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(Jbjnjfts c` [tdtestekdb Njtacls `cr [kejftefflk Jxpjrenjfts)
=4
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?
=.=:nn ;0.::= nn ;0.: nn
;0.::?4
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;
(ufkjrtdefty) 4 4
4.? :.? P :.< P (crljr) 4 4= 4 (prjkesecf) =.4 P (rjpjdtdoebety) (rjprclukeoebety) ? (dkkurdky)
]rcodoebety
ljfsety
Dkkurdky
]rjkesecf Pdbuj
_j`jrjfkj vdbuj
4.;8 (dkkurdky) (prcodoebety ljfsety) (prjkesecf) ( attp8//jf.weiepjled.crg/weie/DkkurdkySdflSprjkesecf 4? ?::7)
?. (segfefflkdft fflgurjs)
(segfefflkdft fflgurjs)
?
: 0 :.4 P, :.? P, . . . ,:.5 P =.4 P
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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qojst q (?.4)
qojstqq
q () xy x y q xojst yojstqx+y< q
q> x+y > (xojst+yojst) (x+y) (?.?)
?.4(bjfgta c` rcpj) ( !)
d > (4 (?4.;4 =.=:)kn; (eflerjkt njdsurjnjfts)
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
5/23
:
(?.?)
> d+o > (4 (;7.5; =.4=) kn ;7.5;
=.4= ;7.1;kn;1.=;kn
o o > (?4.;=7 =.==:)kn
>d+
o > (4 (;7.5?7 =.=::) kn
7 ? () d 7 7
> (;7.5; =.=::) kn
crljr
> (;7.5; =.=0)kn
() ;7.17kn;7.55kn (prcodobj rdfgj c` vdbuj)
(crljr)
crljr
qxy xy
q> xy > (xojst x)(yojst y) >xojstyojst (xojsty +yojstx+xy)
x xy yq xojstyojst (xojsty +yojstx) (?.;)
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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0
qxojsty +yojstx
q
qojst x
xojst+
y
yojst(?. qojst q
@(q) qqojst
(?.:)
(?.@(xy) @(x) +@(y) (?.0)
?.?(drjd c` rjktdfgubdr pbdtj) 4 nn
w
w> (4?.: =.:)kn, > (1.1 =.;)kn ()
Dojst > wojstojst > (4?.: 1.1)kn? > 44= kn?
Dnef> wnefnef> (4?.= 1.:)kn? > 4=? kn?
Dndx> wndxndx> (4;.= 5.4)kn?
> 441.; kn
?
1 4=?kn? 441 kn?
D> (44= 1)kn?
=.;
w
@(w) > =.:
4?.:>
=.;
1.1 > ;.
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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7
7. 7. 1.4 (44= 1)kn? 7.?% rubj c` tauno ()
44= kn?(4.44=?) kn?
crljr () DD (=.4 4=?) kn? rubj c` tauno
@(D) > =.4 4=?
4.4 4=?
> 5.4%
7. (44= 1)kn? D > (4.4 =.4) 4=? kn? rubj c` tauno
(?.0)
crljr
rubj c` tauno ()
(\dybcrs tajcrjn) `(x)=, 4, . . . , (f+ 4)x > k
`(x) >f
i>=
`(i)(k)
i! (x k)i + `
(f+4)()
(f+ 4)! (x k)f+4 (?.7)
xk`(x)x=`(x) `(k) +`(k)(x k) + `
(k)
? (x k)? +. . . (?.1)
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1
`(x) > sef x
sef x x x;
;! +
x:
:! x
7
7! +. . . (?.5)
x rubj c` tauno
(trdfskjfljftdb `ufktecfs) (drgunjft):
;. (rdflcn ufkjrtdeftejs dfl fcrndb lestreoutecf)
(jrrcr)0 (rdflcn ufkjrtdeftejs) (systjndtek ufkjrtdeftejs)7
(rdflcn ufkjrtdeftejs) (rjdktecf tenj) (fcrndb lestreoutecf) (oeds)
(systjndtek ufkjrtdeftejs) 4 nn ( 4.; nn)
;.4 (d) (l) (o) (k)
: sef x x0 (njtrcbcgy)
7 (fcf-systjndtek ufkjrtdeftejs)
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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5
;.48
( ) (kdbeordtj)
;.?8
;.4. (fcrndb lestreoutecf)
() 4= (kn)
?0, ?
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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4=
4=
?;, ?ne>4
@exe (;.;)
n F () @e (rjbdtevj`rjqujfky)`exe F
@e `eF (;.4
@e > 4 (;.:)
(;.:) (fcrndbezdtecf kcfletecf)
(aestcgrdn) ;.;
;.;8 4=
1 (dretanjtek njdf)
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44
(odr aestcgrdn) 4=
?0.
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4?
;.:8 4==
;.08 4,===
;.0 (lestreou-tecfs) (;.0) x x +lx
](x, x+lx) >`(x) lx (;.7)
`(x) lx> 4 (;.1)
4 Yd, o^
](d, o) >
od
`(x) lx (;.5)
(leskrjtj) x x x (;.;)
x >
x `(x) lx (;.4=)
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4;
;.7 (fcrndb lestreoutecf)
;.78
(fcr-ndb lestreoutecf)
`G(x9 Q, ) > 4
?jxp
(xQ)
?
??
(;.44)
(;.44) (Gdussedf lestreoutecf) (pdrdnjtjr) Q Q ;.1
;.18
() (pceft c` efjktecf)5
(;.44) 4 Q
5 x > k `
(k) > =
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4
4F
Fi>4
(x x)? (;.4?)
(;.4?)
[x >
4F 4
Fi>4
(x x)? (;.4;)
F > 4 [x > =/= x > = F > 4 [x
x [x x+[x
](x [x, x+[x) > 4[x
?
x+[xx[x
jxp
(x x)
?
?[?x
> =.01 (;.4x [x 01%
x >
x
t[x
E(t) ](x t[x, x+t[x) > 4
?
tt
jxp
z
?
?
lz (;.4:)
(;.4:) ;.;
;.;8 x > x t[x t
t = =.: 4.= 4.: ?.= ?.: ;.=
E(t) = =.;1 =.01 =.17 =.5:< =.511 =.557
[x t
[x
@([x) > 4
?(F 4)(;.40)
F
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4:
;.?. (prcpdgdtecf c` ufkjrtdeftejs)
(eflerjkt njdsurjnjft) (prcpdgdtecf c` ufkjrtdeftejs)(kcnoefjl ufkjrtdeftejs)
x K (jxdkt funojr) xx[x
]x(x, x+lx) jxp (x x)
?
?[?x
(;.47)
q> x+K q > x +K
]q(q, q+lq) jxp (q q)?
?[?q
> jxp
(x+K x K)?
?[?q
> jxp
(x x)?
?[?q
(;.41)
]x(x, x+lx) >]q(q, q+lq) [q >[x ()
xO q> Ox]x(x, x+lx) ]q(q, q+lq)
]q(q, q+lq) jxp (q/O x)
?
?[?x
> jxp
(q Ox)
?
?(O[x)?
(;.45)
x y
]x(x+lx) jxp x
?
?[?x
, ]y(y+ly) jxp
y
?
?[?x
xy xy
](x, x+lx9 y, y+ly)
jxp
x?
?[
?
x
y?
?[
?
y 9 q> x+y (;.?=)
x?
D +
y?
O >
(x+y)?
D+O +z?9 z? >
(Ox Dy)?DO(D+O)
(;.?4)
]x+y,z jxp
(x+y)
?
?([?x+[?y)
jxp
z
?
?
(;.??)
zzz
]x+y jxp (x+y)
?
?([?x+[?y)
(;.?;)
[x+y >
[?x+[?y
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40
xy x y q> x+y
q> x+y > (x x) + (y y) + (x+ y) (;.? x+y+ +z (;.?:)
qx y[x x [y y qx y
q(x, y) q(x , y) +
q
x
(x x) +
q
y
(y y) (;.?0)
(q/x) (pdrtedb ljrevdtevj)4= q x (x , y)(q/y)
q
[q
> qx
[x?
+qy
[y?
(;.?7)q
[q >
q
x[x
?+
q
y[y
?+ +
q
z[z
?(;.?1)
(;.?1) q> xf f
[q >fxf4[x
@(xf) >f@(x) (;.?5)
@(x) (?.:)
;.;. (stdfldrl ljvedtecf c` taj njdf)
x [x xF
4=` x `x
` x
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47
( )
x F (ixi) /F (;.4;) [x Q xx4, x?. . . , xF Q [x (;.?1)
[x >
F
[xF
?>
[xF
(;.;=)
x F Q
[xx > x [x xx [xx +[x
x x > xojst x >x [xx Yx [x, x+[x^ 01 (kcffflljfkj bjvjb)
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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41
= 4 ? ; < : 0 7
=
:
4=
4:
?=
?:
;=
;:
@crkj vs. dkkjbjrdtecf c` vdrecus ndssjs
Ndss 4
d (n/s?)
@
(F)
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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45
? e
ye > ne
xe+kF
exeye > ne
x?e +kexe
(
x?
y x xyF
x? (x)? (
xyx?
(
4
F 4e
(ye nxe)? ( y
e
x?e
4/?(
-
5/20/2018 Elements of Statistical Methods for Scientific Experiments
20/23
?=
r? (kcj`fflkejftc` ljtjrnefdtecf) = 4 r? 4
r?r? >
ey
?e
ey?e
( nxen ( ?
g (:.4)
g >
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?4
:.;8 g
(kn) \(s) g (kn/s?) (kn) \(s) g (kn/s?) g (n/s?)
:7.; 4.:?4 5.71 4=? =.? =.==; =.=: 4=? 5.71 =.=:04.4 4.:07 5.1?
4=? =.? =.==; =.=:
4=? 5.1?
=.=:
7;.? 4.741 5.75 4=? =.? =.==; =.=: 4=? 5.75 =.=:1;.7 4.1;: 5.14 4=? =.; =.==< =.=: 4=? 5.14 =.=:5:.= 4.5:? 5.1< 4=? =.; =.==< =.=: 4=? 5.1< =.=:
g
g >4:
(5.71 + 5.1? + 5.75 + 5.14 + 5.1 5.14 n/s? (:. 4F
(g4)? + (g?)? + + (g:)? > ?.45kn/s? (:.:)
g
g> (5.14 =.=?)n/s? (:.0)
g g (:. ?.57kn/s? > =.=; n/s? (:.7)
g> (5.14 =.=;)n/s? (:.1)
01%
g (:.?) \? >
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??
=.= 4=.= ?=.= ;=.=
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5/20/2018 Elements of Statistical Methods for Scientific Experiments
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?;
(rj`jrjfkjs)
\dybcr, H._.Df eftrcluktecf tc jrrcr dfdbyses8 \aj stuly c` ufkjrtdeftejs ef paysekdb njdsurj-njfts. ?fl jletecf. Zfevjrsety [kejfkj Occis8 KD, 4557.
Wdbpcbj, _.J.]rcodoebety & stdtesteks `cr jfgefjjrs & skejftests. 5ta jletecf, ]rjftekj Adbb8 Z[D,?=4?.
Jesjfadujr, H.G._jgrjssecf tarcuga taj cregef, \jdkaefg [tdtesteks,?:(;), pp.70-1=, ?==;.
Dftcf A., E. Oevjfs, [. Ldves.Kdbkubus8Jdrby trdfskjfljftdbs. 4=ta jletecf. Webjy8 Z[D, ?=4?.