Mastering Hypothesis Testing for Data Science Interviews

Jul 15, 2023

Hypothesis testing is a fundamental concept in the field of data science that plays a crucial role in making informed decisions based on data analysis. Whether you are a seasoned data scientist or a job seeker preparing for data science interviews, mastering hypothesis testing is essential for success in the field.

This article aims to provide a comprehensive guide to mastering hypothesis testing specifically tailored for data science interviews. We will explore the basics of hypothesis testing, its relevance in data science interviews, and how it intersects with other important topics like A/B testing and SQL.

The article will also delve into different types of hypothesis tests commonly encountered in data science interviews, including the T-test, Z-test, and Binomial test. Understanding the purpose and application of each test will empower you to choose the right one for a given scenario and draw accurate conclusions from your data.

By the end of this article, you will have a solid foundation in hypothesis testing, equipped with the knowledge and skills necessary to confidently tackle hypothesis testing questions during data science interviews. So, let's dive in and unlock the secrets of mastering hypothesis testing for data science success.

Mastering Hypothesis Testing for Data Science Interviews / Image by Author

Introduction to Hypothesis Testing
Hypothesis Testing Questions in Data Science Interviews
2.1. Basic Hypothesis Questions
2.2. Hypothesis Testing + A/B Testing
2.3. Hypothesis Testing & SQL
Types of Hypothesis Tests
3.1. T-Test
3.2. Z-Test
3.3. Bionimal Test
How to Choose the Right Hypothesis Test?

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1. Introduction to Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about a population based on a sample of data. It involves formulating a hypothesis, collecting data, and analyzing the data to determine the likelihood of the hypothesis being true. The process of hypothesis testing typically involves the following steps:

Formulating the null and alternative hypotheses: The null hypothesis (H₀) represents the default assumption or the claim to be tested. The alternative hypothesis (H₁ or Ha) represents the claim that contradicts the null hypothesis and is often the hypothesis of interest.
Choosing the significance level: The significance level (often denoted as α) is the threshold used to determine the level of evidence required to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is actually true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).
Collecting and analyzing the data: Data is collected through experiments or observations. The collected data is then analyzed using statistical techniques to calculate test statistics and determine the likelihood of observing the results under the null hypothesis.
Calculating the test statistic: A test statistic is a numerical value calculated from the data that measures how well the observed data aligns with the null hypothesis. The choice of the test statistic depends on the nature of the data and the hypothesis being tested.
Determining the critical region: The critical region is the range of values of the test statistic for which the null hypothesis will be rejected. It is determined based on the significance level and the distribution of the test statistic.
Making a decision: By comparing the test statistic to the critical region, a decision is made on whether to reject the null hypothesis or not. If the test statistic falls within the critical region, the null hypothesis is rejected in favor of the alternative hypothesis. Otherwise, there is not enough evidence to reject the null hypothesis.
Drawing conclusions: Based on the decision made in step 6, conclusions are drawn regarding the hypothesis being tested. If the null hypothesis is rejected, it suggests that the alternative hypothesis may be true. However, if the null hypothesis is not rejected, it does not necessarily imply that the null hypothesis is true; it simply means there is not enough evidence to support the alternative hypothesis.

Hypothesis testing is widely used in various fields of research and decision-making to draw conclusions based on data and make informed judgments about population parameters. It helps researchers and analysts assess the validity of claims, evaluate the effectiveness of interventions, and make data-driven decisions.

2. Hypothesis Testing Questions in Data Science Interviews

There are three main types of hypothesis questions you will meet in data science interviews:

2.1. Basic Hypothesis Questions

The first type of question is the basic hypothesis question which will measure your understanding of the main concepts of hypothesis testing and the different types of hypothesis testing. Here are examples of the basics questions:

What are the differences between the z-test and t-test?
When to use a z-test Vs a t-test?
Given a specific dataset, how do you calculate t-statistic or z-statistics?

To be able to answer these questions you need to have a good understanding of hypothesis testing and the different types of it.

2.2. Hypothesis Testing + A/B Testing

The second type of questions you will see in data science interviews, especially the analytical focused role is the hypothesis testing and A/B testing. Here is a sample of questions you might see in interviews:

Given a test result, calculate if the result is significant
How to make a launch decision?

To be able to answer these questions you will need to have a good understanding of A/B testing and to be able to use hypothesis testing in practice.

2.3. Hypothesis Testing & SQL

The final type of questions covers the integration of Hypothesis testing and SQL with each other. Here are some examples:

Query average “likes” in control and treatment groups
Compute test statistics and tell if it is significant or not

3. Types of Hypothesis Tests

3.1. T-Test

A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another.

A t-test can only be used when comparing the means of two groups (a.k.a. pairwise comparison). If you want to compare more than two groups, or if you want to do multiple pairwise comparisons, use an ANOVA test or a post-hoc test.

To be able to use the t-test you assume that the data:

are independent
are (approximately) normally distributed
have a similar amount of variance within each group being compared (a.k.a. homogeneity of variance)

If your data do not fit these assumptions, you can try a nonparametric alternative to the t-test, such as the Wilcoxon Signed-Rank test for data with unequal variances.

What type of t-test should you use?

When choosing a t-test, you will need to consider two things: whether the groups being compared come from a single population or two different populations, and whether you want to test the difference in a specific direction.

Paired-samples Vs independent samples Vs One-sample test / Image by **Scribbr**

Here is a short summary of how to choose which type of t-test:

If the groups come from a single population (e.g., measuring before and after an experimental treatment), perform a paired t-test. This is a within-subjects design.
If the groups come from two different populations (e.g., two different species, or people from two separate cities), perform a two-sample t-test (a.k.a. independent t-test). This is a between-subjects design.
If there is one group being compared against a standard value (e.g., comparing the acidity of a liquid to a neutral pH of 7), perform a one-sample t-test.

3.2. Z-Test

A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed.

Z-test is used if the standard deviation of the population is unknown and the sample size is greater than or equal to 30, then the assumption of the sample variance equaling the population variance should be made using the z-test. Regardless of the sample size, if the population standard deviation for a variable remains unknown, a t-test should be used instead.

3.3. Binomial Test

A binomial test uses sample data to determine if the population proportion of one level in a binary (or dichotomous) variable equals a specific claimed value. For example, a binomial test could be run to see if the proportion of leopards at a wildlife refuge that has a solid black coat color is equal to 0.35 (which is expected based on a genetic model).

The test calculates the probability of getting from a specific sample size, n, the number of the desired outcome (in this case, the number of leopards with a solid black coat color) as extreme or more extreme than what was observed if the true proportion actually equaled the claim (0.35). This is calculated using the binomial formula:

Assumptions:

Random samples
Independent observations
The variable of interest is binary (only two possible outcomes).
The number of trials, n, is fixed ahead of time

4. How to Choose the Right Hypothesis Test?

Choosing the right statistical test for your problem is a critical step in designing the experiment and will decide the accuracy of the results. In addition to that it is an important question in data science interviews. Here is a simple you can follow to choose the right hypothesis test for your problem.

First, let's start with the metric of interest if it is :

1. Bernoulli distribution:

If the distribution is Bernoulli then we will check the values of n and p:

If np and n(1-p) are bigger than 10 then we can use the Z-test.
If np and n(1-p) are smaller than 10 then we can use the T-test.

2. Other distributions:

If the distribution is not Bernoulli then we will check the sample size:

The sample size is large (Sample size >30): No need to worry about whether it is normal or not because of CLT. Next, we will check the population variance if it is known then we choose the Z-test else we will choose the T-test.
The sample size is small (Sample size < 30): We will check if the distribution is normal or not. If the distribution is normal we will we will check the population variance if it is known then we choose the Z-test else we will choose the T-test.

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