Suppose an experiment utilizing a random block design has 5 treatments and 11 blocks for a total of 55 observations. Assume that the total Sum of Squares for the response is $\mathrm { SS }$ (Total) $= 400$. If the Sum of Squares for Treatments (SST) is $30 \%$ of SS(Total), and the Sum of Squares for Blocks (SSB) is $20 \%$ of SS (Total), find the $F$ values for this experiment.
A) treatments: $F = 4.80$; blocks: $F = 1.45$
B) treatments: $F = 8.1$; blocks: $F = 2.16$
C) treatments: $F = 6.00$; blocks: $F = 1.60$
D) treatments: $F = 19.00$; blocks: $F = 7.60$

Question

Quizplus · Accepted Answer

The correct answer is C because the F-value for treatments is calculated as SST/(df_treatments * MSE), where MSE is the mean square error. The F-value for blocks is calculated as SSB/(df_blocks * MSE). Given that SST is 30% of SS(Total) and SSB is 20% of SS(Total), we have SST = 0.3 * 400 = 120 and SSB = 0.2 * 400 = 80. The degrees of freedom for treatments is 5 - 1 = 4, and the degrees of freedom for blocks is 11 - 1 = 10. Therefore, the F-value for treatments is 120/(4 * MSE) = 6.00, and the F-value for blocks is 80/(10 * MSE) = 1.60.

Suppose an Experiment Utilizing a Random Block Design Has 5 SS\mathrm { SS }SS

Suppose an Experiment Utilizing a Random Block Design Has 5 $\mathrm { SS }$