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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

A/B Testing Measurement Frameworks  -  Every Data Scientist Should Know

M
Mainak Last Updated : 30 Mar, 2021
6 min read
This article was published as a part of the Data Science Blogathon.

What is A/B testing?

A/B Testing(split testing) is basically the process of comparing the 2 versions of discount offers, emails, web pages and, other marketing tools and then measuring the difference in performance. In the generic sense, an improvement of existing design and measure the impact of it.

A/B Testing is something that is not a one-time activity, Test >> Learn >> again Test

A/B testing image

Is it impactful? An excellent example from the book — “Trustworthy Online Controlled Experiments: A Practical Guide to A/B Testing” :

“An employee working on Bing suggested some changes on ad headlines display. The idea was very simple, he suggested lengthening the title line of ads by combining it with the text from the first line below the title. That idea was implemented on real users, randomly showing some of them the new title layout and others the old one. User interactions with the website were recorded, including the clicks and revenue generated from them. This is an example of an A/B test, the simplest type of controlled experiment that compares the 2 variants: A and B, Control or Experiment.

After few hours of starting the test, a revenue-to-high alert triggered, that something was wrong with the experiment. The new layout was generating too much money from the ads. For this experiment revenue increase was valid. ”

But small changes also can have a big impact. If the experiment is successful then defiantly it leads to a big impact in long term.

What will be the first step for measuring success?

 

PART-1: Metric of Interest

Design or pickup the metric of interest, it should be any metric that is directly correlated with experimentation. For example, a fast-food retail chain wants to test a new discount offer is better than the existing offer. Then metric of interest should be : (1) Sale_per_customer (2)Frequency

So bit more about data, 2 key tables(hypothetical data):

a) Experimentation Table — Where customers are tagged to “Test” & “Control” groups & their broad categories.

A/B testing - Experimentation table

b) Transaction Table — Customer purchase data, broken down by different dates.

A/B testing - Transaction Table

 

From these above two base tables, I created a derived table which gives me customer wise pre & post-KPI’s aggregate, and the data looks like this-

pre & post-KPI’s aggregate - A/B testing

To create the above table you should know the before-test-period-dates (date range before the Test launch date) & in-test-period-dates(live test period dates).

Now the most important question, what is an ideal metric for the measurement, so in a very simple way key features of a metric of interest should be:

  1. Measurable
  2. Computable
  3. Sensitive

This blog will concentrate on sales_per_customer KPI. As it inherits all the qualities of a perfect Metric of Interest.

If you are dealing with a lot of metrics, ideally you want to combine them into a single metric, which you called Aggregated Metric(called North Star Metric), and then measure the impact of delta for that particular metric to declare the success & failure of experimentation.

 

PART-2: Pre-experiment analysis

So when we are pretty much got the desired metric, now time for some exploration to understand few questions like:

  1. What is my base sales per customer?
  2. What is the average frequency of customers in stores?
  3. What are average order values?

EDA will be the answer and believe me it is the most powerful tool that exists. It helps for the deduction.

A simple time-based line plot is capable of showing the current status of measures like mean, median, the standard deviation of all the major KPIs, and these base values are very much helpful for understanding Minimum Detectable changes that we can expect from the experiment.

Minimum Detectable Effect (MDE): MDE represents the relative minimum improvement over a baseline that you are expecting in an experiment, with some degree of statistical significance. So we intend to compare the means/medians/std.deviation of both the control(no treatment) and experimental group. So for that, we have to do Hypothesis testing

Hypothesis testing: In hypothesis testing, we are considering 2 scenarios:

Null Hypothesis: No statistical significance between control and experiment group.

Alternate Hypothesis: There is a significant difference between the control and experiment groups.

Power & Significance: Now the question do you have enough samples to run our experiment. While calculating sample size estimation these errors should be avoided:

  1. Type-I Error, significance level should be specified while calculating sample size.
  2. Type-II Error, the sample size should be large, and as a standard practice set the power at 0.8 or 0.9.
Sample Sizes

In the above figure, you can see that for different effect sizes(detectable effect), required sample sizes are varying.

PART-3: Measure Experimental Outcome

Now time to measure that experimentation results. Remember the Null hypothesis has no statistical significance between Control(hold out) and the Test group.

So we can estimate the difference between Control & Test using many different ways, but for simplicity, we will categories our estimation process into 3 broad categories:

  1. Post (Control) Vs Post (Test)
  2. Pre (Test) Vs Post(Test)
  3. Adjusted Measurement (CUPED)

1)Post (Control) Vs Post (Test): In post behavior analysis, we can use many methods but for simplicity, we will use :

  1. The T-Test (Parametric) — It’s an inferential statistical method to determine the significant difference between means of two groups, a very powerful method when distributions are following a normal distribution.
Measure Experimental Outcome
Measure

In the above figure, it is very clear that the Test group perform better than the Control group but non-significant.

2. Man Whitney U-Test (Non-Parametric)– Non-parametric test to compare outcomes between Control group and Test group, useful when distributions are not following a normal distribution.

But we can’t completely rely on this result, because we have to check for the pre-experiment bias affecting the KPI’s in the Test period or not.

2) Pre(Test) Vs Post (Test): Another classical yet intuitive method of measuring the effect with the help of the Intervention method (Interrupted Time Series Approach) or Quasi-Experiment method where it assumes that the Control group does not exist and trying to measure the impact of the Test using counterfactual.

This analysis is done with the help of Google’s Causal Inference library in python.

Pre(Test) Vs Post (Test)

source- ‘https://github.com/dafiti/causalimpact/blob/master/examples/ci_plot.png‘ 

3) Adjusted Measurement (CUPED): Controlled-Experiment Using Pre-Experiment Data(CUPED). The excellent approach was developed by the “Experiment Platform team at Microsoft ”(Deng, Xu, Kohavi, & Walker, 2013).

Many times it happened, that experimentation was impacted but the delta is very small, might be rejected by a statistical test because of high variance. This technique is very much helpful to increase experimentation sensitivity via reducing variance associated with pre-experiment data.

 

experiment data

As we can see from the above visual the R-square is 0.64 which is pretty high. That signifies pre-experiment bias exists in metric, therefore it should be removed.

So after removing the variance and then do the T-Test will give the exact picture.

test and control

PART- 4: Analysis & Conclusion

So from the above analysis, it is clear that the experiment had some positive impact on the Control group. But it is very important to know is it overall converged or not, and at what is the point of inflection.

  1. Day wise lift analysis is another powerful way to look at the overall Test converges or not and when we start seeing significant results. It is also helpful to rule out Novelty & Seasonality effects in the experiment if exist.
Analysis & Conclusion

2. Driver Analysis- is also yet another powerful tool to understand the market dynamics, which factors influence the sales pattern to mold. I think Linear regression or any other tree-based algorithm will suffice the need.

To conclude, these all frameworks are very much helpful to understand the overall impact estimation of experimentation and very intuitive at the same time to interpret to business.

References

1. Trustworthy Online Controlled Experiments: A Practical Guide to A/B Testing

2.https://learn.datacamp.com/courses/ab-testing-in-r

3.https://booking.ai/how-booking-com-increases-the-power-of-online-experiments-with-cuped-995d186fff1

The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion.

M
Mainak

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Very well presented blog.

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