Statistical Inference and Hypothesis Testing in Data Science Applications from Coursera

This course will focus on theory and implementation of hypothesis testing, especially as it relates to applications in data science. Students will learn to use hypothesis tests to make informed decisions from data. Special attention will be given to the general logic of hypothesis testing, error and error rates, power, simulation, and the correct computation and interpretation of p-values. Attention will also be given to the misuse of testing concepts, especially p-values, and the ethical implications of such misuse.

This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder.

What's inside

Syllabus

Start Here!

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

Fundamental Concepts of Hypothesis Testing

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.

Composite Tests, Power Functions, and P-Values

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.

t-Tests and Two-Sample Tests

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.

Beyond Normality

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.

Likelihood Ratio Tests and Chi-Squared Tests

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Taught by university instructors who are recognized experts in their field

Develops core data science skills and knowledge

Uses hands-on labs and exercises for practical application of concepts

Offered through a reputable and recognized platform

Provides a comprehensive foundation in hypothesis testing for data science

May require prior knowledge of statistics and data analysis

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Statistical Inference and Hypothesis Testing in Data Science Applications with these activities:

Review: 'Introduction to Hypothesis Testing' by John Doe

Show steps

Provides additional context and insights from a reference text, complementing course materials and expanding knowledge.

View Introduction to the Design and Behavior of... on Amazon

Show steps

Read the book and take notes on key concepts.
Summarize the main arguments and examples presented in the book.
Identify connections between the book's content and the course materials.

Review Hypothesis Testing

Show steps

Refreshes understanding of the core concepts of hypothesis testing, making it easier to connect with course materials.

Browse courses on Hypothesis Testing

Show steps

Review definitions of hypothesis, null hypothesis, alternative hypothesis, and significance level.
Review how to calculate p-values and interpret them.
Review common types of hypothesis tests, such as t-tests, chi-squared tests, and ANOVA.

Practice Drills: Solving Hypothesis Testing Problems

Show steps

Reinforces understanding by providing opportunities to solve practical hypothesis testing problems.

Show steps

Solve practice problems involving one- and two-sample hypothesis tests.
Interpret results and make conclusions based on statistical evidence.

Two other activities

Expand to see all activities and additional details

Show all five activities

Mentor a Beginner in Hypothesis Testing

Show steps

Strengthens understanding by explaining concepts to others, reinforcing knowledge while helping fellow learners.

Show steps

Identify a student who needs support with hypothesis testing.
Provide guidance on core concepts, problem-solving techniques, and interpretation of results.
Answer questions and provide feedback to enhance their understanding.

Participate in a Hypothesis Testing Competition

Show steps

Promotes friendly competition and motivates students to excel by demonstrating their skills in a practical setting.

Show steps

Identify and register for a hypothesis testing competition.
Study and prepare for the competition by practicing and reviewing concepts.
Participate in the competition and demonstrate hypothesis testing abilities.

Career center

Learners who complete Statistical Inference and Hypothesis Testing in Data Science Applications will develop knowledge and skills that may be useful to these careers:

Data Scientist

This course is a valuable asset for aspiring Data Scientists. It delves into the theory and implementation of hypothesis testing, equipping you with the ability to draw meaningful insights from data. The focus on ethical implications of hypothesis testing will guide you in using statistical methods responsibly and avoid common pitfalls in data analysis.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians play a crucial role in the field of data science and hypothesis testing. This course provides a solid foundation in hypothesis testing, enabling you to design and implement effective tests to make informed decisions based on data. The understanding of power functions, p-values, and error rates will empower you to conduct rigorous statistical analysis and draw reliable conclusions from complex datasets.

See salaries and explore the career path for Statistician

Machine Learning Engineer

This course can be highly beneficial for Machine Learning Engineers who wish to enhance their understanding of statistical inference and hypothesis testing. The concepts covered, such as error rates, power, and p-values, are essential for evaluating and fine-tuning machine learning models. The course's emphasis on ethical implications will also equip you to navigate the ethical considerations surrounding data analysis and model deployment.

See salaries and explore the career path for Machine Learning Engineer

Epidemiologist

This course is highly relevant for Epidemiologists who rely heavily on statistical methods to investigate the causes and patterns of diseases. The concepts covered, such as hypothesis testing, error rates, and power, are essential for designing and conducting epidemiological studies, interpreting data, and drawing valid conclusions about disease prevalence and risk factors.

See salaries and explore the career path for Epidemiologist

Biostatistician

For those pursuing a career in Biostatistics, this course provides a solid foundation in hypothesis testing, a cornerstone of statistical analysis in the medical field. The understanding of sampling distributions, t-tests, and chi-squared tests will enable you to evaluate the effectiveness of medical interventions, assess the validity of research findings, and make informed decisions in healthcare.

See salaries and explore the career path for Biostatistician

Market Researcher

Market Researchers rely extensively on hypothesis testing to gather insights and inform decision-making. This course will equip you with the skills to design and conduct surveys, analyze data, and draw valid conclusions. The understanding of error rates and power will enable you to optimize research strategies and ensure the accuracy of your findings.

See salaries and explore the career path for Market Researcher

Financial Analyst

For those aspiring to become Financial Analysts, this course provides a valuable foundation in statistical inference and hypothesis testing. The ability to analyze financial data, identify trends, and make informed predictions is crucial in this field. The course's emphasis on p-values and the misuse of testing concepts will help you navigate the complexities of financial markets and make sound investment decisions.

See salaries and explore the career path for Financial Analyst

Quality Assurance Analyst

This course can be beneficial for Quality Assurance Analysts who need to evaluate the quality of products or services using statistical methods. The concepts covered, such as hypothesis testing, error rates, and sampling distributions, will help you design effective testing strategies, analyze data, and make informed decisions about product quality.

See salaries and explore the career path for Quality Assurance Analyst

Process Engineer

For those pursuing a career as Process Engineers, this course may be helpful in understanding the statistical tools used to analyze and improve processes. The concepts covered, such as hypothesis testing and sampling distributions, will enable you to identify process variations, evaluate the effectiveness of process changes, and optimize production efficiency.

See salaries and explore the career path for Process Engineer

Risk Manager

This course can provide a foundation in statistical inference and hypothesis testing for Risk Managers. The understanding of error rates, power, and p-values will enable you to evaluate the likelihood and impact of potential risks, make informed decisions, and develop effective risk management strategies.

See salaries and explore the career path for Risk Manager

Actuary

This course may be useful for Actuaries who need to apply statistical methods to assess risk and uncertainty. The concepts covered, such as hypothesis testing and the interpretation of p-values, will help you evaluate the validity of insurance claims, set insurance premiums, and make informed decisions in the field of risk management.

See salaries and explore the career path for Actuary

Public Health Specialist

This course may be useful for Public Health Specialists who need to analyze data and make informed decisions about public health issues. The understanding of hypothesis testing and the interpretation of p-values will enable you to evaluate the effectiveness of public health interventions, identify risk factors, and develop strategies to improve community health.

See salaries and explore the career path for Public Health Specialist

Operations Research Analyst

This course may provide a helpful foundation for Operations Research Analysts who use statistical methods to improve decision-making. The understanding of hypothesis testing and the interpretation of p-values will enable you to analyze data, identify patterns, and make informed recommendations for optimizing operational processes.

See salaries and explore the career path for Operations Research Analyst

Teacher

This course may be useful for Teachers who wish to incorporate statistical concepts and critical thinking into their teaching. The understanding of hypothesis testing and the interpretation of p-values will enable you to design engaging lesson plans, encourage students to ask questions, and promote data-driven decision-making in the classroom.

See salaries and explore the career path for Teacher

Social Worker

This course may provide a helpful foundation for Social Workers who need to analyze data and evaluate the effectiveness of social programs. The understanding of hypothesis testing and the interpretation of p-values will enable you to assess the impact of interventions, identify areas for improvement, and advocate for evidence-based practices.

See salaries and explore the career path for Social Worker