Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 7 , n _ { 2 } = 7$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.27 , \bar { x } _ { 2 } = 1.99 \text {, and } \bar { x } _ { 3 } = 1.49 \text {. }$ The sample standard deviations were $s _ { 1 } = 0.25 , s _ { 2 } = 0.28 , \text { and } s _ { 3 } = 0.25$ The grand mean is $\bar { x } = 1.593158$
How many degrees of freedom are there for SSTr.
A) 2
B) 3
C) 16
D) 15

Question

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 7 , n _ { 2 } = 7$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.27 , \bar { x } _ { 2 } = 1.99 \text {, and } \bar { x } _ { 3 } = 1.49 \text {. }$ The sample standard deviations were $s _ { 1 } = 0.25 , s _ { 2 } = 0.28 , \text { and } s _ { 3 } = 0.25$  The grand mean is $\bar { x } = 1.593158$ 
How many degrees of freedom are there for SSTr. 
A) 2
B) 3
C) 16
D) 15

Quizplus · Accepted Answer

The degrees of freedom for the treatment sum of squares (SSTr) is calculated as the number of groups minus one. Here, there are three groups, so the degrees of freedom are $3 - 1 = 2$.

Samples Were Drawn from Three Populations n1=7,n2=7n _ { 1 } = 7 , n _ { 2 } = 7n1​=7,n2​=7

Samples Were Drawn from Three Populations $n _ { 1 } = 7 , n _ { 2 } = 7$