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 is part of the Statistical Inference for Data Science Applications Specialization
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Statistical Inference for Data Science Applications SpecializationUniversity of Colorado BoulderAbout this Course
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Course 3 of 3 in the
Intermediate Level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R
Approx. 34 hours to complete
English
Subtitles: English
What you will learn
Define a composite hypothesis and the level of significance for a test with a composite null hypothesis.
Define a test statistic, level of significance, and the rejection region for a hypothesis test. Give the form of a rejection region.
Perform tests concerning a true population variance.
Compute the sampling distributions for the sample mean and sample minimum of the exponential distribution.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Course 3 of 3 in the
Intermediate Level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R
Approx. 34 hours to complete
English
Subtitles: English
Offered by
University of Colorado Boulder
CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
Start working towards your Master's degree
This course is part of the 100% online Master of Science in Data Science from University of Colorado Boulder.
If you are admitted to the full program, your courses count towards your degree learning.
Syllabus - What you will learn from this course
8 hours to complete
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.
8 hours to complete
6 videos (Total 70 min), 5 readings, 2 quizzes
8 hours to complete
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.
8 hours to complete
7 videos (Total 125 min), 7 readings, 2 quizzes
8 hours to complete
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.
8 hours to complete
7 videos (Total 140 min), 7 readings, 2 quizzes
4 hours to complete
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.
4 hours to complete
6 videos (Total 118 min), 6 readings, 2 quizzes
About the Statistical Inference for Data Science Applications Specialization
This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.
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