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 = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)

The number of degrees of freedom corresponding to within-treatments is
A) 60.
B) 59.
C) 5.
D) 4.

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 = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
​
The number of degrees of freedom corresponding to within-treatments is
A) 60.
B) 59.
C) 5.
D) 4.

Quizplus · Accepted Answer

The degrees of freedom within treatments (error or residual degrees of freedom) can be calculated by subtracting the degrees of freedom for treatments from the total degrees of freedom. The total degrees of freedom (df_total) is the total number of observations minus 1, which is 65 - 1 = 64. The degrees of freedom for treatments (df_treatments) is the number of treatments minus 1, which is 5 - 1 = 4. Therefore, the degrees of freedom within treatments is 64 - 4 = 60.

In a Completely Randomized Experimental Design Involving Five Treatments, 13