month
 Pageviews: An aggregated count of Page Views on the given day
 Clicks: An aggregated count of Page Clicks on the given day for the page in question
 Enrollments: An aggregated count of Enrollments by day.
 Payments: An aggregated count of Payments by day.
Next, we inspect the â€śControl Groupâ€ť using glimpse()
the data to get an idea of the data format (column classes and data size).
Last, we can check the â€śExperimentâ€ť group (i.e. the Treatment Group) with glimpse()
as well to make sure itâ€™s in the same format.
Key Points:

37 total observations in the control set and 37 in the experiment set

Data is timebased and aggregated by day  This isnâ€™t the best way to understand complex user behavior, but weâ€™ll go with it

We can see that
Date
is formatted as a character data type. This will be important when we get to data quality. Weâ€™ll extract day of the week features out of it. 
Data between the experiment group and the control group is in the same format. Same number of observations (37 days) since the groups were tested in parallel.
3.5 Data Quality Check
Next, letâ€™s check the data quality. Weâ€™ll go through a process involves:

Check for Missing Data  Are values missing? What should we do?

Check Data Format  Is data in correct format for analysis? Are all features created and in the right class?
We will use mainly dplyr
in this section. Side Note  Data Manipulation with dplyr
, tidyr
, lubridate
(timeseries), stringr
(text), and forcats
(categorical) is taught indepth (Weeks 2 and 3, 60+ lessons, 2 Challenges) in our Business Analysis with R course.
3.5.1 Check for Missing Data
The next series of operations calculates the count of missing values in each column with map(~ sum(is.na(.)))
, converts to long format with gather()
, and arranges descending with arrange()
. Side Note  We teach these functions and techniques in Week 2 of Business Analysis with R course.
Key Point: We have 14 days of missing observations that we need to investigate
Letâ€™s see if the missing data (NA
) is consistent in the experiment set.
Key Point: The count of missing data is consistent (a good thing). We still need to figure out whatâ€™s going on though.
Letâ€™s see which values are missing using the filter()
.
Key Point: We donâ€™t have Enrollment information from November 3rd on. We will need to remove these observations.
3.5.2 Check Data Format
Weâ€™ll just check the data out, making sure its in the right format for modeling.
Key Points:

Date is in character format. It doesnâ€™t contain year information. Since the experiment was only run for 37 days, we can only realistically use the â€śDay of Weekâ€ť as a predictor.

The other columns are all numeric, which is OK. We will predict the number of Enrollments (regression) (taught in Week 6 of Business Analysis with R course)

Payments is an outcome of Enrollments so this should be removed.
3.6 Format Data
Now that we understand the data, letâ€™s put it into the format we can use for modeling. Weâ€™ll do the following:
 Combine the
control_tbl
andexperiment_tbl
, adding an â€śidâ€ť column indicating if the data was part of the experiment or not  Add a â€śrow_idâ€ť column to help for tracking which rows are selected for training and testing in the modeling section
 Create a â€śDay of Weekâ€ť feature from the â€śDateâ€ť column
 Drop the unnecessary â€śDateâ€ť column and the â€śPaymentsâ€ť column
 Handle the missing data (
NA
) by removing these rows.  Shuffle the rows to mix the data up for learning
 Reorganize the columns
Here is the full transformation in one dplyr
pipe. Notice that this entire series of operations is concise and readable. We teach how to do Data Manipulation and Cleaning throughout our Business Analysis with R course. This is the most important skill for a data scientist because itâ€™s where you will spend about 60%80% of your time.
3.7 Training and Testing Sets
With the data formatted properly for analysis, we can now separate into training and testing sets using an 80% / 20% ratio. We can use the initial_split()
function from rsample
to create a split object, then extracting the training()
and testing()
sets.
We can take a quick glimpse of the training data. Itâ€™s 38 observations randomly selected.
And, we can take a quick glimpse of the testing data. Itâ€™s the remaining 8 observations.
3.8 Implement Machine Learning Algorithms
Weâ€™ll implement the new parsnip
R package. For those unfamiliar, here are some benefits:

Interfaces with all of the major ML packages:
glmnet
,xgboost
,sparklyr
, and more! 
Works well with the
tidyverse
(i.e.tibbles
) 
Simple API makes Machine Learning easy
Our strategy will be to implement 3 modeling approaches:
 Linear Regression  Linear, Explainable (Baseline)
 Decision Tree
 Pros: NonLinear, Explainable.
 Cons: Lower Performance
 XGBoost
 Pros: NonLinear, High Performance
 Cons: Less Explainable
3.8.1 Linear Regression (Baseline)
Weâ€™ll create the linear regression model using the linear_reg()
function setting the mode to â€śregressionâ€ť. We use the set_engine()
function to set the linear regression engine to lm()
from the stats
library. Finally, we fit()
the model to the training data specifying â€śEnrollmentsâ€ť as our target. We drop the â€śrow_idâ€ť field from the data since this is a unique ID that will not help the model.
Next, we can make predictions on the test set using predict()
. We bind the predictions with the actual values (â€śEnrollmentsâ€ť from the test set). Then we calculate the error metrics using metrics()
from the yardstick
package. We can see that the model is off by about +/19 Enrollments on average.
.metric  .estimator  .estimate 

rmse  standard  26.0634680 
rsq  standard  0.0636897 
mae  standard  19.4039158 
We can investigate the predictions by visualizing them using ggplot2
. After formatting and plotting the data, we can see that the model had an issue with Observation 7, which is likely the reason for the low Rsquared value (test set).
Ok, so the most important question is whatâ€™s driving the model. We can use the tidy()
function from the broom
package to help. This gets us the model estimates. We can arrange by â€śp.valueâ€ť to get an idea of how important the model terms are. Clicks, Pageviews, and Experiment are judged strong predictors with a pvalue less than 0.05. However, we want to try out other modeling techniques to judge this. We note that the coefficient of Experiment is 17.6, and because the term is binary (0 or 1) this can be interpreted as decreasing Enrollments by 17.6 per day when the Experiment is run.
term  estimate  std.error  statistic  p.value 

Clicks  0.5788150  0.1323455  4.3735162  0.0001533 
Pageviews  0.0503213  0.0148314  3.3928928  0.0020803 
Experiment  17.5541754  7.6074013  2.3075127  0.0286325 
(Intercept)  134.7873196  79.5652606  1.6940474  0.1013534 
DOWMon  25.4287578  17.4786746  1.4548447  0.1568322 
DOWThu  17.4230930  15.8000716  1.1027224  0.2795358 
DOWWed  12.4235287  14.5532451  0.8536604  0.4005376 
DOWSat  11.0150158  15.5347097  0.7090584  0.4841509 
DOWFri  8.5195293  14.2637448  0.5972856  0.5551166 
DOWTue  0.7023031  16.7661840  0.0418881  0.9668852 
We can visualize the importance separating â€śp.valuesâ€ť of 0.05 with a red dotted line.
Key Points:

Our model is on average off by +/19 enrollments (means absolute error). The test set Rsquared is quite low at 0.06.

We investigated the predictions to see if there is anything that jumps out at us. The model had an issue with observation 7, which is likely throwing off the Rsquared value.

We investigated feature importance. Clicks, Pageviews, and Experiment are the most important features. Experiment is 3rd, with a p.value 0.026. Typically this is considered significant.

We can also see the term coefficient for Experiment is 17.6 indicating as decreasing Enrollments by 17.6 per day when the Experiment is run.
Before we move onto the next model, we can setup some helper functions to reduce repetitive code.
3.8.2 Helper Functions
Weâ€™ll make some helper functions to reduce repetitive code and increase readability. SideNote  We teach how to create functions and perform iteration in Week 5 of our Business Analysis with R course.
First, weâ€™ll make a simplified metric reporting function, calc_metrics()
.
Next we can make a simplified visualization function, plot_predictions()
.
3.8.3 Decision Trees
Decision Trees are excellent models that can pick up on nonlinearities and often make very informative models that compliment linear models by providing a different way of viewing the problem. We teach Decision Trees in Week 6 of Business Analysis with R course.
We can implement a decision tree with decision_tree()
. Weâ€™ll set the engine to â€śrpartâ€ť, a popular decision tree package. There are a few key tunable parameters:
cost_complexity
: A cutoff for model splitting based on increase in explainabilitytree_depth
: The max tree depthmin_n
: The minimum number of observations in terminal (leaf) nodes
The parameters selected for the model were determined using 5fold cross validation to prevent overfitting. This is discussed in Important Considerations. We teach 5Fold Cross Validation in our Advanced Modeling Course  Data Science for Business with R.
Next, we can calculate the metrics on this model using our helper function, calc_metrics()
. The MAE of the predictions is approximately the same as the linear model at +/19 Enrollments per day.
.metric  .estimator  .estimate 

rmse  standard  23.85086 
rsq  standard  0.27693 
mae  standard  19.06771 
We can visualize how its performing on the observations using our helper function, plot_predictions()
. The model is having issues with Observations 1 and 7.
And finally, we can use rpart.plot()
to visualize the decision tree rules. Note that we need to extract the underlying â€śrpartâ€ť model from the parsnip
model object using the model_02_decision_tree$fit
.
Interpreting the decision tree is straightforward: Each decision is a rule, and Yes is to the left, No is to the right. The top features are the most important to the model (â€śPageviewsâ€ť and â€śClicksâ€ť). The decision tree shows that â€śExperimentâ€ť is involved in the decision rules. The rules indicate a when Experiment >= 0.5, there is a drop in enrollments.
Key Points:

Our new model has roughly the same accuracy to +/19 enrollments (MAE) as the linear regression model.

Experiment shows up towards the bottom of the tree. The rules indicate a when Experiment >= 0.5, there is a drop in enrollments.
3.8.4 XGBoost
The final model weâ€™ll implement is an xgboost
model. Several key tuning parameters include:
mtry
: The number of predictors that will be randomly sampled at each split when creating the tree models.trees
: The number of trees contained in the ensemble.min_n
: The minimum number of data points in a node that are required for the node to be split further.tree_depth
: The maximum depth of the tree (i.e. number of splits).learn_rate
: The rate at which the boosting algorithm adapts from iterationtoiteration.loss_reduction
: The reduction in the loss function required to split further.sample_size
: The amount of data exposed to the fitting routine.
Understanding these parameters is critical to building good models. We discuss each of these parameters in depth while you apply the XGBoost model in our Business Analysis with R course.
The parameters selected for the model were determined using 5fold cross validation to prevent overfitting. This is discussed in Important Considerations. We teach 5Fold Cross Validation in our Advanced Modeling Course  Data Science for Business with R.
We can get the test set performance using our custom calc_metrics()
function. We can see that the MAE is 11.5 indicating the model is off by on average 11.5 enrollments per day on the test set.
.metric  .estimator  .estimate 

rmse  standard  13.8760506 
rsq  standard  0.7256724 
mae  standard  11.5450172 
We can visualize how its performing on the observations using our helper function, plot_predictions()
. We can see that itâ€™s performing better on Observation 7.
We want to understand which features are important to the XGBoost model. We can get the global feature importance from the model by extracting the underlying model from the parsnip object using model_03_xgboost$fit
and piping this into the function xgb.importance()
.
Feature  Gain  Cover  Frequency 

Pageviews  0.6331988  0.6879569  0.6465324 
Clicks  0.2964312  0.2061510  0.2076063 
Experiment  0.0703701  0.1058921  0.1458613 
Next, we can plot the feature importance. We can see that the model is largely driven by Pageviews and Clicks.
The information gain is 93% from Pageviews and Clicks combined. Experiment has about a 7% contribution to information gain, indicating itâ€™s still predictive (just not nearly as much as Pageviews). This tells a story that if Enrollments are critical, Udacity should focus on getting Pageviews.
This tells a story that if Enrollments are critical, Udacity should focus on getting Pageviews.
Key Points:

The XGBoost model error has dropped to +/11 Enrollments.

The XGBoost shows that Experiment provides an information gain of 7%

The XGBoost model tells a story that Udacity should be focusing on Page Views and secondarily Clicks to maintain or increase Enrollments. The features drive the system.
3.10 Business Conclusions  Key Benefits to Machine Learning
There are several key benefits to performing A/B Testing using Machine Learning. These include:

Understanding the Complex System  We discovered that the system is driven by Pageviews and Clicks. Statistical Inference would not have identified these drivers. Machine Learning did.

Providing a direction and magnitude of the experiment  We saw that Experiment = 1 drops enrollments by 17.6 Enrollments Per Day in the Linear Regression. We saw similar drops in the Decision Tree rules. Statistical inference would not have identified magnitude and direction. Only whether or not the Experiment had an effect.
What Should Udacity Do?
If Udacity wants to maximimize enrollments, it should focus on increasing Page Views from qualified candidates. Page Views is the most important feature in 2 of 3 models.
If Udacity wants alert people of the time commitment, the additional popup form is expected to decrease the number of enrollments. The negative impact can be seen in the decision tree (when Experiment <= 0.5, Enrollments go down) and in the linear regression model term (17.6 Enrollments when Experiment = 1). Is this OK? It depends on what Udacityâ€™s goals are.
But this is where the business and marketing teams can provide their input developing strategies to maximize their goals  More users, more revenue, and/or more course completions.
3.11 Important Considerations: Cross Validation and Improving Modeling Performance
Two important further considerations when implementing an A/B Test using Machine Learning are:

How to Improve Modeling Performance

The need for CrossValidation for Tuning Model Parameters
3.11.1 How to Improve Modeling Performance
A different test setup would enable significantly better understanding and modeling performance. Why?

The data was AGGREGATED  To truly understand customer behavior, we should run the analysis on unaggregated data to determine probability of an individual customer enrolling.

There are NO features related to the Customer in the data set  The customer journey and their characteristics are incredibly important to understanding complex purchasing behavior. Including GOOD features is the best way to improving model performance, and thus insights into customer behavior.
3.11.2 Need for CrossValidation for Tuning Models
In practice, we need to perform crossvalidation to prevent the models from being tuned to the test data set. This is beyond the scope of this tutorial, but is taught in our Advanced Machine Learning Course  Data Science For Business with R DS4B 201R.
The parameters for the Decision Tree and XGBoost Models were selected using 5Fold Cross Validation. The results are as follows.
Model  MAE (Average 5Fold CV) 

Linear Regression  16.2 
XGBoost  16.2 
Decision Tree  19.2 
Itâ€™s interesting to note that the baseline Linear Regression model had as good of performance (average crossvalidation MAE) as XGBoost. This is likely because we are dealing with a simple data set with only a few features.
As we build a better test setup that includes the model performanceboosting recommendations in 3.11.1, I expect that the XGBoost model will quickly take over as the system complexity increases.
4.0 Parting Thoughts and Learning Recommendation
This tutorial scratches the surface of how machine learning can benefit A/B Testing and other multimillion dollar business problems including:

Customer Churn

Employee Attrition

Business Forecasting
The key is understanding how to construct business problems in the format needed to apply Machine Learning.
We teach these skills at Business Science University. The 2 courses that will accelerate your data science knowledge are:

Business Analysis with R Course (101)  Designed for beginners and intermediate students. Week 6 covers Modeling and Machine Learning Algorithms, which has 44 lessons and 5hours of video that teaches how to perform machine learning for business using the
parsnip
package (used in this tutorial). 
Data Science For Business with R Course (201)  Designed for advanced students that want to learn business consulting combined with advanced data science. Automatic Machine Learning, Cross Validation, and Hyper Parameter Tuning are covered in our advanced machine learning course, Week 5, which covers machine learning with
H2O
.
The 2 Courses are integrated, and accelerate you along your data science journey. We condense years of learning into weeks, which is why the program is so effective.
Years of learning are condensed into weeks.
For those that need to learn both beginner and advanced machine learning, we have a Special 101 + 201 Bundle that provides both at an attractive value.