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SUMMARY OF FORMULAS FOR CHAPTER 8
SUMMARY OF FORMULAS FOR CHAPTER 8 369
Formula
Number Name Formula
8.2.1 One-way ANOVA
model
X ij = m + t i +P ij
(Continued )
8.2.2 Total sum-of-squares
8.2.3 Within-group
sum-of-squares
8.2.4 Among-group
sum-of-squares
SST = a
k
SSW = a
k
SSA = a
k
n j
a
j = 1 i = 1
j = 1
i = 1
j = 1 a nj
1x ij - x ##2 2
1x ij - x # j2 2
n j 1x # j - x ##2 2
8.2.5 Within-group
variance
MSW =
k nj
a a
j = 1 i = 1
k
1x ij - x # j2 2
a 1n j - 12
j = 1
8.2.6 Among-group
variance I
s 2 = ns x
2
8.2.7 Among-group
variance II
(equal sample sizes)
8.2.8 Among-group
variance III (unequal
sample sizes)
MSA =
MSA =
n a
k
j = 1
k
a n j 1x # j - x ##2 2
j = 1
1x # j - x ##2 2
1k - 12
1k - 12
8.2.9 Tukey’s HSD
(equal sample sizes)
8.2.10 Tukey’s HSD
(unequal sample
sizes)
MSE
HSD = q a,k,N-k
A n
MSE
HSD* = q a,k,N-k
A n
a 1 + 1 b
n i n j
8.3.1 Two-way ANOVA
model
X ij = m + b i
+ t i +P ij
8.3.2 Sum-of-squares SST SSBl SSTr SSE
representation