Two-Way ANOVA Table & Error in Bluman Textbook ~ University Notes

Two-Way ANOVA Table

It is assumed that main effect A has a levels (and A = a-1 df), main effect B has b levels (and B = b-1 df), n is the sample size of each treatment, and N = abn is the total sample size. Notice the overall degrees of freedom is once again one less than the total sample size.

Source	SS	df	MS	F
Main Effect A	given	A, a-1	SS / df	MS(A) / MS(W)
Main Effect B	given	B, b-1	SS / df	MS(B) / MS(W)
Interaction Effect	given	A*B, (a-1)(b-1)	SS / df	MS(A*B) / MS(W)
Within	given	N - ab, ab(n-1)	SS / df
Total	sum of others	N - 1, abn - 1

Summary

The following results are calculated using the Quattro Pro spreadsheet. It provides the p-value and the critical values are for alpha = 0.05.

*Source of Variation*	SS	df	MS	F	*P-value*	*F-crit*
Seed	512.8667	2	256.4333	28.283	0.000008	3.682
Fertilizer	449.4667	4	112.3667	12.393	0.000119	3.056
Interaction	143.1333	8	17.8917	1.973	0.122090	2.641
Within	136.0000	15	9.0667
Total	1241.4667	29

From the above results, we can see that the main effects are both significant, but the interaction between them isn't. That is, the types of seed aren't all equal, and the types of fertilizer aren't all equal, but the type of seed doesn't interact with the type of fertilizer.

Error in Bluman Textbook

The two-way ANOVA, Example 13-9, in the Bluman text has the incorrect values in it. The student would have no way of knowing this because the book doesn't explain how to calculate the values.
Here is the correct table:

*Source of Variation*	SS	df	MS	F
Sample	3.920	1	3.920	4.752
Column	9.680	1	9.680	11.733
Interaction	54.080	1	54.080	65.552
Within	3.300	4	0.825
Total	70.980	7

The student will be responsible for finishing the table, not for coming up with the sum of squares which go into the table in the first place.