Statistical Inference and Hypothesis Testing in Data Science Applications

Go to Course: https://www.coursera.org/learn/statistical-inference-and-hypothesis-testing-in-data-science-applications

Introduction

**Course Review: Statistical Inference and Hypothesis Testing in Data Science Applications on Coursera** In the ever-evolving field of data science, the ability to make informed decisions based on data is crucial. One of the foundational skills for this is a strong understanding of statistical inference and hypothesis testing. The course titled **Statistical Inference and Hypothesis Testing in Data Science Applications** offered on Coursera is designed to equip learners with these vital skills through a structured and comprehensive syllabus. ### Overview This course delves deeply into the theory and application of hypothesis testing, focusing on practical applications within the realm of data science. Students will not only learn the mechanics of hypothesis tests but will also explore the ethical implications regarding the misuse of testing concepts—especially p-values. This dual focus on technical skills and ethical awareness makes the course particularly relevant in today's data-driven world where misinterpretation of data can lead to significant consequences. ### What You Will Learn The course begins by introducing foundational concepts of hypothesis testing. In the first module, students are welcomed and provided with logistical information to navigate through the course layout. The subsequent modules gradually build on these concepts, covering a range of topics essential for proficient statistical analysis: 1. **Fundamental Concepts of Hypothesis Testing**: An introduction to the basic terminology, including null and alternative hypotheses, significance levels, and designing hypothesis tests. 2. **Composite Tests, Power Functions, and P-Values**: This module expands knowledge to composite hypotheses and introduces the power function, clearing up common misconceptions surrounding p-values. 3. **t-Tests and Two-Sample Tests**: Students will explore t and chi-squared distributions, learning when to implement different hypothesis tests while engaging with real datasets. 4. **Beyond Normality**: Here, the course addresses scenarios where the normal distribution may not be a valid assumption, introducing the uniformly most powerful (UMP) tests. 5. **Likelihood Ratio Tests and Chi-Squared Tests**: The final module focuses on formal approaches to hypothesis testing via the likelihood ratio, alongside practical chi-squared tests for distributional validity. ### Teaching Style and Resources The course is designed with a mix of theoretical knowledge and practical application, anchored by clear explanations and engaging instructional materials. Through a combination of video lectures, readings, quizzes, and hands-on projects, learners are provided with a robust learning environment that encourages active participation. The course also presents simulations that help students visualize the impact of different hypotheses; a critical aspect of understanding statistical principles. ### Target Audience This course is suitable for individuals at various stages of their careers in data science—whether you're a beginner looking to grasp the fundamentals of hypothesis testing, or an experienced professional seeking to reinforce your knowledge and skills. Prior experience with basic statistics and a familiarity with data analysis tools will serve as a beneficial foundation for this course. ### Conclusion In conclusion, **Statistical Inference and Hypothesis Testing in Data Science Applications** is an excellent course for anyone looking to enhance their data analysis skill set through a thorough understanding of hypothesis testing. Its blend of theory and practical application, forthright discussion of ethical considerations, and accessibility make it a must-recommend. With the knowledge gained from this course, you’ll be better equipped to interpret data accurately and make scientifically grounded decisions—essential capabilities in today’s data-centric environment. I highly recommend enrolling in this course if you're looking to sharpen your skills in statistical inference and enhance your professional capabilities. **Take the leap into statistical mastery—sign up on Coursera today!**

Syllabus

Start Here!

Welcome to the course! This module contains logistical information to get you started!

In this module, we will define a hypothesis test and develop the intuition behind designing a test. We will learn the language of hypothesis testing, which includes definitions of a null hypothesis, an alternative hypothesis, and the level of significance of a test. We will walk through a very simple test.

In this module, we will expand the lessons of Module 1 to composite hypotheses for both one and two-tailed tests. We will define the “power function” for a test and discuss its interpretation and how it can lead to the idea of a “uniformly most powerful” test. We will discuss and interpret “p-values” as an alternate approach to hypothesis testing.

In this module, we will learn about the chi-squared and t distributions and their relationships to sampling distributions. We will learn to identify when hypothesis tests based on these distributions are appropriate. We will review the concept of sample variance and derive the “t-test”. Additionally, we will derive our first two-sample test and apply it to make some decisions about real data.

In this module, we will consider some problems where the assumption of an underlying normal distribution is not appropriate and will expand our ability to construct hypothesis tests for this case. We will define the concept of a “uniformly most powerful” (UMP) test, whether or not such a test exists for specific problems, and we will revisit some of our earlier tests from Modules 1 and 2 through the UMP lens. We will also introduce the F-distribution and its role in testing whether or not two population variances are equal.

In this module, we develop a formal approach to hypothesis testing, based on a “likelihood ratio” that can be more generally applied than any of the tests we have discussed so far. We will pay special attention to the large sample properties of the likelihood ratio, especially Wilks’ Theorem, that will allow us to come up with approximate (but easy) tests when we have a large sample size. We will close the course with two chi-squared tests that can be used to test whether the distributional assumptions we have been making throughout this course are valid.