ANOVA and Experimental Design

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ANOVA and Experimental Design

This course is part of Statistical Modeling for Data Science Applications Specialization

Instructor: Brian Zaharatos

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4 modules

Gain insight into a topic and learn the fundamentals.

19 reviews

Intermediate level

Recommended experience

Flexible schedule

4 weeks at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

4 modules

Gain insight into a topic and learn the fundamentals.

19 reviews

Intermediate level

Recommended experience

Flexible schedule

4 weeks at 10 hours a week

Learn at your own pace

Build toward a degree

Learn more

What you'll learn

Identify and interpret the two-way ANOVA (and ANCOVA) model(s) as a linear regression model.
Use the two-way ANOVA and ANCOVA models to answer research questions using real data.
Define and apply the concepts of replication, repeated measures, and full factorial design in the context of two-way ANOVA.

Skills you'll gain

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Assessments

1 quiz, 23 assignments

Taught in English

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This course is part of the Statistical Modeling for Data Science Applications Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

This second course in statistical modeling will introduce students to the study of the analysis of variance (ANOVA), analysis of covariance (ANCOVA), and experimental design. ANOVA and ANCOVA, presented as a type of linear regression model, will provide the mathematical basis for designing experiments for data science applications. Emphasis will be placed on important design-related concepts, such as randomization, blocking, factorial design, and causality. Some attention will also be given to ethical issues raised in experimentation.

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. Logo adapted from photo by Vincent Ledvina on Unsplash

In this module, we will introduce the basic conceptual framework for experimental design and define the models that will allow us to answer meaningful questions about the differences between group means with respect to a continuous variable. Such models include the one-way Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) models.

What's included

9 videos4 readings9 assignments2 programming assignments1 peer review1 discussion prompt2 ungraded labs

9 videos Total 87 minutes

Introduction to Experimental Design 10 minutes
The One-Way ANOVA and ANCOVA Models 6 minutes
ANOVA Variance Decomposition 9 minutes
ANOVA Sums of Squares and the F-test 14 minutes
ANOVA and ANCOVA as Regression Models 10 minutes
One-Way ANOVA Interpretation in the Regression Context 10 minutes
The ANCOVA Model 15 minutes
ANCOVA with Interactions 7 minutes
ANCOVA with Interactions in R 5 minutes

4 readings Total 31 minutes

Course Updates and Accessibility Support 1 minute
Earn Academic Credit for your Work! 10 minutes
Course Support 10 minutes
Assessment Expectations 10 minutes

9 assignments Total 270 minutes

Introduction to ANOVA and Experimental Design 30 minutes
The One-Way ANOVA and ANCOVA Models 30 minutes
ANOVA Variance Decomposition 30 minutes
ANOVA Sums of Squares and the F-Test 30 minutes
ANOVA and ANCOVA as Regression Models 30 minutes
One-Way ANOVA Interpretation in the Regression Context 30 minutes
The ANCOVA Model 30 minutes
ANCOVA with Interactions 30 minutes
ANCOVA with Interactions in R 30 minutes

2 programming assignments Total 120 minutes

Module 1 Autograded 60 minutes
Optional Introduction to Jupyter and R 60 minutes

1 peer review Total 60 minutes

Module 1 Peer-Review Submission 60 minutes

1 discussion prompt Total 10 minutes

Introduce Yourself 10 minutes

2 ungraded labs Total 120 minutes

ANCOVA with Interactions in R 60 minutes
Module 1 Peer-Review Lab 60 minutes

In this module, we will learn how statistical hypothesis testing and confidence intervals, in the ANOVA/ANCOVA context, can help answer meaningful questions about the differences between group means with respect to a continuous variable.

What's included

6 videos2 readings1 quiz3 assignments1 programming assignment1 peer review2 ungraded labs

6 videos Total 91 minutes

Beyond the Full F-test 12 minutes
Planned Comparisons: Defining Contrasts 17 minutes
Planned Comparisons: Hypothesis Testing with Contrasts 14 minutes
Post Hoc Comparisons 14 minutes
Post Hoc Comparisons in R 17 minutes
Type II Error and Power in the ANOVA Context 19 minutes

2 readings Total 20 minutes

Patrizio E. Tressoldi and David Giofré: "The pervasive avoidance of prospective statistical power: major consequences and practical solutions" 10 minutes
Optional: Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors 10 minutes

1 quiz Total 30 minutes

Planned Comparisons: Defining Contrasts 30 minutes

3 assignments Total 90 minutes

Beyond the Full F-test 30 minutes
Planned and Unplanned Comparisons 30 minutes
Type II Error and Power in the ANOVA Context 30 minutes

1 programming assignment Total 120 minutes

Module 2 Autograded Assignment 120 minutes

1 peer review Total 60 minutes

Module 2 Peer-Review Submission 60 minutes

2 ungraded labs Total 120 minutes

Planned Comparisons Using Contrasts in R 60 minutes
Module 2 Peer-Review Lab 60 minutes

In this module, we will study the two-way ANOVA model and use it to answer research questions using real data.

What's included

7 videos6 assignments1 programming assignment1 peer review1 ungraded lab

7 videos Total 79 minutes

Motivating the Two-way ANOVA Model 11 minutes
The two-way ANOVA model 10 minutes
The Two-way ANOVA Model as a Regression Model 9 minutes
Interaction Terms in the Two-way ANOVA Model: Definitions and Visualizations 14 minutes
Interactions in the Two-way ANOVA Model: Formal Tests 15 minutes
Two-way ANOVA Hypothesis Testing (no interaction) 15 minutes
Looking Ahead: Two-Way ANOVA and Experimental Design 5 minutes

6 assignments Total 180 minutes

Motivating the Two-way ANOVA Model 30 minutes
The Two-way ANOVA Model 30 minutes
The Two-way ANOVA Model as a Regression Model 30 minutes
Interaction Terms in the Two-way ANOVA Model: Definitions and Visualizations 30 minutes
Interactions in the Two-way ANOVA Model: Formal Tests 30 minutes
Two-way ANOVA Hypothesis Testing (no interaction) 30 minutes

1 programming assignment Total 180 minutes

Module 3 Autograded Assignment 180 minutes

1 peer review Total 60 minutes

Module 3 Peer-Review Submission 60 minutes

1 ungraded lab Total 60 minutes

Module 3 Peer-Review Lab 60 minutes

In this module, we will study fundamental experimental design concepts, such as randomization, treatment design, replication, and blocking. We will also look at basic factorial designs as an improvement over elementary “one factor at a time” methods. We will combine these concepts with the ANOVA and ANCOVA models to conduct meaningful experiments.

What's included

7 videos2 readings5 assignments1 programming assignment1 peer review2 ungraded labs

7 videos Total 79 minutes

The Conceptual Framework of Experimental Design 19 minutes
The Completely Randomized Design 13 minutes
The Randomized Complete Block Design (RCBD) 8 minutes
The Randomized Complete Block Design (RCBD): Hypothesis Testing 8 minutes
The Factorial Design 11 minutes
Further Issues in Experimental Design 7 minutes
Ethical Issues in Experimental Design 13 minutes

2 readings Total 20 minutes

Causation and Experimental Design 10 minutes
Resources on Ethics 10 minutes

5 assignments Total 150 minutes

The Conceptual Framework of Experimental Design 30 minutes
The Completely Randomized Design 30 minutes
The Randomized Complete Block Design (RCBD) 30 minutes
The Factorial Design 30 minutes
Further Issues in Experimental Design 30 minutes

1 programming assignment Total 120 minutes

Module 4 Autograded Assignment 120 minutes

1 peer review Total 60 minutes

Module 4 Peer-Review Submission 60 minutes

2 ungraded labs Total 180 minutes

A Completely Randomized Design (CRD) in R 60 minutes
Module 4 Peer-Review Lab 120 minutes

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This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

Instructor

Instructor ratings

(9 ratings)

Brian Zaharatos

University of Colorado Boulder

4 Courses 14,837 learners

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University of Colorado Boulder

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Reviewed on Jul 30, 2022

Great course. Really useful and practical, and the exercise is not too difficult.

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