Suppose an experiment utilizing a random block design has 5 treatments and 8 blocks for a total of 40 observations. Assume that the total Sum of Squares for the response is SS(Total)=300 . If the Sum of Squares for Treatments (SST) is 40 % of SS(Total), and the Sum of Squares for Blocks (SSB) is 10 % of SS (Total), find the F values for this experiment.
A) treatments: F=4.48 ; blocks: F=0.70
B) treatments: F=13.00 ; blocks: F=7.43
C) treatments: F=7.8 ; blocks: F=1.11
D) treatments: F=5.60 ; blocks: F=0.80

Question

Suppose an experiment utilizing a random block design has 5 treatments and 8 blocks for a total of 40 observations. Assume that the total Sum of Squares for the response is SS(Total)=300 . If the Sum of Squares for Treatments (SST) is  40 %  of SS(Total), and the Sum of Squares for Blocks (SSB) is  10 %  of SS (Total), find the  F  values for this experiment.
A) treatments:  F=4.48 ; blocks:  F=0.70 
B) treatments:  F=13.00 ;  blocks:  F=7.43 
C) treatments:  F=7.8 ; blocks:  F=1.11 
D) treatments:  F=5.60 ; blocks:  F=0.80

Quizplus · Accepted Answer

The Sum of Squares for Treatments (SST) is 40% of 300, which is 120. The Sum of Squares for Blocks (SSB) is 10% of 300, which is 30. The Sum of Squares for Error (SSE) is 300 - 120 - 30 = 150. The degrees of freedom for treatments is 4, for blocks is 7, and for error is 28. The Mean Square for Treatments (MST) is 120/4 = 30, for Blocks (MSB) is 30/7 ≈ 4.29, and for Error (MSE) is 150/28 ≈ 5.36. The F value for treatments is MST/MSE = 30/5.36 ≈ 5.60, and for blocks is MSB/MSE = 4.29/5.36 ≈ 0.80.

Suppose an Experiment Utilizing a Random Block Design Has 5