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第七章 卡平方 ( ) 测验 PowerPoint PPT Presentation


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第七章 卡平方 ( ) 测验. 第一节 卡平方 ( ) 的定义和分布 第二节 在方差同质性测验中的应用 第三节 适合性测验 第四节 独立性测验 第五节 的可加性和联合分析. 第一节 卡平方 ( ) 的定义和分布. 所谓 ,是指相互独立的多个正态离差平方值的总和,即:. (7·1). 其中, y i 服从正态分布 , 为标准正态离差。.

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第七章 卡平方 ( ) 测验

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5917901

( )

( )


5917901

( )

(71)

yi


5917901

yi

(72)


5917901

v =n

v (7.1)

0+

+

v 2v


5917901

7.1


5917901

(73)

n1 v =n1


5917901

utF

  • 1 ,

  • s

v =1

v s12


5917901

K.Pearson(1900) ()

(74)

OEi=1k v 7.1

ui2 (OE)2/E


5917901

s2C

C> < ,H0


5917901

[7.1] 4517492514522(kg)175.6(kg)2H0: HA: =0.05

6 v =n1=3 /2(1 /2) 0.229.35H00.05H0

:


5917901

CH0 CHA C ,

H0H0

CH0 CHA C H0


5917901

[7.2] 7.150(kg)2

175.6(kg)250(kg)250(kg)2

H0 50HA 50

5%

6

10.540.35H050(kg)2


5917901

s2

, ( )

(75)

(76A)

(76A)

(76B)


5917901

[7.3] 7.1 95%

s2 =175.6 95%L1L2

95%

: L1s2s2L2


5917901

7.1

56.32394.5

n30 n30 N(01)u


5917901

33, ( test for homogeneity among variances )H0 (k)

HA Bartlett(1937)Bartlett( Bartlett test )


5917901

k

,

(77)


5917901

Bartlett

(78)

(79)

niC

(710)

(79)

(711)


5917901

(78)C

H0

H0


5917901

[7.4] 3s12=4.2, s22=6.0, s32=3.1

H0 HA3(HAH03

)

7.1


5917901

7.13


5917901

7.1


5917901

6 >0.7440.500.75H03

C

=27.9496027.14452=0.80508


5917901


5917901

:F134373482113437+3482=69163459.5OE7.2


5917901

7.2


5917901

11

1H011HA11

2 =0.05

3 6


5917901

4

H0 H0

H0

7.2

6 =3.84

=0.2926 H0F111


5917901

( )1/2|OE|1/2

(712)


5917901

7.2

=0.2798 =3.84

2


5917901

30 1

30u

u1.64


5917901

[7.5] F27.331

7.3


5917901

H0F231HA31

=0.05

k=2

6 H031


5917901

(713)

Aan=A+a(713)

(712)


5917901

() (713)7.4

7.4


5917901

[7.6] F29331F27.59331

7.5 F29331


5917901

9331E

E=743(9/16)=417.94

E=743(3/16)=139.31

H0F29331 HA9331

=0.05


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k=4 =k-1=36

, ,H0HAF29331


5917901

9331

(714)

a1a2a3a49331n

(714)

=92.696 =92.706


5917901

(715)

miai

(715)


5917901

()

[7.7] Richland7.65gn s


5917901

7.6

(Steel and Torrie1980)(g)


5917901

H0HA

(E)(P)(n)

1

2 P(5.5y10.5)=P(2.065u1.674)

=0.04710.0195=0.0276

E0.0195229=4.5

0.0276229=6.3


5917901

7.6

=1412=1112 2

6 11 =10.47P0.250.50H0


5917901

(1)n50

(2)5

(3)55Cochran0.51


5917901

7.7

P(55.5y70.5)=P(1.841u3.013)

=0.9887-0.9671=0.0316

0.0316229=7.27,

(OE)2/E=(107.27)2/7.27=1.025

=123=96 9 =10.425P0.250.50


5917901

H0HA

:

(1)

(2)

(3)


5917901

rc =(r1)(c1)

H0 H0HA

22

2C

rc


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22

22

22 =(21)(21)=1


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[7.8] 7.7

7.7


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H0HA

=0.05

O1=26E1=(21076)/460=34.7()

O2=50 E2=(25076)/460=41.3

O3=184E3=(210384)/460=175.3

O4=200E4=(250384)/460=208.7

E7.7


5917901

E

=(21)(21)=16 P<0.05H0


5917901

22 227.8

7.8 22

(716)

(716)


5917901

2C

2CC3

=(21)(c1)=c1c3,


5917901

[7.9] Aph1932237.9Aph

7.9 Aph


5917901

H0HA

=0.05

H0

29E=(19351)/416=23.66

22E=(22351)/416=27.34

7.9


5917901

=(21)(31)=26

P<0.05H0HAAphAph


5917901

2C

( i=123c )

(717)

2C7.10

7.10 2C


5917901

rc

r c r3c3rc

rc =(r1)(c1)


5917901

[7.10] 7.11

7.11


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H0HA

=0.05

H0146E=(481160)/547=140.69

183E=(481205)/547=180.26

7.11


5917901

=(31)(31)=46 ,P>0.05H0


5917901

rc7.12

7.12 rc


5917901

7.12

(718)

( i=12rj=123c )

7.11(718)


5917901

[7.11] 7.13F31F2 313131


5917901

7.13F3(31


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H031HA31H031HA

7.13

1 31


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2 =3.0610.050.1031

3 =3.663312

2 2 =0.60, P=0.500.7531


5917901

7.13F2F33(+11


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