Question

Define ANOVA and fully discuss the F ratio. What information does an ANOVA summary table provide?

Answer 1

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means.

F ratio: The F-statistic is simply a ratio of two variances. Variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion.

I have attched image of anova table and following is the description for the Anova table:

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, and Total. 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."