It quantifies the variability within the groups of interest.

Again, as we'll formalize below, SS(Error) is the sum of squares between the data and the group means.

As the name suggests, it quantifies the variability between the groups of interest.

As we'll soon formalize below, SS(Between) is the sum of squares between the group means and the grand mean.

If there are n total data points collected and m groups being compared, then there are n− m error degrees of freedom.

If there are m groups being compared, then there are m−1 degrees of freedom associated with the factor of interest.

If there are n total data points collected, then there are n−1 total degrees of freedom.

Let's start with the degrees of freedom ( DF) column: Yikes, that looks overwhelming! Let's work our way through it entry by entry to see if we can make it all clear. Hover over the lightbulb for further explanation. 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: Total means 'the total variation in the data from the grand mean' (that is, ignoring the factor of interest).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.

And, sometimes the row heading is labeled as Between to make it clear that the row concerns the variation between the groups. Sometimes, the factor is a treatment, and therefore the row heading is instead labeled as Treatment. In the learning example on the previous page, the factor was the method of learning. 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.MS means 'the mean sum of squares due to the source.'.SS means 'the sum of squares due to the source.'.DF means 'the degrees of freedom in the source.'.In the learning study, the factor is the learning method. In the tire study, the factor is the brand of tire. The factor is the characteristic that defines the populations being compared. 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, and Total.In working to digest what is all contained in an ANOVA table, let's start with the column headings:

Degrees of freedom calculator anova