Lesson 1: Overview of ANOVA
Key Learning Goals for this Lesson: 

Through prior statistics courses analysis of variance has been applied in very simple settings. This course will cover analysis of variance well beyond a one group setting. Along with the increasing complexity of the ANOVA models, this course will also focus somewhat on the design of experiments, specifically related to how the ANOVA model relates to the design. For studies that are observational in nature, ANOVA conclusions are not as rigorous. However, ANOVA can be appropriate for both types of studies. To develop the concepts and methods used in ANOVA we will initially focus on the analysis of designed experiments. (NOTE: if you aren't familiar with the difference between observational and experimental studies you should be reviewing introductory statistical concepts which are ESSENTIAL to success in this course!)
‘Classic’ analysis of variance (ANOVA) is a method to compare average (mean) responses to experimental manipulations in controlled environments. For example, if people who want to lose weight are randomly selected to participate in a weight loss study, each person might be randomly assigned to a dieting group, an exercise group and a "control" group (for which there is no intervention). The MEAN weight loss for each group is compared to every other group.
Recall that a fundamental tenet of the scientific method is that results should be reproducible. A designed experiment provides this through replication and generates data which requires the calculation of mean (average) responses.