Module 13: F-Distribution and One-Way ANOVA

Relationships in an ANOVA Table

Barbara Illowsky & OpenStax et al.

Relationships Within an ANOVA Table

Basic ANOVA Table

 

Above is a basic ANOVA table. How are the cells in this table related? Let’s look at the first two columns of data S.S. and d.f. :

 

Basic ANOVA Table. SS and df columns highlighted.

Notice how the first two cells add up to the total below it in the columns highlighted above. (i.e. 5272.015 + 5763 = 11035.015)

 

Now let’s move onto the third column M.S. . In this case, we need to look at the rows which the cells belong to:

 

Basic ANOVA Table with SS, df and MS columns highlighted

 

Notice how the values in the third column are the quotient of the prior two cells (i.e. 5272.015 ÷ 5 = 1054.403)

 

This leaves us with our last column F.

 

Basic ANOVA Table with MS and F columns highlighted

This again is a division problem. (i.e. 1054.403 ÷ 113 = 9.331)

 

The relationships work for every ANOVA table. However, you may not be given the same elements as you are in this table. In this case, you may have to work backwards and solve for the other missing cells.

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Adapted By Darlene Young Inroductory Statistics by Barbara Illowsky & OpenStax et al. is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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