35. The article “Variation in Moisture and Ascorbic Acid Content from Leaf to Leaf and Plant to Plant in Turnip Greens”

(Southern Cooperative Services Bull., 1951: 13–17) uses a Latin square design in which factor A is plant, factor B is leaf size (smallest to largest), factor C (in parentheses) is time of weighing, and the response variable is moisture content.

Leaf Size (B)

123 1 6.67 (5) 7.15 (4) 8.29 (1)

2 5.40 (2) 4.77 (5) 5.40 (4)

Plant (A) 3 7.32 (3) 8.53 (2) 8.50 (5)

4 4.92 (1) 5.00 (3) 7.29 (2)

5 4.88 (4) 6.16 (1) 7.83 (3)

Leaf Size (B)

4 5 1 8.95 (3) 9.62 (2)

2 7.54 (1) 6.93 (3)

Plant (A) 3 9.99 (4) 9.68 (1)

4 7.85 (5) 7.08 (4)

5 5.83 (2) 8.51 (5)

When all three factors are random, the expected mean squares are E(MSA)
2 N2 A, E(MSB)
2 N 2 B, E(MSC)

2 N 2 C, and E(MSE)
2

. This implies that the F ratios for testing H0A: 2 A
0, H0B: 2 B
0, and H0C: 2 C
0 are identical to those for fixed effects. Obtain the ANOVA table and test at level .05 to see whether there is any variation in moisture content due to the factors.