ANOVA and Experimental Design

ANOVA and Experimental Design

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

Instructor: Brian Zaharatos

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 videos3 readings9 assignments2 programming assignments1 peer review1 discussion prompt2 ungraded labs

9 videosTotal 86 minutes

Introduction to Experimental Design10 minutesPreview module
The One-Way ANOVA and ANCOVA Models6 minutes
ANOVA Variance Decomposition8 minutes
ANOVA Sums of Squares and the F-test14 minutes
ANOVA and ANCOVA as Regression Models10 minutes
One-Way ANOVA Interpretation in the Regression Context10 minutes
The ANCOVA Model15 minutes
ANCOVA with Interactions7 minutes
ANCOVA with Interactions in R4 minutes

3 readingsTotal 30 minutes

Earn Academic Credit for your Work!10 minutes
Course Support10 minutes
Assessment Expectations10 minutes

9 assignmentsTotal 270 minutes

Introduction to ANOVA and Experimental Design30 minutes
The One-Way ANOVA and ANCOVA Models30 minutes
ANOVA Variance Decomposition30 minutes
ANOVA Sums of Squares and the F-Test30 minutes
ANOVA and ANCOVA as Regression Models30 minutes
One-Way ANOVA Interpretation in the Regression Context30 minutes
The ANCOVA Model30 minutes
ANCOVA with Interactions30 minutes
ANCOVA with Interactions in R30 minutes

2 programming assignmentsTotal 120 minutes

Module 1 Autograded60 minutes
Optional Introduction to Jupyter and R60 minutes

1 peer reviewTotal 60 minutes

Module 1 Peer-Review Submission60 minutes

1 discussion promptTotal 10 minutes

Introduce Yourself10 minutes

2 ungraded labsTotal 120 minutes

ANCOVA with Interactions in R60 minutes
Module 1 Peer-Review Lab60 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 videosTotal 91 minutes

Beyond the Full F-test12 minutesPreview module
Planned Comparisons: Defining Contrasts16 minutes
Planned Comparisons: Hypothesis Testing with Contrasts14 minutes
Post Hoc Comparisons13 minutes
Post Hoc Comparisons in R16 minutes
Type II Error and Power in the ANOVA Context18 minutes

2 readingsTotal 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) Errors10 minutes

1 quizTotal 30 minutes

Planned Comparisons: Defining Contrasts30 minutes

3 assignmentsTotal 90 minutes

Beyond the Full F-test30 minutes
Planned and Unplanned Comparisons30 minutes
Type II Error and Power in the ANOVA Context30 minutes

1 programming assignmentTotal 120 minutes

Module 2 Autograded Assignment120 minutes

1 peer reviewTotal 60 minutes

Module 2 Peer-Review Submission60 minutes

2 ungraded labsTotal 120 minutes

Planned Comparisons Using Contrasts in R60 minutes
Module 2 Peer-Review Lab60 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 videosTotal 78 minutes

Motivating the Two-way ANOVA Model10 minutesPreview module
The two-way ANOVA model9 minutes
The Two-way ANOVA Model as a Regression Model9 minutes
Interaction Terms in the Two-way ANOVA Model: Definitions and Visualizations13 minutes
Interactions in the Two-way ANOVA Model: Formal Tests15 minutes
Two-way ANOVA Hypothesis Testing (no interaction)14 minutes
Looking Ahead: Two-Way ANOVA and Experimental Design5 minutes

6 assignmentsTotal 180 minutes

Motivating the Two-way ANOVA Model30 minutes
The Two-way ANOVA Model30 minutes
The Two-way ANOVA Model as a Regression Model30 minutes
Interaction Terms in the Two-way ANOVA Model: Definitions and Visualizations30 minutes
Interactions in the Two-way ANOVA Model: Formal Tests30 minutes
Two-way ANOVA Hypothesis Testing (no interaction)30 minutes

1 programming assignmentTotal 180 minutes

Module 3 Autograded Assignment180 minutes

1 peer reviewTotal 60 minutes

Module 3 Peer-Review Submission60 minutes

1 ungraded labTotal 60 minutes

Module 3 Peer-Review Lab60 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.