4
If in the analysis of variance of a completely randomized design, the df. for the treatment sum of squares is 4 and the mean
sum of squares due to error is 2, while the observed F-value for testing significance of treatment differences is 12.5, then
which one of the following represents correctly the treatment sum of squares?
EXPLANATION
Applied Statistical Methods
- ANOVA Relationship in Completely Randomized Design (CRD):
- Given parameters:
- Degrees of freedom for Treatment Sum of Squares ($df_{\text{treatment}}$) = 4
- Mean Sum of Squares due to Error ($MSE$) = 2
- Observed $F$-ratio ($F_{\text{cal}}$) = 12.5
- In ANOVA, the $F$-statistic is defined as:
- Rearranging gives the Treatment Mean Sum of Squares ($MST$):
- The Treatment Sum of Squares ($SST$) is the product of $MST$ and its degrees of freedom:
- Conclusion: The Treatment Sum of Squares is 100 (Option 4).
Correct option: (4) 100
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