The document reports the results of a statistical analysis experiment with five factors (A, B, C, D, E) and their interactions. The analysis of variance showed significant effects of factors A, B, C and their interactions on the response variable. Specifically, it found that 80% of the variability in the response was explained by factors A, B, C and their interactions based on an F-test comparison of the mean squares. Tables are included showing the experimental design and results.

1. ( A,B,C,D,E)( , , , , )
EDCBA
AEDCB
BAEDC
CBAED
DCBAE
ijk i j k l ijklmy

2. 11 1
: 0: 0 : 0
, ,
: 0: 0 : 0
O jO i O k
ji k
HH H
HH H
SPSS
0.05
General linear model univariteAnalyses
SS
2 25
... ....
2
1
2 25
. .. ....
2
1
2 25
.. . ....
2
1
2 25
... ....
2
1
25 5 5 5
....
2
1 1 1 1
10
5 5
342.8
5 5
12
5 5
24.4
5 5
436
5
i
baste
i
j
dama
j
k
katalizor
k
l
ghelzat
l
total ijkl
i j k l
error total
Y Y
SS
Y Y
SS
Y Y
SS
Y Y
SS
Y
SS Y
SS SS ghelzat katalizor dama basteSS SS SS SS
1 , ( 1) ( 4)
1, 1, 1, 1
total error
baste ghelzat katalizor dama
df n df n i j k l
df i df l df k df j
1 2: ( , )O ORH F F n n

4. ( )( )( )

5. oFoFoF

6. ( ) ( ) ( ) ( )ijk i j k ij ik jk ijk ijklY
1
1
1
1
1
1
1
: 0 , : 0
: 0 , : 0
: 0 , : 0
:( ) 0 , :( ) 0
:( ) 0 , :( ) 0
:( ) 0 , :( ) 0
:( ) 0 , :( ) 0
O i i
O j j
O k k
O ij ij
O ik ik
O jk jk
O ijk ijk
H H
H H
H H
H H
H H
H H
H H
SPSS0.05
General linear model univariteAnalyses
univaritetype modelfull factorial
Typsource

7. Sum of squares
SStotal= SSA + SSB + SSC + SSAB + SSAC + SSBC + SSABC + SSerror
df
Mean Square
dfSSMs =
MsMsFO =
FO
FOF
P-valueFO
sigP-valueHO

8. HO
R2
( )ijk i ik ijkly
Rsquare= 80 %

9. ( A )
( B )

10. E(A2B2)F(A2B3)D(A2B1)C(A1B3)B(A1B2)A(A1B1)
D(A2B1)E(A2B2)F(A2B3)B(A1B2)A(A1B1)B(A1B3)
C(A1B3)D(A2B1)A(A1B1)F(A2B3)E(A2B2)C(A1B2)
F(A2B3)C(A1B3)B(A1B2)A(A1B1)D(A2B1)D(A2B2)
B(A1B2)A(A1B1)E(A2B2)D(A2B1)C(A1B3)E(A2B3)
A(A1B1)B(A1B2)C(A1B3)E(A2B2)F(A2B3)F(A2B1)

11. ijkl i j k l ijklmij
y
11 1
1 1
: 0: 0: 0
, ,
: 0: 0 : 0
: 0 : 0
,
: 0 : 0
O ijO jO
ji ij
O k O l
k l
HHH
HH H
H H
H H
SPSS
SS
( )
total A B AB C D error
error total A B AB C D
SS SS SS SS SS SS SS
SS SS SS SS SS SS SS
1 , ( 1) ( 4)
1, 1, 1, 1
total error
A C D B
df n df n i j k l
df i df l df k df j

12. SS
Ms
df
, ,
1 1 1 1
,
1 1
A B AB
A B AB
C D
C D
SS SS SS
Ms Ms Ms
a b a b
SS SS
Ms Ms
c d
error
Ms
F
Ms
1 2: ( , )O ORH F F n n
FO
FOF
P-valueFO
sigP-valueHO
HO
R2

14. This document was created with Win2PDF available at http://www.daneprairie.com.
The unregistered version of Win2PDF is for evaluation or non-commercial use only.