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For an ANOVA, if you had the group totals of [tex]$T_1=10, T_2=15, T_3=5$[/tex], with [tex]$SS$[/tex] values of [tex]$SS_1=9, SS_2=6, SS_3=9$[/tex], and [tex][tex]$\Sigma X^2=94$[/tex][/tex], and if you had [tex]$n = 5$[/tex] in each treatment, what would [tex]$SS_{\text{total}}$[/tex] be?

A. 8
B. 59
C. 34
D. 26



Answer :

GinnyAnswer
Sure, let's perform a step-by-step calculation to determine the total sum of squares ([tex]\(SS_{\text{total}}\)[/tex]) for the given ANOVA problem.

1. Determine the total number of observations (N):
Given that there are 3 groups and each group has [tex]\(n = 5\)[/tex] observations:
[tex]\[ k = 3 \quad(\text{number of groups}) \][/tex]
[tex]\[ N = n \times k = 5 \times 3 = 15 \quad(\text{total number of observations}) \][/tex]

2. Calculate the grand total (G):
Sum the totals from all groups:
[tex]\[ G = T_1 + T_2 + T_3 = 10 + 15 + 5 = 30 \][/tex]

3. Calculate [tex]\(G\)[/tex] squared divided by the total number of observations:
[tex]\[ \frac{G^2}{N} = \frac{30^2}{15} = \frac{900}{15} = 60 \][/tex]

4. Calculate the sum of squares total ([tex]\(SS_{\text{total}}\)[/tex]):
Given [tex]\(\sum X^2 = 94\)[/tex]:
[tex]\[ SS_{\text{total}} = \sum X^2 - \frac{G^2}{N} = 94 - 60 = 34 \][/tex]

Therefore, the total sum of squares ([tex]\(SS_{\text{total}}\)[/tex]) is:
[tex]\[ SS_{\text{total}} = 34 \][/tex]

So, the correct answer is:
[tex]\[ 34 \][/tex]

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