Question

consider the following table:

	ss	df	ms	f
error			626.7
total	12825.12	18

step 6 of 8: what is the variation of the individual measurements about their respective means? please round your answer to two decimal places.
answer
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Explanation:

Step1: Recall the relationship in ANOVA

In ANOVA, the total sum - of - squares (SS Total) is the sum of the sum - of - squares among treatments (SS Among) and the sum - of - squares of error (SS Error), i.e., $SS_{Total}=SS_{Among}+SS_{Error}$. The variation of the individual measurements about their respective means is the sum of squares of error (SS Error). We know that $SS_{Total} = 12825.12$ and we can find $SS_{Among}$ using the formula for the mean square among treatments $MS_{Among}=\frac{SS_{Among}}{DF_{Among}}$. Given $DF_{Among} = 6$ and $MS_{Among}=884.12$, then $SS_{Among}=MS_{Among}\times DF_{Among}=884.12\times6 = 5304.72$.

Step2: Calculate SS Error

Using the formula $SS_{Error}=SS_{Total}-SS_{Among}$, we substitute $SS_{Total}=12825.12$ and $SS_{Among}=5304.72$. So, $SS_{Error}=12825.12 - 5304.72=7520.40$.

Answer:

$7520.40$