三因素方差分析
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.
. p q r p×q×r
Y ijkl= + j+ k+ l
+ ( )jk+ ( )jl+( )kl
+( )jkl+ ijkl
(i=1,2,……,n; j=1,2,……,p;
k=1,2,……,q; l=1,2,……,r)
SS = SS + SS
= (SSA + SSB + SSC + SSAB
+ SSAC + SSBC + SSABC)
+SS
•
1.
2. p q r p×q×r •
2 x 2 x 2
2 ( x 2 x2
Y ijkl= + j+ l+( )jl+ i(jl)
+ k+( )jk+( )kl
+( )jkl+( )ki(jl)
+ ijkl
(i=1,2,......n; j=1,2,......p;
k=1,2,......q; l=1,2,......r)
SS =SS +SS
=(SSA+SSC+SSAC+SS (AC))
+(SSB+SSAB+SSBC+SSABC
+SS B (AC)
)
•
.
. p q r p×q×r a1 a1 a1 a1a2a2 a2 a2
b1 b1 b2 b2 b1 b1 b2 b2
c1 c2 c1 c2 c1 c2 c1 c2
----------------------------------------------------------------s1
s2
s3
s4
s5
s6
s7
s8
---------------------------------------------------------------
Y ijkl= + j+ i(j)
+ k+( )jk+( )ki(j)
+ l+ ( )jl+( )li(j)
+( )kl+( )jkl
+( )kli(j)+ ijkl
(i=1,2,……,n; j=1,2,……,p;
k=1,2,……,q; l=1,2,……,r)
SS =SS +SS
=(SSA+SS (A))
+(SSB+SSAB+SS B (A)
+SSC+SSAC+SS C (A) +SSBC+SSABC+SS B×C (A))
•
1.
2. p q r
p×q×r
Y ijkl= + i+ i+( )ij
+ k+( )ik+ l+( )il
+( )jk+( )ijk
+( )jl+( )ijl
+( )kl+( )ikl
+( )jkl+( )ijkl+ ijkl
(i=1,2,……,n; j=1,2,……,p;
k=1,2,……,q; l=1,2,……,r)
i ;
j A j
( )ji j i k B k
( )ki k i l C l
( )li l i ( )jk j k
( )jki j k i ( )jl j l
( )jli j l i ( )kl k l
( )kli k l i ( )jkl j k l ( )jkli j k l i
SS =SS +SS
=SS +(SSA +SS A
+SSB +SS B +SSC +SS C
+SSAB +SS A ×B +SSAC +SS A ×C +SSBC +SS B ×C
+SSABC +SS A ×B ×C
)
SS = (SSA + SSB + SSC + SSAB
+ SSAC + SSBC+SSABC)
+SS
268.9 = (153.1 + 12.5 + 3.1 + 24.5
+ 1.1 + 12.5 + 24.5)
+37.5
SS =SS +SS
=(SSA+SSC+SSAC+SS (AC))
+(SSB+SSAB+ SSBC+SSABC+SS B (AC)) 268.9 = (153.1 + 3.125 + 1.125 +30.5)
+ (12.5 + 24.5 + 12.5 + 24.5 +7.0)
SS =SS +SS
=(SSA+SS (A))
+(SSB+SSAB+SS B (A)
+SSC+SSAC+SS C (A) +SSBC+SSABC+SS B×C (A))
268.9 = (153.1 +28.25)
+ (12.5 + 24.5 +2.5
+ 3.1 + 1.1 +2.25
+ 12.5 + 24.5 +4.5)
SS = SS + SS
=SS + (SSA +SS A
+SSB +SS B
+SSC +SS C
+SSAB +SS A×B
+SSAC +SS A×C
+SSBC +SS B×C
+SSABC +SS A×B×C ) 268.9 =22.625+ (153.125 +5.625
+ 12.500 +1.750
+ 3.125 +0.125
+ 24.500 +0.750
+ 1.125 +2.125
+ 12.500 +1.250
+ 24.500 + 3.250)