Unformatted text preview: total variation
Denoted SS(Total) for the total Sum of
Denoted
Squares (variation)
Squares
Sum of Squares is another name for variation 11 OneWay ANOVA
OneWay Are all of the sample means identical? No, so there is some variation between the
No,
groups
groups
This is called the between group variation
Sometimes called the variation due to the
Sometimes
factor
factor
Denoted SS(B) for Sum of Squares (variation)
Denoted
between the groups
between 12 OneWay ANOVA
OneWay Are each of the values within each group
Are
identical?
identical? No, there is some variation within the groups
This is called the within group variation
Sometimes called the error variation
Denoted SS(W) for Sum of Squares
Denoted
(variation) within the groups
(variation) 13 OneWay ANOVA
OneWay There are two sources of variation the variation between the groups, SS(B), or
the
the variation due to the factor
the
the variation within the groups, SS(W), or the
the
variation that can’t be explained by the factor
so it’s called the error variation
so 14 OneWay ANOVA
OneWay Here is the basic oneway ANOVA table Source SS df MS F p Between
Within
Total
15 OneWay ANOVA
OneWay Grand Mean k The grand mean is the average of all the
The
values when the factor is ignored
values
It is a weighted average of the individual
It
sample means
sample x= 1 2 1 2 2 i =1
k k i i ∑n
i =1 n x + n x +L + n x
x=
n + n +L + n
1 ∑n x
i k k 16 OneWay ANOVA
OneWay Grand Mean for our example is 65.08 7 ( 75.71) + 9...
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 Spring '13
 mrs
 Variance

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