Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 5 , n _ { 2 } = 6$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.95 , \bar { x } _ { 2 } = 1.73 , \text { and } \bar { x } _ { 3 } = 1.44 \text {. }$ The sample standard deviations were $s _ { 1 } = 0.28 , s _ { 2 } = 0.43 , \text { and } s _ { 3 } = 0.48$ The grand mean is $\overline { \bar { x } } = 1.708125$
How many degrees of freedom are there for SSE.
A) 13
B) 12
C) 3
D) 2

Question

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 5 , n _ { 2 } = 6$ and $n _ { 3 } = 5$ The sample means were $\bar { x } _ { 1 } = 1.95 , \bar { x } _ { 2 } = 1.73 , \text { and } \bar { x } _ { 3 } = 1.44 \text {. }$ The sample standard deviations were $s _ { 1 } = 0.28 , s _ { 2 } = 0.43 , \text { and } s _ { 3 } = 0.48$  The grand mean is $\overline { \bar { x } } = 1.708125$
How many degrees of freedom are there for  SSE.
A) 13
B) 12
C) 3
D) 2

Quizplus · Accepted Answer

The degrees of freedom for SSE (Sum of Squares due to Error) in an ANOVA context is calculated by summing the degrees of freedom for each sample and subtracting the number of samples. Here, it's $(n_1 - 1) + (n_2 - 1) + (n_3 - 1) = (5-1) + (6-1) + (5-1) = 4 + 5 + 4 = 13$.

Samples Were Drawn from Three Populations n1=5,n2=6n _ { 1 } = 5 , n _ { 2 } = 6n1​=5,n2​=6

Samples Were Drawn from Three Populations $n _ { 1 } = 5 , n _ { 2 } = 6$