Biometrija_2011
.pdf
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,
,
.( X = 16,8; D = 4,25; (x) = 2.06)
3.6. (n = 50)
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90-94 |
95-99 |
100-104 |
105-109 |
110-114 |
115-119 |
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120-124 |
125-129 |
130-134 |
135-139 |
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N |
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. ( N = 113,5; D = 96,2; (x) = 9,8)
3.7. -
(n = 50) :
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,
.(N . = 16,4; D = 4,6;
(x)= 2,1)
3.8. 15 -
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0,203 |
0,195 |
0,197 |
0,199 |
0,207 |
0,208 |
0,198 |
0,193 |
0,202 |
0,197 |
0,202 |
0,201 |
0,198 |
0,203 |
0,197 |
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,
0,9. ( P =0,2; 0,002 )
62
3.9. (n = 50)
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- 125,5 ( 1 = 10,1 )
- 113,5 ( 2 = 9,8 )
. (d = 6,032 ; >0,999)
100 , , 50 , . , -
, 2,5 ( (x)= 0,8), , - 2,2 ( (x)= 0,78 ). -
. (d = 2,2; -
= 0,95)
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N |
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36,9 |
37,3 |
37,4 |
37,5 |
37,2 |
37,7 |
37,8 |
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36,8 |
37,0 |
37,3 |
36,9 |
36,8 |
37,3 |
37,6 |
. (d=1,87; =0,9).
3.12.
) D ;
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4,2 |
4,0 |
3,8 |
3,5 |
3,8 |
3,5 |
3,7 |
4,6 |
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.D |
3,8 |
3,7 |
3,7 |
3,0 |
3,4 |
3,2 |
3,7 |
3,9 |
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D . (d =1,96; 0,9)
63
IV.
4.1
, ,
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) ( ). ,
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, , .
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. , -
. -
, .
" ". , -
, .
4.2
,
( ) ( .
64
" " ) -
. -
, -
. . 4.1 -
.
4.3
.
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(r q, ). -
( ) -
.
, -
-1 +1. r>0, ,
r<0 - . -
r ,
|r| < 0.3 |
- ; |
0.3 |r| 0.7 |
- ( ); |
|r| > 0.7 |
- . |
, r=0 |r| =1 ,
( . . 4.1 (a- ) ( - )).
,
. -
X Y Y X, X Y.
. -
- q(y/x) q(x/y), q(y/x) q(x/y).C -
q(y/x) q(x/y). -
q(x/y)=q(y/x). -
, -
r q 0 1. -
q(y/x) q(x/y) -
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, r=-1 |
. 4.1
X Y.
66
4.4
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n
( X i X ) (Yi Y )
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(4.1) |
n x |
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: Xi Yi - X Y;
X Y - X Y;
x y - X Y; n - .
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( X i Yi ) |
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r i 1 |
C x C y |
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X, Y, . .
r -
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X i ; |
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X i 2 |
Yi 2 . |
i 1 |
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i 1 |
i 1 |
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r .
67
1
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. 20 . -
. 4.1 [1].
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r .
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- X Y, . -
. 4.2. |
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4.1 |
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Xi * Yi |
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10.0 |
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7.000 |
100 00 |
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10.8 |
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0.73 |
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7.884 |
116.64 |
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0.533 |
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11.3 |
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0.75 |
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8.475 |
127.69 |
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0.563 |
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10.0 |
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7.000 |
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0.490 |
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10.1 |
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6.656 |
102.01 |
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0.423 |
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11.1 |
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7.215 |
123.21 |
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0.423 |
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7.910 |
127.69 |
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0.490 |
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0.61 |
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6.222 |
104.04 |
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0.372 |
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0.70 |
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9.450 |
182.25 |
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0.490 |
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0.369 |
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7.150 |
121.00 |
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0.427 |
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0.72 |
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8.640 |
144.00 |
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0.518 |
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11.8 |
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0.69 |
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8.142 |
139.24 |
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0.476 |
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0.78 |
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10.452 |
179.56 |
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0.608 |
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0.70 |
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7.980 |
129.96 |
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0.490 |
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7.200 |
244.00 |
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0.360 |
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15.6 |
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0.85 |
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13.260 |
243.36 |
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0.730 |
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0.80 |
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10.400 |
169.00 |
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0.640 |
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12.1 |
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0.75 |
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9.075 |
146.41 |
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0.560 |
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237.4 |
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167.939 |
2861.60 |
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9.9598 |
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68
X Y,
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r. r, (4.2)
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(237.4)2 |
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Cx = 2861,60 |
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CY = 9,9598 - |
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r 167 ,919 237 |
,4 14 ,06 / 20 0,564 ; |
43 ,662 |
0,076 |
r .
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, q(y,x) q(x,y) ( . 4.7).
4.5
r
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r . Y,
0.9
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0.6 |
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. 4.2 4.1:
69
, , r 0 ,
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X Y -
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r .
r Z-
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( . r -
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Ln |
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1.15129 Lg |
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( 4.3) |
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Z - r
4 . Z -
Tz :
Tz Z n 3 . |
(4.4) |
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= 0.05) k = n - 2 2 ,
tk,p . r , Tz tk,p .
r Z -
X,Y
r .
Tr , :
T r |
r n 2 . |
(4.5) |
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r ,
Tr tk,p. Tz tk,p Tr tk,p
n. -
nmin ,
r. , nmin > n,
n , nmin n .
4.6
( . ) -
X Y, ,
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n min |
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3 . |
(4.6) |
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- ,
. -
, p = 0.95 ( . = 0.05) =1.96, p = 0.99 ( = 0.01 ) = 2,58, p = 0,999( = 0.001) = 3,29.
-
r nmin .
. -
r =0.564 -
20. ,
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Z - . 4
r=0.564 Z= 0.633. Tz :
Tz 0,633 (20 3) 2,61
2 ,
= 0.05 k = 20-2=18; tk,p = 2,1. Tz = 2.61 > tk,p = 2,1, r = 0.05.
r
0.05. = 0.05 ,
P = 1 - = 0.95, = 1.96.
nmin:
n = (1.96)2 /(0.633)2 + 3 = 12.58 13.