Two-way ANOVA with repeated measures in both factors. Why three subject SS?

If you ask Prism to report two-way ANOVA with repeated measures in both factors, the ANOVA table portion of the results will look like this:

Note that there are three rows for subject: One for its interaction with the row factor, one for its interaction with the column factor, and one for just plain variation among subjects. Some books and programs show this as a single value. That is easy to compute by hand:

• Add up the three sum-of-square (SS) values. That is the overall sum-of-squares for subject. 
• Add up the three df values. That is the overall df for subject. 
• Do not add up the three MS values. That would be incorrect. 
• Divide the total sum-of-squares by the total df. The result is the total mean square (MS) value. 

If you performed a randomized block experiment, all is the same except that "subject" should be "block".