Statistics Dictionary
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Sums of Squares
A sum of squares is the sum of squared deviations from a mean score. For example, a one-way analysis of variance makes use of three sums of squares:
- Between-groups sum of squares. The between-groups sum of squares (SSB) measures variation of group means around the grand mean.
It can be computed from the following formula:
SSB =
kΣj=1
n jΣi=1
(
X j -
X )
2
=
kΣj=1
n
j (
X j -
X )
2
- Within-groups sum of squares. The within-groups sum of squares (SSW) measures variation of all scores around their respective group means.
It can be computed from the following formula:
SSW =
kΣj=1
n jΣi=1
( X
i j -
X j )
2
- Total sum of squares. The total sum of squares (SST) measures variation of all scores around the grand mean.
It can be computed from the following formula:
SST =
kΣj=1
n jΣi=1
( X
i j -
X )
2
It turns out that the total sum of squares is equal to the between-groups sum of squares plus the within-groups sum of squares, as shown below:
SST = SSB + SSW
