This video provides a comprehensive crash course on A/B testing in data science, covering its fundamental concepts, key parameters, and practical implementation. It explains how to formulate hypotheses, identify primary metrics, design experiments, and analyze results using Python. The course also includes a hands-on case study to demonstrate these techniques in a real-world scenario.
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(0:00:00) Video Introduction
In this applied data science crash course, you learn all about AB testing from the concepts to the practical details they can apply in business. AB testing is commonly used in data science. It's an experiment on two variants to see which performs better based on a given metric. This course merges in-depth statistical analysis with the kind of data science theories big tech firms rely on. Tatev, from Lun Tech, developed this course. She is a very experienced A/B scientist and teacher.
Welcome to the hands-on AB testing crash course where we will do some refreshment when it comes to AB testing. If you're looking for that one course where you can learn and quickly refresh your memory for AB testing and how to actually do an AB testing case study hands-on in Python, then you are in the right place.
In this crash course, we are going to refresh our memory for the A/B test design, including the power analysis and defining those different PRs such as minimum detectable effect, statistical significance level, and also the uh type two probability, so the power of the test. Then we are going to do a hands-on case study project where we will be conducting an AB testing results analysis in Python.
At the end of this course, you can expect to know everything about designing an AB test, what it means to design a proper AB test, and how to do an AB test results analysis in Python in a proper way.
I'm Tatev Vas, co-founder at Lun Tech, and I have been in data science for the last 5 years. I have learned AB testing end to end after following numerous blogs, research papers, and courses. I've noticed that there is not a single place, one course that covers all the fundamentals and necessary stuff, both the theory and implementation in Python in one place. And that's about to change, as we have this crash course that will help you to do exactly that. To learn how to design an AB test in a proper way as a good and consolidated scientist and to showcase your skills by doing Python AB testing results analysis.
Don't forget to subscribe, like, and comment to help the algorithm to make this content more accessible to everyone across the world. And if you want to get free resources, make sure to check the free resources section at Lun Tech. And if you want to become a job-ready data scientist and you are looking for this accessible boot camp that will help you to make your job-ready data scientist, consider enrolling in the data science boot camp.
So whether you are a product scientist, whether you are a data analyst, data scientist, or a product manager who wants to learn about AB testing at a high level and how it can be done in Python, then you are in the right place. Because in this crash course, we're going to refresh our memory: what it means to properly design an A/B test. Which means doing power analysis and also calculating the sample size by hand, by following the statistical guidelines and ensuring that everything is done properly.
And then as the second part of this crash course, we are also going to do a hands-on case study in Python when it comes to performing AB testing results analysis. So we are going to cover all these important concepts such as P-values, sample size, and also uh interpreting the AB test results using standard error, calculating those uh estimates, pooled variance, and then evaluating the AB test results including confidence interval, generalizability of the results, reproducibility of the results. So without further ado, let's get started.
(0:03:49) Introduction to Data Science and A/B Testing
AB testing is an important topic for data scientists to know because it's a powerful method for evaluating changes or improvements to products or services. It allows us to make data-driven decisions by comparing the performance of two different versions of a product or a service, usually referred to as treatment or control.
For example, AB testing allows data scientists to measure the effectiveness of changes to your product or a service. This is important as it enables data scientists to make data-driven decisions rather than relying on intuition or assumptions.
Secondly, AB testing helps data scientists to identify the most effective change, changes to a product or a service, which is really important because it allows us to optimize the performance of a product or a service, which can then lead to increased customer satisfaction and sales.
AB testing helps us also to validate certain hypotheses about what changes will improve a product or service. This is important because it helps us to build a deeper understanding of the customers and the factors that influence customer behavior.
Finally, AB testing is a common practice in many industries such as e-commerce, digital marketing, website optimization, and many others. So, data scientists who have knowledge and experience in AB testing will be more valuable to these companies. No matter in which industry you want to enter as a data scientist, and what kind of job you will be interviewed for, and even if you believe more technical data science is your cup of tea, be prepared to know at least a high-level understanding and the details behind this method. It will definitely help you to know about this topic when you are speaking with product owners, stakeholders, product scientists, and other people involved in the business.
(0:05:38) Basics of A/B Testing in Data Science
Let's briefly discuss the perfect audience for the section of the course and prerequisites. There are no prerequisites for this section in terms of AB testing concepts that you should know already. But knowing the basics in statistics, which you can find in the "Fundamentals to Statistics" section, is highly recommended.
This section will be great if you have no prior AB testing knowledge and you want to identify and learn the essential AB testing concepts from scratch. So this will help you to prepare for your job interviews. It will also be a good refresher for anyone who does have AB testing knowledge but who wants to refresh their memory or wants to fill in the gaps in their knowledge.
(0:07:06) Key Parameters of A/B Testing for Data Scientists
In this lecture, we will start off the topic about A/B testing where we will formally define what A/B testing is, and we will look at the high-level overview of the A/B testing process step by step.
By definition, A/B testing or split testing originated from the statistical randomized control trials and is one of the most popular ways for businesses to test new UX features, new versions of a product, or an algorithm to decide whether your business should launch that new UX feature or should productionalize that new recommender system, create that new product, that new button, or that new algorithm.
The idea behind A/B testing is that you should show the variated or the new version of the product to a sample of customers, often referred to as the experimental group, and the existing version of the product to another sample of customers, referred to as the control group. Then the difference in the product performance in experimental versus control group is tracked to identify the effect of these new versions of the product on the performance of the product. So the goal is then to track the metric during the test period and find out whether there is a difference in the performance of the product and what type of difference is it.
The motivation behind this test is to test new product variants that will improve the performance of the existing product and will make this product more successful and optimal, showing a positive treatment effect. What makes this testing great is that businesses are getting direct feedback from their actual users by presenting them the existing versus the variated product version. And in this way, they can quickly test new ideas. In case an A/B test shows that the variated version is not effective, at least businesses can learn from this and can decide whether they need to improve it or need to look for other ideas.
Let us go through the steps included in the A/B testing process, which will give you a high-level overview into the process.
The first step in conducting A/B testing is stating the hypothesis of the A/B test. This is a process that includes coming up with business and statistical hypotheses that you would like to test with this test, including how you measure the success, which will be the primary metric.
Next step in A/B testing is to perform what we call power analysis and design the entire test, which includes making assumptions about the most important parameters of the test and calculating the minimum sample size required to claim statistical significance.
The third step in A/B testing is to run the actual A/B test, which in practical sense for the data scientist means making sure that the test runs smoothly and correctly, collaborating with engineers and product managers to ensure that all the requirements are satisfied. This also includes collecting the data of control and experimental groups, which will be used in the next step.
Next step in A/B testing is choosing the right statistical test, whether it is Z-test, T-test, Chi-square test, etc., to test the hypothesis from the step one by using the data collected from the previous step and to determine whether there is a statistically significant difference between the control versus experimental group.
The fifth and the final step in A/B testing is continuing to analyze the results and find out whether besides statistical significance, there is also practical significance. In this step, we use the second step's power analysis, so the assumptions that we made about model parameters and the sample size, and the four steps results to determine whether there is a practical significance besides of the statistical significance.
This summarizes the A/B testing process at a high level. In the next couple of lectures, we'll go through the steps one at a time. So buckle up and let's learn about A/B testing.
(0:09:24) Formulating Hypotheses and Identifying Primary Metrics in Data Science A/B Testing
In this lecture, lecture number two, we will discuss the first step in the A/B testing process. So let's bring our diagram back. As you can recall from the previous lecture, when we were discussing the entire process of A/B testing at a high level, we saw that in the first step in conducting A/B testing is stating the hypothesis of the A/B test. This process includes coming up with a business and statistical hypothesis that you would like to test with this test, including how you measure the success, which we call a primary metric.
So, what is the metric that we can use to say that the product that we are testing performs well? First, we need to state the business hypothesis for our A/B test from a business perspective. So, a business hypothesis describes what the two products are that are being compared and what is the desired impact or the difference for the business. So, how to fix a potential issue in the product where a solution of these two problems will influence what we call a key performance indicator or the KPI of interest.
A business hypothesis is usually set as a result of brainstorming and collaboration of relevant people on the product team and data science team. The idea behind this hypothesis is to decide how to fix a potential issue in the product where a solution of these problems will improve the target KPI. One example of a business hypothesis is that changing the color of the "Learn More" button, for instance, to green, will increase the engagement of the web page.
Next, we need to select what we call the primary metric for our A/B testing. There should be only one primary metric in your A/B test. Choosing this metric is one of the most important parts of an A/B test, since this metric will be used to measure the performance of the product or feature for the experimental and control groups, and it will be used to identify whether there is a difference or what we call a statistically significant difference between these two groups.
By definition, a primary metric is a way to measure the performance of the product being tested in the A/B test for the experimental and control groups. It will be used to identify whether there is a statistically significant difference between these two groups. The choice of the success metric depends on the underlying hypothesis that is being tested with this A/B test. This is, if not the most, one of the most important parts of the A/B test because it determines how the test will be designed and also how will the proposed ideas perform. Choosing poor metrics might disqualify a large amount of work or might result in wrong conclusions.
For instance, the revenue is not always the end goal. Therefore, in A/B testing, we need to tie up the primary metric to the direct and the higher-level goals of the product. The expectation is that if the product makes more money, then this suggests the content is great. But in achieving that goal, instead of improving the overall content of the material and writing, one can just optimize the conversion funnel.
One way to test the accuracy of the metric you have chosen as your primary metric for your A/B test could be to go back to the exact problem you want to solve. You can ask yourself the following question, what I tend to call the metric validity question. So, if the chosen metric were to increase significantly while everything else stayed constant, would we achieve our goal and would we address our business problem? Is it higher revenue? Is it higher customer engagement? Or is it higher views that we are chasing in the business?
So the choice of the metric will then answer this question. Though you need to have a single primary metric for your A/B test, you still need to keep an eye on the remaining metrics to make sure that all the metrics are showing a change and not only the target one. Having multiple metrics in your A/B test will lead to false positives since you will identify many significant differences while there is no effect, which is something you want to avoid. So it's always a good idea to pick just a single primary metric but to keep an eye and monitor all the remaining metrics.
So, if the answer to the metric validity question is "higher revenue," which means that you are saying that the higher revenue is what you are chasing, and better performance means higher revenue for your product, then you can use your primary metric, what we call a conversion rate.
Conversion rate is a metric that is used to measure the effectiveness of a website, a product, or a marketing campaign. It is typically used to determine the percentage of visitors or customers who take a desired action, such as making a purchase, filling out a form, or signing up for a service.
The formula for conversion rate is: Conversion Rate = (Number of Conversions) / (Number of Total Visitors) * 100%. For example, if a website has 1,000 visitors and 50 of them make a purchase, the conversion rate would be equal to 50 / 1,000 * 100%, which gives us 5%. This means that our conversion rate in this case is equal to 5%.
Conversion rate is an important metric because it allows us and businesses to measure the effectiveness of their website, a product, or a marketing campaign. It can help businesses to identify areas for improvement, such as increasing the number of conversions or improving the user experience. Conversion rate can be used for different purposes. For example, if a company wants to measure the effectiveness of an online store, the conversion rate would be the percentage of visitors who make a purchase. On the other hand, if a company wants to measure the effectiveness of a landing page, the conversion rate would be the percentage of visitors who fill out a form or sign up for a service.
So, if the answer to the metric validity question is "higher engagement," then you can use the click-through rate or CTR as your primary metric. This is, by the way, a common metric used in A/B testing whenever we are dealing with e-commerce, product search engines, recommender systems.
Click-through rate or CTR is a metric that measures the effectiveness of a digital marketing campaign or the user engagement with some feature on your web page or your website. And it's typically used to determine the percentage of users who click on a specific link, or button, or call to action (CTA) out of the total number of users who view it.
The formula for the click-through rate can be represented as follows: So, CTR = (Number of Clicks) / (Number of Impressions) * 100%. Not to be confused with click-through probability because there is a difference between the click-through rate and click-through probability. For example, if an online advertisement receives 1,000 impressions, which means that we are showing it to the customers for a thousand times, and there were 25 clicks, which means 25 out of all these impressions resulted in clicks. This means that the click-through rate for this specific example would be equal to 25 / 1,000 * 100%, which gives us 2.5%. This means that for this particular example, our click-through rate is equal to 2.5%.
Click-through rate is an important metric because it allows businesses to measure the effectiveness of their digital marketing campaigns and the user engagement with their website or web pages. High click-through rate indicates that a campaign or the web page or feature is relevant and appealing to the target audience because they are clicking on it. While low click-through rate indicates that a campaign or the web page needs an improvement. Click-through rate can be used to measure the performance of different digital marketing channels such as paid search, display advertising, email marketing, and social media. It can also be used to measure the performance of different ad formats such as text advertisements, banner advertisements, video advertisements, etc.
Next, and the final task in this first step in the process of A/B testing, is to state the statistical hypothesis based on the business hypothesis and the chosen primary metric.
Next, and in the final task in this first step of the A/B testing process, we need to state the statistical hypothesis based on the business hypothesis we stated and the chosen primary metric. In the section of "Fundamentals through Statistics" of this course, in lecture number seven, we went into details about statistical hypothesis testing, including what a null hypothesis is and what an alternative hypothesis is. So do have a look to get all the insights about this topic.
A/B testing should always be based on a hypothesis that needs to be tested. This hypothesis is usually set as a result of brainstorming and collaboration of relevant people on the product team and data science team. The idea behind this hypothesis is to decide how to fix a potential issue in a product where a solution of these problems will influence the key performance indicators or the KPI of interest. It's also highly important to make prioritization out of a range of product problems and ideas to test, while you want to pick that fixing this problem would result in the biggest impact for the product.
We can put the hypothesis that is subject to rejection so that we want to reject. In the ideal world, under the null hypothesis, what we define by H0, well, we can put the hypothesis subject to acceptance. So the desired hypothesis that we would like to have as a result of A/B testing under the alternative hypothesis defined by H1.
For example, if the KPI of the product is to increase the customer engagement by changing the color of the "Read More" button from blue to green, then under the null hypothesis, we can state that the click-through rate of the "Learn More" button with blue color is equal to the click-through rate of the green button. Under the alternative, we can then state that the click-through rate of the "Learn More" button with green color is larger than the click-through rate of the blue button. So, ideally, we want to reject this null hypothesis, and we want to accept the alternative hypothesis, which will mean that we can improve the click-through rate, so the engagement of our product by simply changing the color of the button from blue to green.
(0:19:55) Designing an A/B Test: Data Science Approach
Once we have set up the business hypothesis, selected the primary metrics, and stated the statistical hypothesis, we are ready to proceed to the next stage in the A/B testing process.
In this lecture, we will discuss the next, second step in the A/B testing process, which is designing the A/B test, including the power analysis and calculating the minimum sample sizes for the control and experimental groups. Stay tuned, as this is a very important part of the A/B testing process, commonly appearing during data science interviews.
Some argue that A/B testing is an art, and others say that it's a business-adjusted common statistical test. But the borderline is that to properly design this experiment, you need to be disciplined and intentional while keeping in mind that it's not really about testing, but it's about learning.
Following our steps, you need to take to have a solid design for your A/B test. So let's bring the diagram back. So in this step, we need to perform the power analysis for our A/B test and calculate the minimum sample size in order to design our A/B test.
A/B test design includes three steps: The first step is power analysis, which includes making assumptions about model parameters, including the power of the test, the significance level, etc. The second step is to use these parameters from power analysis to calculate the minimum sample size for the control and experimental groups. And then the final, third step is to decide on the test duration depending on several factors. So let's discuss each of these topics one by one.
Power analysis for A/B testing includes these three specific steps: The first one is determining the power of the test. This is our first parameter. The power of the statistical test is a probability of correctly rejecting the null hypothesis. Power is the probability of making a correct decision, so to reject the null hypothesis when the null hypothesis is false. If you're wondering what is the power of the test, what are these different concepts that we just talked about, what is this null hypothesis, and what does it mean to reject the null hypothesis, then head towards the "Fundamentals to Statistics" section of this course, as we discuss this topic in detail.
As part of that section, the power is often defined by 1 minus beta, which is equal to the probability of not making a type two error, where type two error is a probability of not rejecting the null hypothesis while the null is actually false. It's common practice to pick 80% as the power of the A/B test, which means that we allow 20% of type two error, and this means that we are fine with not detecting, so failing to reject the null hypothesis 20% of the time, which means that we are failing to detect a true treatment effect while there is an effect, which means that we are failing to reject the null. However, the choice of value of this parameter depends on the nature of the test and the business constraints.
Secondly, we need to determine a significance level for our A/B test. The significance level, which is also the probability of type one error, is the likelihood of rejecting the null hypothesis, detecting a treatment effect while the null is actually true and there is no statistically significant impact. This value, often defined by a Greek letter alpha, is a probability of making a false discovery, often referred to as a false positive rate. Generally, we use the significance level of 5%, which indicates that we have a 5% risk of concluding that there exists a statistically significant difference between the experimental and control variant performances when there is no actual difference. So we are fine by having five out of 100 cases detecting a treatment effect while there is no effect. It also means that you have a significant result difference between the control and the experimental groups within 95% confidence.
Like in the case of the power of the test, the choice of the alpha is dependent on the nature of the test and the business constraints. For instance, if running this A/B test is related to high engineering cost, then the business might decide to pick a high alpha, such that it would be easier to detect a treatment effect. On the other hand, if the implementation costs of the proposed version in production are high, you can then pick a lower significance level, since this proposed feature should really have a big impact to justify the high implementation cost. So it should be harder to reject the null hypothesis.
Finally, as the last type of power analysis, we need to determine a minimum detectable effect for the test. Last parameter, as part of the power analysis, we need to make assumptions about what is known as the minimum detectable effect or Delta, from the business point of view. So, what is the substantive to statistical significance that the business wants to see as a minimum impact of the new version to find this variant investment worthy? The answer to this question is what is the amount of change we aim to observe in the new version's metric compared to the existing one to make recommendations to the business that this feature should be launched in production, that its investment is worthy.
An estimate of this parameter is what is known as as a minimum detectable effect, often defined by a Greek letter Delta, which is also related to the practical significance of the test. So, this MDE or the minimum detectable effect is a proxy that relates to the smallest effect that would matter in practice for the business, and it's usually set by stakeholders, as this parameter is highly dependent on the business. There is no common level of it. Instead, this minimum detectable effect is basically the translation from statistical significance to practical significance. And here, we want to see and we want to answer the question: what is this percentage increase in the performance of the product that we want to experiment with that will tell to the business that this is good enough to invest in this new feature or in this new product? And this can be, for instance, 1% for one product, it can be 5% for another one, and it really depends on the business and what is the underlying KPI.
A popular reference to the parameters involved in the power analysis for A/B testing is like this: so, 1 minus beta for the power of the test, Alpha for the significance level, Delta for the minimum detectable effect. To make sure that our results are repeatable, robust, and can be generalized to the entire population, we need to avoid P-hacking. To ensure real statistical significance and to avoid biased results, so we want to make sure that we collect enough amount of observations and we run the test for a minimum predetermined amount of time. Therefore, before running the test, we need to determine the sample size of the control and experimental groups, as well as later on in this lecture, we will see also how long we need to run the test.
So, this is another important part of A/B testing which needs to be done using the defined power of the test, which was the one minus beta, the significance level, and a minimum detectable effect. So all the parameters that we decided upon when conducting the power analysis, calculation of the sample size depends on the underlying primary metric as well, that you have chosen for tracking the progress of the control and experimental versions of the product. So we need to distinguish here two cases.
So when discussing the primary metric, we saw that there are different ways that we can measure the performance of different types of products. If we are interested in engagement, then we are looking at a metric such as click-through rate, which is in the form of averages. So, Case 1 will be where the primary metric of A/B testing is in the form of a binary variable. It can be, for instance, conversion or no conversion, click or no click. And Case 2 where the primary metric of the test is in the form of proportions or averages, which means mean order amount or mean click-through rate.
So, let's say we want to test whether the average click-through rate of the control is equal to the average click-through rate of the experimental group. And under H1, we have that the mean control is equal to the mean experimental. And under H1, we have that the mean control is not equal to the mean experimental. So here, the mean control and mean experimental are simply the average of the primary metric for the control group and for the experimental group, respectively. So this is the formal hypothesis we want to test with our A/B test, and we can assume that this mean control is, for instance, the click-through rate of the control group, and the mean experimental is the click-through rate of the experimental group.
So, this is the formal statistical hypothesis we want to test with our A/B test. If you haven't done so, I would highly suggest you to head towards the "Fundamentals to Statistics" section of this course, where in lecture number seven and eight of the statistical part of this course, I go into detail about statistical hypothesis testing, the means, averages, significance level, etc. This also holds for the theorem that the sample size calculation is based upon, called the Central Limit Theorem. So check out the last lecture about inferential statistics, where I covered the Central Limit Theorem, which we will also use in this section. And finally, also check the lecture number five in that section where we cover the normal distribution. Another thing that we will use as part of this section, so the Central Limit Theorem states that given a sufficiently large sample size from an arbitrary distribution, the sample mean will be approximately normally distributed regardless of the shape of the original population distribution. This means that the distribution of the sample means will be approximately normal if we take a large enough sample, even if the distribution of the original sample is not normal.
So, when we are dealing with a primary performance tracking metric that is in the form of an average, such as this one that we are covering today, which is a click-through rate, we intend to compare the means of the control and experimental groups. Then we can use the Central Limit Theorem as stated, that the mean sampling distribution of both control and experimental groups follow a normal distribution. Consequently, the sampling distribution of the difference of the means of these two groups also will be normally distributed.
So, this can be expressed like this, where we see that the mean of the control group and mean of the experimental group follow a normal distribution with mean mu control and mu experimental, respectively, and with a variance of sigma control squared and sigma experimental squared, respectively. Though derivation of this proof is out of the scope of this course, we can state that the difference between the means of the two groups, so X-bar control minus X-bar experimental, also follows a normal distribution with a mean mu control minus mu experimental, and with a variance of sigma control squared / (2 * n control) + sigma experimental squared / (2 * n experimental). So the sample size of the experimental group and the sample size of the control group, hence the sample size needed to compare the mean of the two normally distributed samples using a two-sided test, which prespecifies significance of alpha, power level, and minimum detectable effect, can be calculated as follows:
So, here you can see the mathematical representation of the minimum sample size. So, the N, which stands for the minimum sample size, is equal to (sigma control squared + sigma experimental squared) / Delta squared, multiplied by Z(1 - alpha / 2) + Z(1 - beta) squared. And here, the alpha, beta, and delta, we have made assumptions about as part of the power analysis, and the sigma control squared and sigma experimental squared are the estimates of the variance that we can come up with using so-called A/B testing. I would say you do not necessarily need to know this derivation, as there are many online calculators that will ask you for the alpha, beta, and delta values, as well as the sample estimates for the sigma squared control and experimental, and then these calculators will automatically calculate the minimum sample size for you.
If you're wondering what this A/B testing is and how we can come up with the sigma squared control and sigma experimental squared, as well as all the other values, then make sure to check out the blog that I posted before and that I mentioned before, as I explained in detail all these values, as well as check out the resource section where I've included many resources regarding this. But for now, just keep in mind that the Z(1 - alpha / 2) and Z(1 - beta) are just two constants and come from the normal distribution and standard normal distribution tables. I would say you do not necessarily need to know this derivation, as there are many online calculators that will ask you for this alpha, beta, and delta values, as well as the sample estimates for the sigma squared control and experimental, and then will calculate automatically the sample size for you.
Effectively, one example of such a calculator is this AB Testy online calculator, but if you Google it, you will find many others that will ask you for the minimum detectable effect, for the statistical significance, or the statistical power, and then it will automatically calculate for you the minimum sample size that you should have in order to have a statistical significance and in order to have a valid A/B test.
One thing to keep in mind is that you will notice that the statistical significance level is set to 95% in here, which is not what we have seen when we were discussing the alpha significance level. So sometimes these online calculators will confuse or will interchangeably use the significance level versus the confidence level, which are the opposite. So the significance level is usually at the level of 5% or 1%. Confidence level is around 95%, which is basically 100% minus the alpha. Therefore, whenever whenever you see this 95%, know that this means that your alpha should be 5%. So it's really important to understand how to use this calculator, not to end up with the wrong minimum sample size, conduct an entire A/B test, and then at the end realize that you have used the wrong significance level.
The final step is to calculate the test duration. This question needs to be answered before you run your experiment and not during the experiment. Sometimes people stop the test when they detect statistical significance, which is what we call P-hacking, and that's absolutely not what you want to do. To determine the baseline of the duration time, a common approach is to use this formula as you can see: Duration = N / (Number of Visitors per Day), where N is your minimum sample size that we just calculated in the previous step, and the number of visitors per day is the average number of visitors that you expect to see as part of your experiment.
For instance, if this formula results in 14 days, or 14, this suggests that running the test for two weeks is a good idea. However, it's highly important to take many business-specific aspects into account when choosing the time to run the test and for how long you need to run it, and simply using this formula is not enough. For example, if you want to run an experiment at the end of the month, December, with Christmas breaks, when higher than expected or lower than expected number of people are usually checking your web page, then this external and uncertain event had an impact on the page usage. For some businesses, this means, for example, if you want to run an experiment at the end of the month of December with Christmas breaks, when higher than expected or, in some cases, lower than expected number of people are usually checking the web page, so depending on the nature of your business or the product, then this external and uncertain event can have an impact on the page usage. For some businesses, which means that for some businesses, a high increase in the page usage can be the result, and for some, a huge decrease in usability.
In this case, running an A/B test without taking into account this external factor would result in inaccurate results, since the activity period would not be a true representation of a common page usage, and we no longer have this randomness, which is a crucial part of A/B testing. Besides this, when selecting a specific test duration, there are a few other things to be aware of. Firstly, too small a test duration might result in what we call novelty effects. Users tend to react quickly and positively to all types of changes, independent of their nature, so it's referred to as a novelty effect, and it varies in time, and it is considered illusory. So it would be wrong to attribute this effect to the experimental version itself and to expect that it will continue to persist after the novelty effect wears off. Hence, when picking a test duration, we need to make sure that we do not run the test for too short an amount of time period, otherwise we can have a novelty effect. Novelty effect can be a major threat to the external validity of an A/B test, so it's important to avoid it as much as possible.
Secondly, if the test duration is too large, then we can have what we call maturation effects. When planning an A/B test, it's usually useful to consider a longer test duration for allowing users to get used to a new feature or product. In this way, one will be able to observe the real treatment effect by giving more time to returning users to cool down from an initial positive reaction or a spike of interest due to a change that was introduced as part of a treatment. This should help to avoid novelty effect and is a better predictive value for the test outcome. However, the longer the test period, the larger is the likelihood of external effect impacting the reaction of the users and possibly contaminating the test results. This is what we call maturation effect, and therefore running the A/B test for too short an amount of time or too long an amount of time is not recommended, as it's a very involved topic. We can talk for hours about this part of the A/B test and also a topic that is asked a lot during the data science and product scientist interviews. Therefore, I highly suggest you to check out this book about A/B testing, which is a hands-on tutorial about everything you need to know about A/B testing, as well as check out the interview preparation guide in this section that contains 30 most popular A/B testing related questions you can expect during your data science interviews. So, stay tuned, and in the next couple of lectures, we will cover the next stages of the A/B testing process.
If you are looking for one place to learn everything about A/B testing without unnecessary difficulties, but also with a good statistical and data science background, then make sure to check out the A/B testing course at Lun Tech. So
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(0:00:00) Video Introduction
In this applied data science crash course, you learn all about AB testing from the concepts to the practical details they can apply in business. AB testing is commonly used in data science. It's an experiment on two variants to see which performs better based on a given metric. This course merges in-depth statistical analysis with the kind of data science theories big tech firms rely on. Tatev, from Lun Tech, developed this course. She is a very experienced A/B scientist and teacher.
Welcome to the hands-on AB testing crash course where we will do some refreshment when it comes to AB testing. If you're looking for that one course where you can learn and quickly refresh your memory for AB testing and how to actually do an AB testing case study hands-on in Python, then you are in the right place.
In this crash course, we are going to refresh our memory for the A/B test design, including the power analysis and defining those different PRs such as minimum detectable effect, statistical significance level, and also the uh type two probability, so the power of the test. Then we are going to do a hands-on case study project where we will be conducting an AB testing results analysis in Python.
At the end of this course, you can expect to know everything about designing an AB test, what it means to design a proper AB test, and how to do an AB test results analysis in Python in a proper way.
I'm Tatev Vas, co-founder at Lun Tech, and I have been in data science for the last 5 years. I have learned AB testing end to end after following numerous blogs, research papers, and courses. I've noticed that there is not a single place, one course that covers all the fundamentals and necessary stuff, both the theory and implementation in Python in one place. And that's about to change, as we have this crash course that will help you to do exactly that. To learn how to design an AB test in a proper way as a good and consolidated scientist and to showcase your skills by doing Python AB testing results analysis.
Don't forget to subscribe, like, and comment to help the algorithm to make this content more accessible to everyone across the world. And if you want to get free resources, make sure to check the free resources section at Lun Tech. And if you want to become a job-ready data scientist and you are looking for this accessible boot camp that will help you to make your job-ready data scientist, consider enrolling in the data science boot camp.
So whether you are a product scientist, whether you are a data analyst, data scientist, or a product manager who wants to learn about AB testing at a high level and how it can be done in Python, then you are in the right place. Because in this crash course, we're going to refresh our memory: what it means to properly design an A/B test. Which means doing power analysis and also calculating the sample size by hand, by following the statistical guidelines and ensuring that everything is done properly.
And then as the second part of this crash course, we are also going to do a hands-on case study in Python when it comes to performing AB testing results analysis. So we are going to cover all these important concepts such as P-values, sample size, and also uh interpreting the AB test results using standard error, calculating those uh estimates, pooled variance, and then evaluating the AB test results including confidence interval, generalizability of the results, reproducibility of the results. So without further ado, let's get started.
(0:03:49) Introduction to Data Science and A/B Testing
AB testing is an important topic for data scientists to know because it's a powerful method for evaluating changes or improvements to products or services. It allows us to make data-driven decisions by comparing the performance of two different versions of a product or a service, usually referred to as treatment or control.
For example, AB testing allows data scientists to measure the effectiveness of changes to your product or a service. This is important as it enables data scientists to make data-driven decisions rather than relying on intuition or assumptions.
Secondly, AB testing helps data scientists to identify the most effective change, changes to a product or a service, which is really important because it allows us to optimize the performance of a product or a service, which can then lead to increased customer satisfaction and sales.
AB testing helps us also to validate certain hypotheses about what changes will improve a product or service. This is important because it helps us to build a deeper understanding of the customers and the factors that influence customer behavior.
Finally, AB testing is a common practice in many industries such as e-commerce, digital marketing, website optimization, and many others. So, data scientists who have knowledge and experience in AB testing will be more valuable to these companies. No matter in which industry you want to enter as a data scientist, and what kind of job you will be interviewed for, and even if you believe more technical data science is your cup of tea, be prepared to know at least a high-level understanding and the details behind this method. It will definitely help you to know about this topic when you are speaking with product owners, stakeholders, product scientists, and other people involved in the business.
(0:05:38) Basics of A/B Testing in Data Science
Let's briefly discuss the perfect audience for the section of the course and prerequisites. There are no prerequisites for this section in terms of AB testing concepts that you should know already. But knowing the basics in statistics, which you can find in the "Fundamentals to Statistics" section, is highly recommended.
This section will be great if you have no prior AB testing knowledge and you want to identify and learn the essential AB testing concepts from scratch. So this will help you to prepare for your job interviews. It will also be a good refresher for anyone who does have AB testing knowledge but who wants to refresh their memory or wants to fill in the gaps in their knowledge.
(0:07:06) Key Parameters of A/B Testing for Data Scientists
In this lecture, we will start off the topic about A/B testing where we will formally define what A/B testing is, and we will look at the high-level overview of the A/B testing process step by step.
By definition, A/B testing or split testing originated from the statistical randomized control trials and is one of the most popular ways for businesses to test new UX features, new versions of a product, or an algorithm to decide whether your business should launch that new UX feature or should productionalize that new recommender system, create that new product, that new button, or that new algorithm.
The idea behind A/B testing is that you should show the variated or the new version of the product to a sample of customers, often referred to as the experimental group, and the existing version of the product to another sample of customers, referred to as the control group. Then the difference in the product performance in experimental versus control group is tracked to identify the effect of these new versions of the product on the performance of the product. So the goal is then to track the metric during the test period and find out whether there is a difference in the performance of the product and what type of difference is it.
The motivation behind this test is to test new product variants that will improve the performance of the existing product and will make this product more successful and optimal, showing a positive treatment effect. What makes this testing great is that businesses are getting direct feedback from their actual users by presenting them the existing versus the variated product version. And in this way, they can quickly test new ideas. In case an A/B test shows that the variated version is not effective, at least businesses can learn from this and can decide whether they need to improve it or need to look for other ideas.
Let us go through the steps included in the A/B testing process, which will give you a high-level overview into the process.
The first step in conducting A/B testing is stating the hypothesis of the A/B test. This is a process that includes coming up with business and statistical hypotheses that you would like to test with this test, including how you measure the success, which will be the primary metric.
Next step in A/B testing is to perform what we call power analysis and design the entire test, which includes making assumptions about the most important parameters of the test and calculating the minimum sample size required to claim statistical significance.
The third step in A/B testing is to run the actual A/B test, which in practical sense for the data scientist means making sure that the test runs smoothly and correctly, collaborating with engineers and product managers to ensure that all the requirements are satisfied. This also includes collecting the data of control and experimental groups, which will be used in the next step.
Next step in A/B testing is choosing the right statistical test, whether it is Z-test, T-test, Chi-square test, etc., to test the hypothesis from the step one by using the data collected from the previous step and to determine whether there is a statistically significant difference between the control versus experimental group.
The fifth and the final step in A/B testing is continuing to analyze the results and find out whether besides statistical significance, there is also practical significance. In this step, we use the second step's power analysis, so the assumptions that we made about model parameters and the sample size, and the four steps results to determine whether there is a practical significance besides of the statistical significance.
This summarizes the A/B testing process at a high level. In the next couple of lectures, we'll go through the steps one at a time. So buckle up and let's learn about A/B testing.
(0:09:24) Formulating Hypotheses and Identifying Primary Metrics in Data Science A/B Testing
In this lecture, lecture number two, we will discuss the first step in the A/B testing process. So let's bring our diagram back. As you can recall from the previous lecture, when we were discussing the entire process of A/B testing at a high level, we saw that in the first step in conducting A/B testing is stating the hypothesis of the A/B test. This process includes coming up with a business and statistical hypothesis that you would like to test with this test, including how you measure the success, which we call a primary metric.
So, what is the metric that we can use to say that the product that we are testing performs well? First, we need to state the business hypothesis for our A/B test from a business perspective. So, a business hypothesis describes what the two products are that are being compared and what is the desired impact or the difference for the business. So, how to fix a potential issue in the product where a solution of these two problems will influence what we call a key performance indicator or the KPI of interest.
A business hypothesis is usually set as a result of brainstorming and collaboration of relevant people on the product team and data science team. The idea behind this hypothesis is to decide how to fix a potential issue in the product where a solution of these problems will improve the target KPI. One example of a business hypothesis is that changing the color of the "Learn More" button, for instance, to green, will increase the engagement of the web page.
Next, we need to select what we call the primary metric for our A/B testing. There should be only one primary metric in your A/B test. Choosing this metric is one of the most important parts of an A/B test, since this metric will be used to measure the performance of the product or feature for the experimental and control groups, and it will be used to identify whether there is a difference or what we call a statistically significant difference between these two groups.
By definition, a primary metric is a way to measure the performance of the product being tested in the A/B test for the experimental and control groups. It will be used to identify whether there is a statistically significant difference between these two groups. The choice of the success metric depends on the underlying hypothesis that is being tested with this A/B test. This is, if not the most, one of the most important parts of the A/B test because it determines how the test will be designed and also how will the proposed ideas perform. Choosing poor metrics might disqualify a large amount of work or might result in wrong conclusions.
For instance, the revenue is not always the end goal. Therefore, in A/B testing, we need to tie up the primary metric to the direct and the higher-level goals of the product. The expectation is that if the product makes more money, then this suggests the content is great. But in achieving that goal, instead of improving the overall content of the material and writing, one can just optimize the conversion funnel.
One way to test the accuracy of the metric you have chosen as your primary metric for your A/B test could be to go back to the exact problem you want to solve. You can ask yourself the following question, what I tend to call the metric validity question. So, if the chosen metric were to increase significantly while everything else stayed constant, would we achieve our goal and would we address our business problem? Is it higher revenue? Is it higher customer engagement? Or is it higher views that we are chasing in the business?
So the choice of the metric will then answer this question. Though you need to have a single primary metric for your A/B test, you still need to keep an eye on the remaining metrics to make sure that all the metrics are showing a change and not only the target one. Having multiple metrics in your A/B test will lead to false positives since you will identify many significant differences while there is no effect, which is something you want to avoid. So it's always a good idea to pick just a single primary metric but to keep an eye and monitor all the remaining metrics.
So, if the answer to the metric validity question is "higher revenue," which means that you are saying that the higher revenue is what you are chasing, and better performance means higher revenue for your product, then you can use your primary metric, what we call a conversion rate.
Conversion rate is a metric that is used to measure the effectiveness of a website, a product, or a marketing campaign. It is typically used to determine the percentage of visitors or customers who take a desired action, such as making a purchase, filling out a form, or signing up for a service.
The formula for conversion rate is: Conversion Rate = (Number of Conversions) / (Number of Total Visitors) * 100%. For example, if a website has 1,000 visitors and 50 of them make a purchase, the conversion rate would be equal to 50 / 1,000 * 100%, which gives us 5%. This means that our conversion rate in this case is equal to 5%.
Conversion rate is an important metric because it allows us and businesses to measure the effectiveness of their website, a product, or a marketing campaign. It can help businesses to identify areas for improvement, such as increasing the number of conversions or improving the user experience. Conversion rate can be used for different purposes. For example, if a company wants to measure the effectiveness of an online store, the conversion rate would be the percentage of visitors who make a purchase. On the other hand, if a company wants to measure the effectiveness of a landing page, the conversion rate would be the percentage of visitors who fill out a form or sign up for a service.
So, if the answer to the metric validity question is "higher engagement," then you can use the click-through rate or CTR as your primary metric. This is, by the way, a common metric used in A/B testing whenever we are dealing with e-commerce, product search engines, recommender systems.
Click-through rate or CTR is a metric that measures the effectiveness of a digital marketing campaign or the user engagement with some feature on your web page or your website. And it's typically used to determine the percentage of users who click on a specific link, or button, or call to action (CTA) out of the total number of users who view it.
The formula for the click-through rate can be represented as follows: So, CTR = (Number of Clicks) / (Number of Impressions) * 100%. Not to be confused with click-through probability because there is a difference between the click-through rate and click-through probability. For example, if an online advertisement receives 1,000 impressions, which means that we are showing it to the customers for a thousand times, and there were 25 clicks, which means 25 out of all these impressions resulted in clicks. This means that the click-through rate for this specific example would be equal to 25 / 1,000 * 100%, which gives us 2.5%. This means that for this particular example, our click-through rate is equal to 2.5%.
Click-through rate is an important metric because it allows businesses to measure the effectiveness of their digital marketing campaigns and the user engagement with their website or web pages. High click-through rate indicates that a campaign or the web page or feature is relevant and appealing to the target audience because they are clicking on it. While low click-through rate indicates that a campaign or the web page needs an improvement. Click-through rate can be used to measure the performance of different digital marketing channels such as paid search, display advertising, email marketing, and social media. It can also be used to measure the performance of different ad formats such as text advertisements, banner advertisements, video advertisements, etc.
Next, and the final task in this first step in the process of A/B testing, is to state the statistical hypothesis based on the business hypothesis and the chosen primary metric.
Next, and in the final task in this first step of the A/B testing process, we need to state the statistical hypothesis based on the business hypothesis we stated and the chosen primary metric. In the section of "Fundamentals through Statistics" of this course, in lecture number seven, we went into details about statistical hypothesis testing, including what a null hypothesis is and what an alternative hypothesis is. So do have a look to get all the insights about this topic.
A/B testing should always be based on a hypothesis that needs to be tested. This hypothesis is usually set as a result of brainstorming and collaboration of relevant people on the product team and data science team. The idea behind this hypothesis is to decide how to fix a potential issue in a product where a solution of these problems will influence the key performance indicators or the KPI of interest. It's also highly important to make prioritization out of a range of product problems and ideas to test, while you want to pick that fixing this problem would result in the biggest impact for the product.
We can put the hypothesis that is subject to rejection so that we want to reject. In the ideal world, under the null hypothesis, what we define by H0, well, we can put the hypothesis subject to acceptance. So the desired hypothesis that we would like to have as a result of A/B testing under the alternative hypothesis defined by H1.
For example, if the KPI of the product is to increase the customer engagement by changing the color of the "Read More" button from blue to green, then under the null hypothesis, we can state that the click-through rate of the "Learn More" button with blue color is equal to the click-through rate of the green button. Under the alternative, we can then state that the click-through rate of the "Learn More" button with green color is larger than the click-through rate of the blue button. So, ideally, we want to reject this null hypothesis, and we want to accept the alternative hypothesis, which will mean that we can improve the click-through rate, so the engagement of our product by simply changing the color of the button from blue to green.
(0:19:55) Designing an A/B Test: Data Science Approach
Once we have set up the business hypothesis, selected the primary metrics, and stated the statistical hypothesis, we are ready to proceed to the next stage in the A/B testing process.
In this lecture, we will discuss the next, second step in the A/B testing process, which is designing the A/B test, including the power analysis and calculating the minimum sample sizes for the control and experimental groups. Stay tuned, as this is a very important part of the A/B testing process, commonly appearing during data science interviews.
Some argue that A/B testing is an art, and others say that it's a business-adjusted common statistical test. But the borderline is that to properly design this experiment, you need to be disciplined and intentional while keeping in mind that it's not really about testing, but it's about learning.
Following our steps, you need to take to have a solid design for your A/B test. So let's bring the diagram back. So in this step, we need to perform the power analysis for our A/B test and calculate the minimum sample size in order to design our A/B test.
A/B test design includes three steps: The first step is power analysis, which includes making assumptions about model parameters, including the power of the test, the significance level, etc. The second step is to use these parameters from power analysis to calculate the minimum sample size for the control and experimental groups. And then the final, third step is to decide on the test duration depending on several factors. So let's discuss each of these topics one by one.
Power analysis for A/B testing includes these three specific steps: The first one is determining the power of the test. This is our first parameter. The power of the statistical test is a probability of correctly rejecting the null hypothesis. Power is the probability of making a correct decision, so to reject the null hypothesis when the null hypothesis is false. If you're wondering what is the power of the test, what are these different concepts that we just talked about, what is this null hypothesis, and what does it mean to reject the null hypothesis, then head towards the "Fundamentals to Statistics" section of this course, as we discuss this topic in detail.
As part of that section, the power is often defined by 1 minus beta, which is equal to the probability of not making a type two error, where type two error is a probability of not rejecting the null hypothesis while the null is actually false. It's common practice to pick 80% as the power of the A/B test, which means that we allow 20% of type two error, and this means that we are fine with not detecting, so failing to reject the null hypothesis 20% of the time, which means that we are failing to detect a true treatment effect while there is an effect, which means that we are failing to reject the null. However, the choice of value of this parameter depends on the nature of the test and the business constraints.
Secondly, we need to determine a significance level for our A/B test. The significance level, which is also the probability of type one error, is the likelihood of rejecting the null hypothesis, detecting a treatment effect while the null is actually true and there is no statistically significant impact. This value, often defined by a Greek letter alpha, is a probability of making a false discovery, often referred to as a false positive rate. Generally, we use the significance level of 5%, which indicates that we have a 5% risk of concluding that there exists a statistically significant difference between the experimental and control variant performances when there is no actual difference. So we are fine by having five out of 100 cases detecting a treatment effect while there is no effect. It also means that you have a significant result difference between the control and the experimental groups within 95% confidence.
Like in the case of the power of the test, the choice of the alpha is dependent on the nature of the test and the business constraints. For instance, if running this A/B test is related to high engineering cost, then the business might decide to pick a high alpha, such that it would be easier to detect a treatment effect. On the other hand, if the implementation costs of the proposed version in production are high, you can then pick a lower significance level, since this proposed feature should really have a big impact to justify the high implementation cost. So it should be harder to reject the null hypothesis.
Finally, as the last type of power analysis, we need to determine a minimum detectable effect for the test. Last parameter, as part of the power analysis, we need to make assumptions about what is known as the minimum detectable effect or Delta, from the business point of view. So, what is the substantive to statistical significance that the business wants to see as a minimum impact of the new version to find this variant investment worthy? The answer to this question is what is the amount of change we aim to observe in the new version's metric compared to the existing one to make recommendations to the business that this feature should be launched in production, that its investment is worthy.
An estimate of this parameter is what is known as as a minimum detectable effect, often defined by a Greek letter Delta, which is also related to the practical significance of the test. So, this MDE or the minimum detectable effect is a proxy that relates to the smallest effect that would matter in practice for the business, and it's usually set by stakeholders, as this parameter is highly dependent on the business. There is no common level of it. Instead, this minimum detectable effect is basically the translation from statistical significance to practical significance. And here, we want to see and we want to answer the question: what is this percentage increase in the performance of the product that we want to experiment with that will tell to the business that this is good enough to invest in this new feature or in this new product? And this can be, for instance, 1% for one product, it can be 5% for another one, and it really depends on the business and what is the underlying KPI.
A popular reference to the parameters involved in the power analysis for A/B testing is like this: so, 1 minus beta for the power of the test, Alpha for the significance level, Delta for the minimum detectable effect. To make sure that our results are repeatable, robust, and can be generalized to the entire population, we need to avoid P-hacking. To ensure real statistical significance and to avoid biased results, so we want to make sure that we collect enough amount of observations and we run the test for a minimum predetermined amount of time. Therefore, before running the test, we need to determine the sample size of the control and experimental groups, as well as later on in this lecture, we will see also how long we need to run the test.
So, this is another important part of A/B testing which needs to be done using the defined power of the test, which was the one minus beta, the significance level, and a minimum detectable effect. So all the parameters that we decided upon when conducting the power analysis, calculation of the sample size depends on the underlying primary metric as well, that you have chosen for tracking the progress of the control and experimental versions of the product. So we need to distinguish here two cases.
So when discussing the primary metric, we saw that there are different ways that we can measure the performance of different types of products. If we are interested in engagement, then we are looking at a metric such as click-through rate, which is in the form of averages. So, Case 1 will be where the primary metric of A/B testing is in the form of a binary variable. It can be, for instance, conversion or no conversion, click or no click. And Case 2 where the primary metric of the test is in the form of proportions or averages, which means mean order amount or mean click-through rate.
So, let's say we want to test whether the average click-through rate of the control is equal to the average click-through rate of the experimental group. And under H1, we have that the mean control is equal to the mean experimental. And under H1, we have that the mean control is not equal to the mean experimental. So here, the mean control and mean experimental are simply the average of the primary metric for the control group and for the experimental group, respectively. So this is the formal hypothesis we want to test with our A/B test, and we can assume that this mean control is, for instance, the click-through rate of the control group, and the mean experimental is the click-through rate of the experimental group.
So, this is the formal statistical hypothesis we want to test with our A/B test. If you haven't done so, I would highly suggest you to head towards the "Fundamentals to Statistics" section of this course, where in lecture number seven and eight of the statistical part of this course, I go into detail about statistical hypothesis testing, the means, averages, significance level, etc. This also holds for the theorem that the sample size calculation is based upon, called the Central Limit Theorem. So check out the last lecture about inferential statistics, where I covered the Central Limit Theorem, which we will also use in this section. And finally, also check the lecture number five in that section where we cover the normal distribution. Another thing that we will use as part of this section, so the Central Limit Theorem states that given a sufficiently large sample size from an arbitrary distribution, the sample mean will be approximately normally distributed regardless of the shape of the original population distribution. This means that the distribution of the sample means will be approximately normal if we take a large enough sample, even if the distribution of the original sample is not normal.
So, when we are dealing with a primary performance tracking metric that is in the form of an average, such as this one that we are covering today, which is a click-through rate, we intend to compare the means of the control and experimental groups. Then we can use the Central Limit Theorem as stated, that the mean sampling distribution of both control and experimental groups follow a normal distribution. Consequently, the sampling distribution of the difference of the means of these two groups also will be normally distributed.
So, this can be expressed like this, where we see that the mean of the control group and mean of the experimental group follow a normal distribution with mean mu control and mu experimental, respectively, and with a variance of sigma control squared / (2 * n control) + sigma experimental squared / (2 * n experimental). So the sample size of the experimental group and the sample size of the control group, hence the sample size needed to compare the mean of the two normally distributed samples using a two-sided test, which prespecifies significance of alpha, power level, and minimum detectable effect, can be calculated as follows:
So, here you can see the mathematical representation of the minimum sample size. So, the N, which stands for the minimum sample size, is equal to (sigma control squared + sigma experimental squared) / Delta squared, multiplied by Z(1 - alpha / 2) + Z(1 - beta) squared. And here, the alpha, beta, and delta, we have made assumptions about as part of the power analysis, and the sigma control squared and sigma experimental squared are the estimates of the variance that we can come up with using so-called A/B testing. I would say you do not necessarily need to know this derivation, as there are many online calculators that will ask you for the alpha, beta, and delta values, as well as the sample estimates for the sigma squared control and experimental, and then these calculators will automatically calculate the minimum sample size for you.
If you're wondering what this A/B testing is and how we can come up with the sigma squared control and sigma experimental squared, as well as all the other values, then make sure to check out the blog that I posted before and that I mentioned before, as I explained in detail all these values, as well as check out the resource section where I've included many resources regarding this. But for now, just keep in mind that the Z(1 - alpha / 2) and Z(1 - beta) are just two constants and come from the normal distribution and standard normal distribution tables. I would say you do not necessarily need to know this derivation, as there are many online calculators that will ask you for this alpha, beta, and delta values, as well as the sample estimates for the sigma squared control and experimental, and then will calculate automatically the sample size for you.
Effectively, one example of such a calculator is this AB Testy online calculator, but if you Google it, you will find many others that will ask you for the minimum detectable effect, for the statistical significance, or the statistical power, and then it will automatically calculate for you the minimum sample size that you should have in order to have a statistical significance and in order to have a valid A/B test.
One thing to keep in mind is that you will notice that the statistical significance level is set to 95% in here, which is not what we have seen when we were discussing the alpha significance level. So sometimes these online calculators will confuse or will interchangeably use the significance level versus the confidence level, which are the opposite. So the significance level is usually at the level of 5% or 1%. Confidence level is around 95%, which is basically 100% minus the alpha. Therefore, whenever whenever you see this 95%, know that this means that your alpha should be 5%. So it's really important to understand how to use this calculator, not to end up with the wrong minimum sample size, conduct an entire A/B test, and then at the end realize that you have used the wrong significance level.
The final step is to calculate the test duration. This question needs to be answered before you run your experiment and not during the experiment. Sometimes people stop the test when they detect statistical significance, which is what we call P-hacking, and that's absolutely not what you want to do. To determine the baseline of the duration time, a common approach is to use this formula as you can see: Duration = N / (Number of Visitors per Day), where N is your minimum sample size that we just calculated in the previous step, and the number of visitors per day is the average number of visitors that you expect to see as part of your experiment.
For instance, if this formula results in 14 days, or 14, this suggests that running the test for two weeks is a good idea. However, it's highly important to take many business-specific aspects into account when choosing the time to run the test and for how long you need to run it, and simply using this formula is not enough. For example, if you want to run an experiment at the end of the month, December, with Christmas breaks, when higher than expected or lower than expected number of people are usually checking your web page, then this external and uncertain event had an impact on the page usage. For some businesses, this means, for example, if you want to run an experiment at the end of the month of December with Christmas breaks, when higher than expected or, in some cases, lower than expected number of people are usually checking the web page, so depending on the nature of your business or the product, then this external and uncertain event can have an impact on the page usage. For some businesses, which means that for some businesses, a high increase in the page usage can be the result, and for some, a huge decrease in usability.
In this case, running an A/B test without taking into account this external factor would result in inaccurate results, since the activity period would not be a true representation of a common page usage, and we no longer have this randomness, which is a crucial part of A/B testing. Besides this, when selecting a specific test duration, there are a few other things to be aware of. Firstly, too small a test duration might result in what we call novelty effects. Users tend to react quickly and positively to all types of changes, independent of their nature, so it's referred to as a novelty effect, and it varies in time, and it is considered illusory. So it would be wrong to attribute this effect to the experimental version itself and to expect that it will continue to persist after the novelty effect wears off. Hence, when picking a test duration, we need to make sure that we do not run the test for too short an amount of time period, otherwise we can have a novelty effect. Novelty effect can be a major threat to the external validity of an A/B test, so it's important to avoid it as much as possible.
Secondly, if the test duration is too large, then we can have what we call maturation effects. When planning an A/B test, it's usually useful to consider a longer test duration for allowing users to get used to a new feature or product. In this way, one will be able to observe the real treatment effect by giving more time to returning users to cool down from an initial positive reaction or a spike of interest due to a change that was introduced as part of a treatment. This should help to avoid novelty effect and is a better predictive value for the test outcome. However, the longer the test period, the larger is the likelihood of external effect impacting the reaction of the users and possibly contaminating the test results. This is what we call maturation effect, and therefore running the A/B test for too short an amount of time or too long an amount of time is not recommended, as it's a very involved topic. We can talk for hours about this part of the A/B test and also a topic that is asked a lot during the data science and product scientist interviews. Therefore, I highly suggest you to check out this book about A/B testing, which is a hands-on tutorial about everything you need to know about A/B testing, as well as check out the interview preparation guide in this section that contains 30 most popular A/B testing related questions you can expect during your data science interviews. So, stay tuned, and in the next couple of lectures, we will cover the next stages of the A/B testing process.
If you are looking for one place to learn everything about A/B testing without unnecessary difficulties, but also with a good statistical and data science background, then make sure to check out the A/B testing course at Lun Tech. So if you want to learn all this background information including what is statistical significance, what is A/B testing, how can A/B testing be done, and you want to have this end-to-end A/B testing course, then make sure to check the A
