Lesson 3: The ANOVA Model
|Key Learning Goals for this Lesson:|
In this Lesson we take a more formal look at the ANOVA. In the first two sections we simply worked with data and some basic computations. We will focus here on the, a) deviations of each observation from overall mean, and b) deviations of each observation from treatment level mean, and the deviations of treatment level means from the overall mean. Using these devaitions we can formulate a linear additive statistical model for ANOVA.
Before we get started, it is important to talk about models. The ANOVA can be formulated in a number of ways that are equivalent. This creates a point of potential confusion that you should be aware of. Our textbook, in Sections 16.1 through 16.4, develops one model approach (a means model) that centers on an estimation of an overall vs. treatment level means, and is tied to regression methods with indicator coding of the categorical treatment levels. Alternatively, in textbook sections 16.5 through 16.7, a different modelling approach is discussed (the effects model) which is a traditional way to compute the ANOVA from datasets using a simple calculator to compute the various deviations. The effects model is formulated in regression methods using a different type of coding (effect coding) and this is shown in the textbook section 16.8.
Please note that our lesson sequence in the course notes differs from the textbook sequence in that we develop the ANOVA model using the effects model approach first (textbook sections 16.5-7). Then, in Lesson 3.7 we compare the means vs effects models using regression.
In Lesson 3 we will also look at how well a model is fitting and whether or not we are meeting the assumptions needed to employ the ANOVA. We will look closely at how a SAS program works, and to identify the steps we use in Minitab to run the one-way ANOVA that we have introduced so far. Finally, we will consider how to quantify the power associated with the analysis.