ANOVA and Experimental Design

Overview

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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

Syllabus

Introduction to ANOVA and Experimental Design

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.

Hypothesis Testing in the ANOVA Context

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.

Two-Way ANOVA and Interactions

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

Experimental Design: Basic Concepts and Designs

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.