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การวิเคราะห์ความแปรปรวน PowerPoint PPT Presentation


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การวิเคราะห์ความแปรปรวน. การวิเคราะห์ความแปรปรวนสามารถนำมาใช้ประโยชน์ในการหาคำตอบเกี่ยวกับเรื่องต่างๆ ที่ทำการวิเคราะห์โดยวิธีอื่นไม่สามารถทำได้ดังนี้.

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1. 3 1 1 1 1

(One - way analysis of variance)


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2. 2 1 1

(Two - way analysis of variance)


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3. (experimental unit) 2


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1.


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2. 2

3.


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k

i, i = 1, 2, 3, , k

ni i

n


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xij j

i , j = 1, 2, 3, , ni

T1

i

i

T


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T


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(total mean square)

MS (T)

SS(T)

(Total sum of square)

df(T)

(total deree of freedom)


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(between mean square)

MS(B)

SS(B)

(between sum of square)

df(T)

(between degree of freedom) = k-1


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(within mean square)

MS(W)

SS(W)

(within sum of square)

df(W)

(within degree of freedom) = n-k


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k

F (F-distribution) k-1 n-k

F (asymmetrical shape)


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k

Ho F


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Ho H1


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(df)

(SS)

(MS)

F

k-1

n-k

n-1


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1

4 3 3 0.05


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()

5 8 8 5 4

11 8 12 19

2 7 8 10 11 12

7 9 10 9 10


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Ho :

H1 :

i j


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1

2

3

4

5

6

5

8

8

5

4

2

7

8

10

11

12

4

49

64

100

121

144

7

9

10

9

10

49

81

100

81

100

11

8

12

19

121

64

144

361

25

64

64

25

16

Ti

30

50

45

50


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T = 175


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MS

d.f.

SS

f

SS(B)=1,626.67-1531.25

95.42/3

31.81/9.4

3

= 95.42

=31.81

=3.38

SS(W)=1,777-1,626.67

150.33/16

16

=150.33

=9.4

SS(T)=1,777-1,531.25

19

=245.75

F F 0.05 d.f. (3,16) 3.24


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F 3.38 > 3.24

Ho H1

4 3 0.05


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Tukey LSD Scheffe Student-Newman


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(two-way analysis of variance)

-

-

/


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r

c

n


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Xij i j

j

i

i

j

T


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d.f.

SS

MS

F

r-1

c-1

(r-1)(c-1)

rc-1


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4 3 ANOVA

df SS MS F

10.53

237

79

3

(237/3)

(79/7.5)

(302-20-45)

1.33

10

2

20

(20/2)

(10/7.5)

7.5

45

6

[(6)(7.5)]

11

302


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) H0: 4

H1: 4

) H0: 3

H1: 3


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) F0.5,3,6 =

4.76

5.14

) F0.5,2,6 =

) F

10.53 > 4.76 H0 H1

) F

1.33 < 5.14 H0 H1


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2

3 4


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C

R

L

M

17

34

23

74

15

26

21

62

1

23

8

32

6

22

16

44

39

105

68

212

0.05


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. Ho:

3

H1:

3

. Ho:

4

H1:

4


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Ti.

C

X2

R

L

X2

M

X2

X2

15

26

21

289

1,156

529

225

676

441

1

23

8

1

529

64

6

22

16

36

484

256

39

105

68

17

34

23

=

4,292.5

62

74

32

T.j

44

=4,093.32

T = 212

= 3,745.33


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SS

MS

F

d.f.

SS(R)=4,292.5-3,745.33

2

=547.17

=273.585

=36.07()

SS(C)=4,093.32-3,745.33

3

=347.99

=115.99

=15.29()

SS(W)=940.67-547.17-347.99

6

=45.51

=7.585

SS(T)=4,686-3,745.33

11

=940.67


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0.05

F(0.05,3,6) = 5.14

F(0.05,3,6) = 4.76

F Ho 3 36.07 5.14

F Ho 4 15.29 4.76


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Ho 3 4


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4


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