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Chapter 11
One Way Analysis of Variance
In the notation that is used on Pages 199 - 200, we have noticed some inconsistencies in the first edition that we originally intended to correct. What was presented in this second edition is the same as the first edition. However, here we present versions of steps 1 - 7 that are more consistent and hopefully more intuitive.
Step 1 = Find ΣXij = ΣX.1 + ΣX.2 + ..... + ΣX.j
For this example: ΣX.1 + ΣX.2 + ΣX.3
= -110 + -20 + -5 = -135
Step 2 = Find ΣX2ij = ΣX.12 + ΣX.22 + ..... + ΣX.j2
For this example: ΣX.12 + ΣX.22 + ΣX.32
Step 3 = Find (ΣXij/Nij) = (Step 1/Nij) = -135/30 = -4.5
Where Nij = Σn.j = n.1 + n.2 + ..... + n.j
For this example: n.1 + n.2 + n.3 = 10 + 10 + 10 = 30
Step 4 - 6 = Find [(ΣX.j)2/n.j] for each available group
Step 4 = (ΣX.1)2/n.1 = (-110)2/10 = 12100/10 = 1210
Step 5 = (ΣX.2)2/n.2 = (-20)2/10 = 400/10 = 40
Step 6 = (ΣX.3)2/n.3 = (-5)2/10 = 25/10 = 2.5
Step 7 = Σ[(ΣX.j)2/n.j] = Step 4 + Step 5 + Step 6