ab
a
B c1 , c2
b1 , b2 , b3
C
b2 c2 b1 c1 b3 c1
b2 c1 b1 c2 b3 c2
b1 c2 b3 c1 b2 c2 b1 c1 b2 c1 b3 c2
b1 c1 b3 c2 b2 c1 b3 c1 b2 c2 b1 c2
b2 c1 b2 c2 b3 c2 b1 c1 b1 c2 b3 c1
b3 c2 b1 c2 b2 c2 b2 c1 b3 c1 b1 c1
b1 c1 b3 c1 b2 c2
b2 c 1 b1 c 2 b3 c 2
b1 c1 b3 c2 b1 c2 b2 c2 b3 c1 b2 c1
b2 c2 b3 c1 b1 c2 b3 c2 b1 c1 b2 c1
b1 c 2 b1 c 1 b3 c 1 b2 c 2 b2 c 1 b3 c 2
b3 c1 b2 c1 b1 c1 b1 c2 b3 c2 b2 c2
A
c1 c2
b3 b1
c2
c2
c1
c1
b1 b2
c1
c2
c2
c1
b2 b3
c1 c2
A
b2
c1 c2
b3
c2 c1
b1
c1 c2
b3
c1 c2
b1
c2 c1
b2
c1 c2
yijk = µ + τ i + β j + (τ β )ij + γ k + (τ γ )ik + (βγ ) jk + (τ βγ )ijk
yijk
A B
µ τ i , β j
C
(τ β )ij A
AB
i = 1, 2, . . . , a ; j = 1, 2, . . . , b k = 1, 2, . . . , c
B γ k , (τ γ )ik , (βγ ) jk
(τ βγ )ijk C
AC
BC AB ABC
B H 0 : β j = 0 =0 H 1 : β j ̸
j = 1, b j = 1, b C
H 0 : γ k = 0 =0 H 1 : γ k ̸
k = 1, c k = 1, c BC
H 0 : (βγ ) jk = 0 H 1 : (βγ ) jk ̸ =0
A B AB C AC BC ABC
j = 1, b k = 1, c j = 1, b k = 1, c
a− 1 b− 1 (a− 1)(b− 1) c− 1 (a− 1)(c− 1) (b− 1)(c− 1) (b− 1)(a− 1)(c− 1) abc − 1
SC A =
1 bc a
Y ... =
a
∑ i=1 b
SC A SC B SC E AB SC C SC AC SC BC SC E ABC SC T
Y ...2 yi.. − abc 2
c
∑∑∑
yijk
i=1 j =1 k=1
SC B =
1 ac
b
∑
j =1
Y ...2 y.j. − abc 2
CM A CM B CM E AB CM C CM AC CM BC CM E ABC
CM B CM E AB CM C CM E ABC CM BC CM E ABC
SC E AB =
1 c
a
b
∑∑
yij. −
bc
i=1 j =1
SC C =
SC AC =
SC BC =
1 b
1 a
a
1 ab
c
∑∑ i=1 k=1 b
∑ 2
y..k
k=1
1
2
yi.. −
i=1
c
∑
b
∑
ac j
=1
Y ...2 y.j. + abc 2
Y ...2 − abc
Y ...2 − SC A − SC C yi.k − abc 2
c
∑∑
a
1
2
2
y.jk
j =1 k=1
Y ...2 − − SC B − SC C abc
SC E ABC = SC T − SC C − SC AC − SC BC − SC A − SC B − SC E AB a
SC T =
b
c
∑∑∑ i=1 j =1 k=1
2
yijk
Y ...2 − abc
B H 0 : β j = 0 H 1 : β j ̸ =0
j = 1, 3 j = 1, 3 C
H 0 : γ k = 0 H 1 : γ k = ̸ 0
k = 1, 4 k = 1, 4
BC H 0 : (βγ ) jk = 0 H 1 : (βγ ) jk ̸ =0
j = 1, 3 k = 1, 4 j = 1, 3 k = 1, 4
2 2 4 3 6 6 12 35
A B AB C AC BC ABC
77,5556 128,3889 36,2778 434,0833 20,6667 75,1667 50,8333 822,9722
38,7778 64,1944 9,0694 144,6944 3,4444 12,5278 4,2361
7, 0781 34, 1574 2, 9574
B
C
CM E ABC = 4, 2361 CM E AB = 9, 0694
[1] [2]
