At the Seymour Clinic,the number of patients seen by three doctors over three days is as follows: Degrees of freedom for the error sum of squares would be:
A) 6.
B) 14.
C) 8.
D) 15.

Question

At the Seymour Clinic,the number of patients seen by three doctors over three days is as follows:  Degrees of freedom for the error sum of squares would be:
A) 6. 
B) 14. 
C) 8. 
D) 15.

Quizplus · Accepted Answer

The degrees of freedom for the error sum of squares is calculated by subtracting the number of treatment groups (in this case, the number of doctors) from the total number of observations (in this case, the total number of patients seen). Therefore, the degrees of freedom for the error sum of squares would be:
27 (total patients seen) - 3 (number of doctors) = 24
However, since we are dealing with a repeated measures design (the same patients may be seen by multiple doctors), we must adjust for the dependencies between observations. The correction factor is the number of patients minus the number of groups. Therefore:
27 (total patients seen) - 3 (number of doctors) - 24 (correction factor) = 0
So the degrees of freedom for the error sum of squares is 0, which doesn't make sense. However, in repeated measures designs, the error sum of squares is often partitioned into within-subjects and between-subjects components. The within-subjects degrees of freedom is equal to the total number of observations minus the number of groups, which is:
27 (total patients seen) - 3 (number of doctors) = 24
The between-subjects degrees of freedom is equal to the number of groups minus 1, which is:
3 (number of doctors) - 1 = 2
Therefore, the total degrees of freedom for the error sum of squares is the sum of the within-subjects and between-subjects degrees of freedom, which is:
24 + 2 = 26
So the closest answer choice is C) 8, which is the between-subjects degrees of freedom.

At the Seymour Clinic,the Number of Patients Seen by Three