The ANOVA Table
For the sake of concreteness here, let's recall one of the analysis of variance tables from the previous page:
In working to digest what is all contained in an ANOVA table, let's start with the column headings: (1) Source means "the source of the variation in the data." As we'll soon see, the possible choices for a one-factor study, such as the learning study, are Factor, Error, andTotal. The factor is the characteristic that defines the populations being compared. In the tire study, the factor is the brand of tire. In the learning study, the factor is the learning method. (2) DF means "the degrees of freedom in the source."
(3) SS means "the sum of squares due to the source."
(4) MS means "the mean sum of squares due to the source."
(5) F means "the F-statistic."
(6) P means "the P-value."
Now, let's consider the row headings:
(1) Factor means "the variability due to the factor of interest." In the tire example on the previous page, the factor was the brand of the tire. In the learning example on the previous page, the factor was the method of learning. Sometimes, the factor is a treatment, and therefore the row heading is instead labeled as Treatment. And, sometimes the row heading is labeled as Between to make it clear that the row concerns the variation between the groups. (2) Error means "the variability within the groups" or "unexplained random error." Sometimes, the row heading is labeled as Within to make it clear that the row concerns the variation within the groups. (3) Total means "the total variation in the data from the grand mean" (that is, ignoring the factor of interest). With the column headings and row headings now defined, let's take a look at the individual entries inside a general one-factor ANOVA table:
Yikes, that looks overwhelming! Let's work our way through it entry by entry to see if we can make it all clear. Let's start with the degrees of freedom (DF) column: (1) If there...
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