Information Technology Reference
In-Depth Information
side of Table D1 summarize the individual deviation calculations for the
total, between-groups, and within-groups deviations. For example, the
first participant's
S
AT score
Y
1, 1
(re
ad
“
Y
one, one”) is subtracted from
the grand mean
Y
T
, yielding
Y
1, 1
−
43, the
total deviation. Likewise, the between-groups deviation is computed by
subtracting the treatm
en
t group mean for level
a
1
(the ze
ro
m
on
ths
of prior study group)
Y
1
from the grand mean, yielding
Y
1
−
Y
T
=
370
−
535
.
43
=−
165
.
Y
T
=
412
Lastly, the within-groups deviation is com-
puted by subtracting the first parti
cip
ant's SAT score
Y
1, 1
from the treat-
ment group mean, yielding
Y
1, 1
−
.
86
−
535
.
43
=−
122
.
57
.
Y
1
=
−
.
=−
.
.
These
summary deviations depicted in the columns of Table D1 labeled “Devia-
tions” provided the ingredients for computing the sums of squares using
the deviational formulas.
The deviational formulas for the sums of squares are as follows:
370
412
86
42
86
total deviations
=
Y
T
)
2
(
Y
ij
−
43)
2
43)
2
57)
2
57)
2
=
(
−
165
.
+
(155
.
+···+
(114
.
+
(124
.
=
27, 367
.
084
+
24, 158
.
484
+···+
13, 126
.
284
+
15, 517
.
684
=
270,268.5
.
(D.5)
between
-g
rou
ps
deviations
=
Y
T
)
2
(
Y
j
−
57)
2
57)
2
43)
2
43)
2
=
(
−
122
.
+
(
−
122
.
+···+
(88
.
+
(88
.
=
15, 023
.
404
+
15, 023
.
404
+···+
7, 819
.
865
+
7, 819
.
865
=
230.496.5
.
(D.6)
within-group
s d
eviations
=
Y
j
)
2
(
Y
ij
−
86)
2
86)
2
14)
2
14)
2
=
(
−
42
.
+
(
−
32
.
+···+
(26
.
+
(36
.
=
1, 836
.
980
+
1, 079
.
780
+···+
683
.
300
+
1, 306
.
010
=
39,772
.
(D.7)
As we note at the top of Table D1, the total deviation (sum of squares
total) is equal to the between-groups deviation (sum of squares between
groups) plus the within-groups deviation (sum of squares within groups).
This relationship can be expressed symbolically as
Y
T
)
2
Y
T
)
2
Y
j
)
2
(
Y
ij
−
=
(
Y
j
−
+
(
Y
ij
−
270, 268
.
5
=
230, 496
.
5
+
39, 772
.
(D.8)
