In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations).Also, the design provided the following information.
SSTR = 200 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)

The mean square due to error (MSE) is
A) 50.
B) 10.
C) 200.
D) 600.

Question

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations).Also, the design provided the following information. ​
SSTR = 200 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
​
The mean square due to error (MSE) is
A) 50.
B) 10.
C) 200.
D) 600.

Quizplus · Accepted Answer

MS error = SST/SSE = (Total sum of squares) / (Degrees of freedom for error)
Total sample size = 65
Degrees of freedom for total = n - 1 = 64
Degrees of freedom for treatments = a - 1 = 4
Degrees of freedom for error = (n - 1) - (a - 1) = 60
Thus, MSE = SST/SSE = 800/60 = 13.33
Since the MSE is the mean square error, it cannot be equal to the sum of squares due to treatments (SSTR). Therefore, options A, C and D can be eliminated. The correct answer is B.

In a Completely Randomized Experimental Design Involving Five Treatments, 13