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Statistical Inference and Hypothesis Testing in Data Science Applications
  • Level Professional
  • Duration 37 hours
  • Course by University of Colorado Boulder
  • Offered by

About

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.

Modules

Welcome to Hypothesis Testing

    • 3 Readings
    • 1 Discussion
    • 1 Lab
Show info about module content

1 Discussions

  • Introduce Yourself

1 Labs

  • Introduction to Jupyter Notebooks and R

3 Readings

  • Earn Academic Credit for your Work!
  • Course Support
  • Course Resources

Let's Get Started!

    • 1 Videos
    • 1 Readings
    • 1 Lab
Show info about module content

1 Labs

  • An Introduction to R and Jupyter Notebooks

1 Videos

  • What is Hypothesis Testing?

1 Readings

  • What is Hypothesis Testing?

Types of Hypotheses

    • 1 Videos
    • 2 Readings
Show info about module content

1 Videos

  • Types of Hypotheses

2 Readings

  • Types of Hypotheses
  • Video Slides for Types of Hypotheses

Computations Involving the Normal Distribution

    • 1 Videos
    • 2 Readings
Show info about module content

1 Videos

  • Normal Computations

2 Readings

  • Normal Computations
  • Video Slides for Normal Computations

Errors in Hypothesis Testing

    • 1 Videos
    • 2 Readings
    • 1 Lab
Show info about module content

1 Labs

  • Visualizing Errors in Hypothesis Testing

1 Videos

  • Errors in Hypothesis Testing

2 Readings

  • Errors in Hypothesis Testing
  • Video Slides for Errors in Hypothesis Testing

Test Statistics and Significance

    • 1 Videos
    • 2 Readings
Show info about module content

1 Videos

  • Test Statistics and Significance

2 Readings

  • Test Statistics and Significance
  • Video Slides for Test Statistics and Level of Significance

A First Test

    • 1 Videos
    • 2 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • A First Test

2 Readings

  • A First Test
  • Video Slides for A First Test

1 Quiz

  • Introduction to Hypothesis Testing

Programming Assignments

    • 1 Programming
Show info about module content

1 Programming

  • Intro to Hypothesis Testing Lab

Lesson 1: Composite Hypotheses and Level of Significance

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Composite Hypotheses and Level of Significance

1 Readings

  • Video Slides for Composite Hypotheses and Level of Significance

Lesson 2: One-Tailed Tests for the Mean of a Normal Distribution

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • One-Tailed Tests

1 Readings

  • Video Slides for One-Tailed Tests

Lesson 3: Power Functions

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Power Functions

1 Readings

  • Video Slides for Power Functions

Lesson 4: P-Values and QQ-Plots

    • 1 Videos
    • 1 Readings
    • 1 Lab
Show info about module content

1 Labs

  • Distributions of P-Values

1 Videos

  • Hypothesis Testing with P-Values

1 Readings

  • Video Slides for Hypothesis Testing with P-Values

Lesson 5: Two-Tailed Tests for the Mean of a Normal Distribution

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Two Tailed Tests

1 Readings

  • Video Slides for Two-Tailed Tests

Lesson 6: A Quick Review of the Central Limit Theorem

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • CLT: A Brief Review

1 Readings

  • Video Slides for CLT: A Brief Review

Lesson 7: Confidence Intervals for Proportions

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • Hypothesis Tests for Proportions

1 Readings

  • Video Slides for Hypothesis Tests for Proportions

1 Quiz

  • Constructing Tests

Module Assignments

    • 1 Programming
Show info about module content

1 Programming

  • The Basics of Hypothesis Testing

Lesson 1: The t and Chi-Squared Distributions

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • The t and Chi-Squared Distributions

1 Readings

  • Video Slides for the t and Chi-Squared Distributions

Lesson 2: The Sample Variance for the Normal Distribution

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • The Sample Variance for the Normal Distribution

1 Readings

  • Video Slides for the Sample Variance and the Normal Distribution

Lesson 3: The t-Test

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • t-Tests

1 Readings

  • Video Slides for t-Tests

Lesson 4: Two-sample Tests Involving Means of Normal Distributions

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Two Sample Tests for Means

1 Readings

  • Video Slides for Two Sample Tests for Means

Lesson 5: Two-Sample t-Tests for a Difference in Two Population Means

    • 1 Videos
    • 1 Readings
    • 1 Lab
Show info about module content

1 Labs

  • t-Tests and Two Sample Tests

1 Videos

  • Two Sample t-Tests for a Difference of Means

1 Readings

  • Video Slides for Differences in Population Means

Lesson 6: Welch's Test and Paired Data

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • Welch's t-Test and Paired Data

1 Readings

  • Video Slides for Welch's Test and Paired Data

1 Quiz

  • More Hypothesis Tests!

Lesson 7: Comparing Two Population Proportions

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Comparing Population Proportions

1 Readings

  • Video Slides for Comparing Population Proportions

Module Assignments

    • 1 Programming
Show info about module content

1 Programming

  • t-Tests

Lesson 1: Properties of the Exponential Distribution

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Properties of the Exponential Distribution

1 Readings

  • Video Slides for Properties of the Exponential Distribution

Lesson 2: Two Hypothesis Tests for the Rate of an Exponential Distribution

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Two Tests

1 Readings

  • Video Slides for Two Hypothesis Tests for the Exponential

Lesson 3: "Best" Tests

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • Best Tests

1 Readings

  • Video Slides for Best Tests

1 Quiz

  • Best Tests and Some General Skills

Lesson 4: Uniformly Most Powerful Tests

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • UMP Tests

1 Readings

  • Video Slides for UMP Tests

Lesson 5: Normal Distribution Population Variance

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • A Test for the Variance of the Normal Distribution

1 Readings

  • Video Slides for a Normal Variance Test

Lesson 6: The F-Distribution and a Ratio of Variances

    • 1 Videos
    • 1 Readings
    • 1 Quiz
Show info about module content

1 Videos

  • The F-Distribution and a Ratio of Variances

1 Readings

  • Video Slides for an F-Distribution and a Ratio of Variances

1 Quiz

  • Uniformly Most Powerful Tests and F-Tests

Lesson 1: A Review of Maximum Likelihood Estimation

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • MLEs

1 Readings

  • Video Slides for MLEs

Lesson 2: The Generalized Likelihood Ratio Test

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • The GRLT

1 Readings

  • Video Slides for the GLRT

Lesson 3: Wilks' Theorem for Large Sample GLRTs

    • 1 Videos
    • 1 Readings
    • 1 Quiz
    • 1 Lab
Show info about module content

1 Labs

  • Exploring Wilks' Theorem

1 Videos

  • Wilks' Theorem

1 Readings

  • Video Slides for Wilks' Theorem

1 Quiz

  • Adventures in GLRTs

Lesson 4: Chi-Squared Goodness of Fit Tests

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Chi-Squared Goodness of Fit Test

1 Readings

  • Video Slides for Chi-Squared Goodness of Fit Test

Lesson 5: Chi-Squared Test for Independence

    • 1 Videos
    • 1 Readings
Show info about module content

1 Videos

  • Independence and Homogeneity

1 Readings

  • Video Slides for Independence and Homogeneity

Module Assignments

    • 1 Programming
Show info about module content

1 Programming

  • Chi-Squared Tests and Mo

Auto Summary

"Statistical Inference and Hypothesis Testing in Data Science Applications" is a professional-level course on Coursera focused on the theory and implementation of hypothesis testing in data science. Taught by CU Boulder faculty, it covers error rates, power, simulation, and p-value interpretation, while addressing ethical misuse. Part of the MS-DS degree, the 2220-minute course suits learners with backgrounds in computer science, information science, mathematics, or statistics. Available for academic credit with flexible subscriptions.

Jem Corcoran
Instructor

Jem Corcoran