-

,

..

-

2010

519.2: 519.6 ..

/ . : , 2010.102 .

.

211000 , 211000.68

2007-2008 , , . 2015 , .

, 2010 .., 2010

2

1. .....................................................................................................4 1.1. ...................................................................................4 1.2. ......................................................................5 1.3. STATISTICA .....................................................7 2. ..............................................................................9 2.1. ..............................................................................................9 2.2. .............................................................................11 2.3. .....................................11 2.4. ............................................................................14 2.5. , .................16 2.6. .........................................................................18 3. ............................................................20 3.1. , ..........................................................................20 3.2. ........................................................................................................22 4. , , ........................................................................................22 4.1. . . .......................................................................................22 4.2. ...........................23 4.3. .........24 4.4. ......24 4.5. ...................................................26 4.6. STATISTICA .....27 5. ...................................................30 5.1. ...................................................................30 5.2. , ....................................................35 5.3. , ............................................................................................................37 5.4. STATISTICA............................................................38 6. ..........................................40 6.1. ........................40 6.2. .....................44 6.3. STATISTICA................................................46 7. ....................................................................50 7.1. .....................................................................................50 7.2. .....................................................................54

3

7.3. ........................................................................55 7.4. STATISTICA........................................59 8. ............................................................................61 8.1. , ...................................................61 8.2. STATSTICA...............................................65 9. ...............................................................67 9.1. , .......................................................67 9.2. STATISTICA...................................69 10. ..................................................................................74 10.1. ..............................................74 10.2. .............................82 11. ...........................................................................84 11.1. .................................................84 11.2. .....................................94 12. .......................................................98 12.1. ............................................................................98 12.2. ..............................................................................98 13. .......99

4

1.

. : . . [3] . . [2].

1.1.

, .

( . experimentum , ), , . , , . , ( ). , , [4].

, . , - . , , . , , , . , , . . . , , , . .

5

, .

(. measurement) , . , , , , .

. ; , , , . , , . , . ; .

, (experimental design techniques) - , .

, , () .

, , .. .

1.2. ,

, . , ; , , , [1]. , .

6

- . , . ; . , .

, .

(. [1]). ,

. , 210 . . , , , (205 ), (215 ).

, , 211,3 . , , , , , , , 211,3000 , , , 211,3001 .

, . . , . , , . , .

, . , , . , , . . , , , , . , , , , .

, ,

7

. , , . ( 0,5106 ). , .

, , . , . , , . , , , . ( ). .

. (, , . .) . , .

. . , 3 , ( ) , , 2,5 3,5 2,99 3,01 . , .

. , , , .

1.3. STATISTICA STATISTICA

, StatSoft [7]. STATISTICA (. 1.3.1) (data analysis), (data management), (data mining), (data visualization).

8

STATISTICA . :

Base , , ;

Advanced Linear/Non-Linear Models , , , , . ;

Multivariate Exploratory Techniques , STATISTICA , , ;

QC (quality control) , , , ;

Neural Networks , , , ;

Data Miner , . STATISTICA

OS Windows. STATISTICA STATISTICA.

9

1.3.1. STATISTICA.

2.

2.1. ,

. ( ). .

. ) , :

, . )

, , 180 , . : () , , , .

10

() , ( ) . .

, [2].

, , , D, . . . , W ; : , . .

, ( ) , , .

, - , , .

, : , , , , . . , , , ( , , . .) -.

, , , , . , (, , , . .).

, , , .

, . , , , ... , W , , A B C ... W = U.

, .

.

11

) . () .

) . : .

, . .

, , , .

2.2. ,

. ,

. , A , A A.

2.3. ()

.

Q , , N . :

NMQ (2.3.1)

. 100 , 45. , = 45, N = 400, Q = 0,40.

, , . .:

10 Q (2.3.2) ,

, . , . .

12

, , . , , .

, . , 12 000 24 000 , 0,5016 0,5005. , , , , , 0,5.

, N Q , , , . N Q , , , . , .

)(Ap . .

, - , . ( ). , , ( ), :

nmnmp , , (2.3.3)

: m , ; n ; p .

, .

. : , ,

13

. ( ).

. :

1pNMp

N

, (2.3.4)

. (2.3.4)

, (2.3.3). , . , , . , , .

(2.3.3) , , , , .

, , . 1 0 , .

, , , , , .

. 1001 1000 , , 0,001, , . 0,001 , .

, , , , , , .

, .

, . .

14

0)( Vp , (2.3.5) V .

, . . 0)( Up , (2.3.6)

U . ,

, , . .

mmp

nmp

010

. (2.3.7)

, ,

10 p . (2.3.8) ,

.

, . .

1)()( ApAp , (2.3.9) , . :

nmnAp

nmAp

)(

)(. (2.3.10)

2.4.

, . nAAA ...,, 21 .

, , :

)...,,( 21 nAAAB . (2.4.1) (2.4.1)

:

15

n

ii

n

AB

AAAB

1

21 ...

. (2.4.2)

.

, . .

n

ii

n

ii

nn

ApAp

ApApApAAApBp

11

2121 )(...)()()...()(. (2.4.3)

, (.. ).

. a , b , c , d e . , , , (. . , ).

: , ; A1 , ; A2 , ; A3 , ; A4 , ; A5 , . : 321 AAAB . , (2.3.3)

, :

nc

nb

na

edcbacba

nmBp

)(

16

nbAp

nbAp

naAp

)(

)(

)(

3

2

1

,

: )()()()( 321 ApApApBp

. ,

(2.4.3) .

2.5. , ,

, . .

, , .

, .

, ( ) .

.

. )

. ) . ) . ,

, .

. ,

, .

17

, , .

, , , .

: )/( BAp A,

, ; ),...,/( 21 nBBBAp ,

, nBBB ,..., 21 . , :

)()/()()/(

BpABpApBAp . (2.5.1)

( ). , :

)()/()()/(

BpABpApBAp . (2.5.1)

, , .

, , - , . , , " -". , , . , , "" , , .. . , , "" . , . , , "

18

", . , (WCC), , , WCC .

2.6.

.

, . . .

, , D . A : DCBA .

, B , nAAA ...,, 21 , :

)...(

)...,,(

21

21

n

n

AAAB

AAAB. (2.6.1)

. , . .

n

ii

nn

n

Ap

AAAApAAApAApApAAApBp

1

121213121

21

).../(...)/()/()()...()(

(2.6.2)

(2.6.2) :

)/()()/()()( BApBpABpApABp . (2.6.3) , , ,

, :

.

, (2.6.2):

19

1

1

2133

122

/)(

...)/()(

)/()(

n

iinn AApAp

AAApApAApAp

: )(...)()()()...( 32121 nn ApApApApAAAp (2.6.3)

, , , . .

. : 1a 1b , 2a 2b .

, , .

: : 1A ; 2A ;

21 AAA .

, )()( 21 AApAp .

(2.3.3).

m n, m n ( ).

2a . , :

21 aam . , ,

: ))(( 2211 baban .

:

20

))(()(

2211

21

babaaaAp

(2.6.4)

(2.6.4):

)()(

11

11 ba

aAp

, :

)()(

22

22 ba

aAp

. (2.6.4) :

)()()( 21 ApApAp (2.6.5) . (2.6.5) ,

() n , ,

n

ii

n

ii ApAp

11)( (2.6.6)

, , , , , :

pApApAp n )(...)()( 21 :

nn

ii pAp

1)( (2.6.7)

3.

3.1. ,

, . . . , , n .

, ( ) . . A, . . A , A . , n k , . . )(kPn .

21

n , . . : , . . , n .

, A , A , 1)()()( ApApAAp .

:

AAAAAAAA . :

1)()()()()()( 2 ApApAApAApAApAAp , n :

1)()( nApAp . (3.1.1) (3.1.1)

(n + 1) .

: kknk

nn pqCkP)( , (3.1.2)

: )(kPn k n ;

)!(!!

knkkC kn

(3.1.3)

n k; p ; q .

n k , :

n

ennn

2! (3.1.4)

(3.1.4) n. ( %) n. . (3.1.3) (3.1.4), , n = 10 0,8 %, n = 20 0,4 %.

. 1, . . 1)()( ApAp , , n , nAp )( .

22

, , , :

nApAp )(1)( . (3.1.5) 3.2.

,

, , : ( ) , , . , , (3.1.1) , , k0 , p n.

npk 0 (3.2.1) k0 .

, (3.2.1) , .

(3.2.1) .

4. , ,

4.1. . .

, , . , , .

: () .

23

, (, 0, 1, 2, 3; 0, 1, 2, 3, 4, 5; ).

, , . .

, , . , . . , . , ; .

X, Y, Z , x, y, z, (, X ; 1, 2, 3, . . . , n X n ; 1, 2, 3, . . . , n x ).

4.2.

, , , . . 1, 2, 3, . . . , n, ( ) .

, , .

:

; ,

, X;

,

24

, .

4.3.

X, ),( pnB , x : 0, 1, 2, ..., n. X :

kknkn pqCkKP

][ , (4.3.1)

: nk ...,1,0 ; pq 1 ; !)!(

!kkn

nC kn n k.

STATISTICA [7], binom(x; p; n) , , X, n, p x.

, ][ xXP , :

x

k

kknkn

x

kpqCkKP

00][ (4.3.2)

, STATISTICA ibinom(x; p; n).

: e

kkKP

k

!][ , (4.3.3)

STATISTICA poisson(k; ), ipoisson(k; ).

: 1)1(][ kpkKP (4.3.4)

STATISTICA geom(k; p), igeom(k; p).

4.4. [a,b], R(a,b),

, :

],[,0

],[,1)(

bax

baxabxp (4.4.1)

25

)(xP , :

.,0

),(,

;,0

)()(

bx

baxabax

ax

dxxpxPx

(4.4.2)

, :

x

expmx2

2

2)(

21)( , (4.4.3)

P(x) :

x myx

dyedyypxP 22

2)(

21)()(

(4.4.4)

m (m) ( 2 ) X:

mdxexXMmx2

2

2)(

21][

, (4.4.5)

222)(

222 22

21])[(][][

mdxexXMXMXDmx

(4.4.6)

.

STATISTICA (4.4.3) , normal(x; m; ). x: inormal(x; m; ).

m=0, , 2=1, .

:

x

expx2

)( 2

21)( . (4.4.7)

:

x t

dtexP 2)( 2

21)(

(4.4.8)

, , :

26

0,00,)(

xxexp

x (4.4.9)

. P(x) X,

:

0,0

0,1)( 0

x

xedtexP

xxt . (4.4.10)

STATISTICA (4.4.9) , expon(x; ). x: iexpon(x; ).

, , , .

, , :

21

2

0

12

0

12

1

1)(

n

tn

tn

nx

dtetn

dtetxp

(4.4.11)

: n . STATISTICA

, student(x, n). x: istudent(x, n).

4.5.

(X,Y) p(x,y), :

22

22

21

2121

21

2

221

)())((2)()1(2

1exp

121),(

mymymxmx

yxp

(4.5.1)

m1, m2, 1, 2, (m) ( 2 ) X, Y , .

X, p(x), :

21

21

1 2)(exp

21),()(

mxdyyxpxpX (4.5.2)

27

Y, p(y), :

22

22

2 2)(exp

21),()(

mxdxyxfypY (4.5.3)

(4.5.2, 4.5.3) , p(x,y) X, Y , : M[X]=m1, D[X]=12 M[Y]=m2, D[Y]=22.

X Y :

2121

21

),())((

))((),cov(

dxdyyxpmymx

mYmXMYX. (4.5.4)

(4.5.4) , X Y.

X Y =0, (4.5.1) :

)()(),( ypxpyxp YX . (4.5.5)

.

4.6. STATISTICA STATISTICA 8.0.

, . STATISTICA , :

Spreadsheet ( .), , ;

Workbook ( .),

Spreadsheet , .

Workbook, .. . Workbook , : FileNew Workbook Insert empty spreadsheet ( ) OK.

spreadsheet (1010), . , , Excel ,

28

, : InsertAdd Cases, (How many), (Insert after cases). InsertAdd Variables

, (FileSave As) .

(4.4.3, 4.4.4), 50-.

Var1 =normal(x; m; ), , Var1, Var1 ( ) Variable Specs Long name, =normal(v0;25;10) OK. v0, ( ) 1, 2, 3 , v0-1 0, 1, 2

Long name (Var2) =inormal(v0;25;10), Var3 , Long name (Var3) =v1.

, STATISTICA . Graphs2D GraphsScatterplots, Advanced Graph typeDouble-Y : FitSpline. Variables X: Var3, Y Left: Var1 Y Right: Var2. OK. 4.6.1. , , , , , .

29

4.6.1.

.

. STATISTICA . . (0,max) =rnd(max), max . Long name (Var4) =vnormal(rnd(1);25;10), . , StatisticsBasic Statistics/Tables Descriptive statistics, Var4, Variables, Histograms, 4.6.2. STATISTICA F1.

30

4.6.2.

.

5.

5.1.

[3]. . . , , , , , . () (). , . .

, , . , , (, ); (, ); (, , ) . . , , , .

31

, . .

, , , , . , . , , . , , , , , , . , , .

. . , . . , (, , , ) 1, 2, 3, 4. , , , (, ), , , .

, , . ( ) , , . , . . [5].

. " " , , . , , " ", . , , , , . :(a) , (b) (), (c) (d)

32

( ). , : (a) , (b) (), (c) (d) .

a.) . , , ; . , , 2 (, ). - , , , .. .

b.) () , , . " " " ". . - . , , , , , 18% . : , , .

c.) , . , , , . , 40 , 30 , 20 40 30 40 .

d.) . , , , , : x , y. . , , , 200 , 100 , . (, ) . ,

33

.

. , . , , . ( : , . .) (. . ) . , . . , . , , . , , , , . , , , . , .

, - , , , . , , . , , . . , , , . , 15 % , 15 %. , , .

, , , , . , , . , , .

34

, . . , .

. . , , , : m ( ) m . ( ) ( , .).

, . . . .

, . m , , . , X mmm PX ,, , mX m, m , mP , , . )...,,( 21 mm xxxX m , X mP .

, lk XX , , k, l , .

lX X , ll Xx , kX X kk Xx . . .

, , .

.

35

5.2. ,

: , . .

. X , ...,, 21 xx ...,, 21 pp [] X :

i

ii pxXM ][ (5.2.1)

, (5.2.1) . (5.2.1) , , .

:

dxxpxXM )(][ (5.2.2)

)(xp X. . 1. [] = , . 2. [] = [] [+ ] = [] + , . 3. Z

X: Z = h(X). , Z =tg(X). Z M[Z], :

i

ii pxhZM )(][ (5.2.2)

, (5.2.2) . 4. nXXX ...,,, 21

. :

32121 ...... XMXMXMXXXM n . (5.2.3) 5. Y

. YX :

][][][ YMXMYXM . (5.2.4)

. , (5.2.4) ,

, .

36

X D[X]. :

1

22 ])[(]])[[(][i

ii pXMxXMXMXD , (5.2.5)

, (5.2.5) . ][XD

X. . 1. 0][ XD . 2. X ,

: 0][ XD . 3. ][][ 2 XDccXD , c=const. 4. ][][ XDcXD , c=const. 5. Y

: ][][][ YDXDYXD

, , X N. X:

N

iixN

x1

1 (5.2.6)

:

N

iix xxN 1

22 )(1 (5.2.7)

2x :

N

iix xxN 1

2)(1 . (5.2.8)

x :

N

iix xxN 1

2)(1

1 . (5.2.9)

, (5.2.9) , (5.2.8) ( N), X.

37

5.3. ,

nxxx ...,, 21 , :

ng xxxx ...21 (5.3.1) :

n

xx

n

ii

g

1

)lg()lg( (5.3.2)

xH : 1

1

11

n

i iH xn

x (5.3.3)

, : [/], [/] ..

, :

Hg xxx . (5.3.4) X

: , , , .

X.

, .

X (Q1, Q2, Q3) (. 5.3.1), :

213 QQRQ

. (5.3.5)

5.3.1. .

38

90- 10- : 1.09.01090 xxPP (5.3.6)

:

xV x , (5.3.7)

: %100

xC xV

. (5.3.8)

x ),( 21 , 1p :

121 xP . (5.3.9) 1 ,

. 1 , 0,90; 0,95; 0,99. X.

, , , X. :

n

iii ppxH

12log)( . (5.3.10)

:

dxxpxpxH )(log)()( 2 (5.3.11)

(5.3.9) n , .. n, , .

( , ..) .

5.4. STATISTICA .

. . , ,

39

. ( " ") : .

, 68% 1 , 2 95% . , , , -2 +2, 5% ( , ( )). STATISTICA, , , ; , z- (.. , ) 4, , STATISTICA .0001, (.. 99.99%) 4 .

StatisticsBasic Statistics/Tables Descriptive statistics Summary Statistics. ( ) (Valid N), (Mean), (Std.Dev.), (Minimum) (Maximum) . Descriptive statistics .

(Probability Calculator). (. 5.4.1.) . StatisticsProbability CalculatorDistributions , ( ), : (mean), (st.dev.), (p) (x: Xx ). (Density Function) (Distributtion Function).

40

5.4.1. .

6.

6.1.

() . , .

X . X. , X; , . , , X N(0, 1); , N(m, 1), bma , . , 1/3 (1, 5); X [3].

X . .

41

0. 0 () H1,. , 0 , 00 : H , 0 , :

;:;:;:;: 1)4(

10)3(

10)2(

10)1(

1 HHHH 10 , , . .

, 0, . X, Z, . 00 : H , .

, , , , . . , . V Z, a Vk , , 0, Vk :

0/ HVZP k . (6.1.1) Bz Z,

. : 0, kB Vz ; 0, kB VVz \ . , , . Vk Z, 0, ; V \Vk 0.

Vk. Z 1. , 00 : H , 1, 001 : H , () Z, . . :

1zZ zZ , (6.1.2)

42

1z z Z 1 , 0. , - .

01 : H , Z, . . :

2

21

zZ

zZ . (6.1.3)

.

: 1. 0H 1H ,

. 2. . 3. Z 0H . 4. Z

, 0H . 5. Vk

: 1zZ zZ , :

2

21

zZ

zZ

6. Bz .

7. : kB Vz , 0H

; , kB VVz \ 0H , . . , 0H

. 0H

, 0H . , , 0H , . , 0H , . ,

43

, 0H , . . (6.1.2).

, 0H , 1H . ( 1H ) [3]:

1/\ HVVZP k . (6.1.4)

2 . 2 ,

rknp

npn

k

kk ...,,2,1,)( ,

, N(0,1). , , 5knp . , .

nxxx ...,, 21 X. 0H , , X F(x).

0H 2 . X. , X r ,..., 21 , , r , X , , , X.

kn , k ,

rk ..,,2,1 . , nnr

kk

1.

X, kp , X k , . . rkXPp kk ...,,2,1, . ,

r

kkp

11 .

:

r

k k

kk

npnpn

1

22 )( (6.1.5)

0H , :

44

)1(212 lr , (6.1.5)

)1(21 lr 1 2 )1( lr , l , ; :

)1(212 lr , (6.1.6)

0H .

6.2. :

, , , . t- . . , , . . , . . .

, , (. . ), , .

. , , . , : , , , (, ) / ().

, , , .

( ) .

45

. n : , ( , , , . .), () n. n k , k n. , , k n k n, . , .

1. : 1n 2n . 0H : .

: 1) ; 2) ; 3) . 2. : niyx ii ...,,2,1),,(

X Y, . 0H : X Y .

: , .

3. : knnn ...,,, 21 . 0H : .

: 1) ; 2) . 4. : n.

0H : .

: 1) ; 2) . 5. : k n.

0H : .

: 1) ;

46

2) . 6. , . 1) : n

X Y, (0, 1 +, , . .).

0H : . : . 2) : n

kXXX ...,,, 21 , . 0H : . : . 7. , . 1) : X Y,

. 0H : X Y . : 22 (

, 2 ). 2) : X Y,

. X k , Y r .

0H : X Y . : rk ( 2 ).

, , [35].

6.3. STATISTICA (p-)

"" ( " "). , p- ( Brownlee, 1960) , . p- . , p- , . , p- = .05 (.. 1/20) , 5% , . , ,

47

, . (, , , 5% 95% ; , , ). p- .05 " " .

, "". , , . , (.. ) , , , . p=0.05 , , (5%). , p =0.01 , p=0.005 p=0.001 . , , .

, , ( ) . , 10 ( 45 ), , ( 20) p .05, . , , , , , . , ( ) -

48

. .

, Nisbett, et al., 1987. 2 . , 120 , 12. , , 50/50. , . , ? , , . , . , ( ) .

, "" (.. ), . , , , , . , "" ( ) , . . , . , (, 60% , 40% ), 10 , , , , , : 6 4 . , 10 -? , , , , , 10 . , , , , . 10 , , , - . , , , , . : , .

2 (6.1.5). STATISTICA

49

. StatisticsDistribution Fitting, (. 6.3.1), Normal. (), Parametrs . (Chi-Square), (df) (p). (p) .

6.3.1. .

STATTSTICA

StatisticsNonpametrics (.6.3.2).

6.3.2. .

50

Nonpametrics . -. (. 6.3.2), (. 6.3.2), (. 6.3.3), (Mann-Whitney U-test). (p-level) 0H , , .

6.3.3. .

7.

7.1. ,

. , , , ; . . , , , - . .

51

. (, ...) (, , ) , () , , . , , . , , . "" () , , , , , . , . . , , , A, B, - " A B", .. . () , .

. , , - , . , , " -". , , . , , "" , , .. . , , "" . , . ,

52

, " ", . , (WCC), , , WCC .

, () . , , , - . , . . , - . , WCC : WCC. , .

, . Y nxxx ...,, 21 , , Y. Y (), nxxx ...,, 21 , .

, , . .

, , , , - ().

m mxxx ...,, 21 , :

)...,,( 21 nxxxfY , (7.1.1)

53

: )...,,( 21 nxxxf Y, )...,,( 21 nxxxf , a . . , (7.1.1) . , , , , () . , , , . .. , .

(, STATISTICA) nxxx ...,, 21 .

: . : , , , .

, :

: xY 10 ; (7.1.2)

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66

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12.1. 1. . . . . .: , 1985. 272 .: . 2. . . : . 2- ., . . ., , 1983. 223 . 3. . . . STATISTICA, EXCEL: . .: : -, 2004. 464 . 4. . . . .: 1974. 120 .: . 5. . ., . ., . . . . .: , 1983. 420 .: . 6. A. E. : . 2- .: . 2006. 752 .: .

12.2. 7. . [ ] . . . : . . -, 2010 : http://slovari.yandex.ru/~//, . . . . ., . 8. StatSoft : http://www.statsoft.ru/ . StatSoft Russia 2010. 9. Wolfram Research, Inc. (http://www.wolfram.com/). Wolfram, Mathematica. 10. . [ ] : . http://psi-logic.narod.ru/fft/fft.htm. 11. [ ] : . http://alglib.sources.ru/fft/fft.php. 12. . : . [ ] : . http://www.gotai.net/documents/doc-nn-002.aspx

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