Assume the following data obey the one-way analysis of variance model.

(a) Decompose each observation \(y_{i j}\) as \[y_{i j}=\bar{y}+\left(\bar{y}_{i}-\bar{y}\right)+\left(y_{i j}-\bar{y}_{i}\right)\]

(b) Obtain the sums of squares and degrees of freedom for each array.

(c) Construct the analysis of variance table and test for differences among the treatments with \(\alpha=0.05\).

Transcribed Image Text:

Treatment I: 89 Treatment II: 54 Treatment III: 35 12 7 84 8 1 001