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 number of degrees of freedom corresponding to between-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 = 200 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
​
The number of degrees of freedom corresponding to between-treatments is
A) 60.
B) 59.
C) 5.
D) 4.

Quizplus · Accepted Answer

The total degrees of freedom for the ANOVA table is typically equal to the total number of observations minus one, or n-1. In this case, n = 65.

Since there were 5 treatments, the degrees of freedom for Treatments would be 5-1 = 4.

The degrees of freedom for error or within-treatments can be found by subtracting the degrees of freedom for treatments from the total degrees of freedom:

df(Error) = (n-1) - df(Treatments) = 65-1-4 = 60.

The degrees of freedom for Total is simply n-1:

df(Total) = 65-1 = 64.

Therefore, the number of degrees of freedom corresponding to between-treatments is 4, as stated in option D.

In a Completely Randomized Experimental Design Involving Five Treatments, 13