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试验设计与数据分析.pdf

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试验设计与数据分析.pdf

1、?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ?13778566781Email: ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ?(?)? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering?

2、 ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?BiometryBiometry? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(?)?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?17?18?18?19?20?2010Sichuan University of Science

3、& Engineering? ? ? ? ? ? ? ? ?1?2?(1) t-?(2) ?2-?(3) ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3?1?2?3?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?population? ? ?sample? ?2010Sichuan Universi

4、ty of Science & Engineering? ? ? ? ? ? ? ? ? ?parameter? ? ?statistic? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?(variation)? ? ?(variate)? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?error?1?systematic error?2?random error?2010Sichuan University of Scie

5、nce & Engineering? ? ? ? ? ? ? ? ?1 1? ?systematic error? ?1?2?3?4?5?6?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?random error? ? ?2 2?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?accuracy? ? ?precise? ?2010Sichuan University of Science & Engineering? ? ?

6、? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ?=+=niinnxnxxxx1121x =+=NiiNNxNxxx1121?2010Sichuan University of Science & E

7、ngineering? ? ? ? ? ? ? ? ? ?1?0?2?a?0)(1=niixx22)()(axxx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ?30?xi?i?fi?i? k?ffxfxffffxfxfxfxkiikiiikkk=+=11212211?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?1?Md?2?M0?2010Sichuan University of Science & Engine

8、ering? ? ? ? ? ? ? ? ? n?n?G? ?nnnnxxxxxxxxG1)(321321=)lglg(lg1lg211nxxxnG+=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?H.? ?=+=xnxxxnnH1111111)(121?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ?

9、 ? ? ? ?range? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?variance? ?0? ?SS?2)(xxSSi=2)(=ixSS?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?n?1?N? ?S2?2?) 1()(22=nxxSiNxi22)(=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?S2?S? ? ?) 1

10、()(2=nxxSiNxi2)(=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?n?n?(x-)=0?n-1? ?k?n-k?n-1?n? ?n-1?S2?x?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1?2?C?3?1)(2=nxxSi1)(22=nnxxSii2)(nx1)(22=nnxfxfSiiii?2010Sichuan University of Science & Engineering? ? ? ? ? ?

11、 ? ? ? ? ?a?a?a?a? ?68.7%?95.45%?2?99.73%?3?1.96?95%?2.58?99%?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ?C.V.?%100.=xSVC?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?3?14?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan Univers

12、ity of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1.? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2.? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3.? ?(?)? ? ?U? ?V? ? ?2010Sichuan University

13、 of Science & Engineering? ? ? ? ? ? ? ? ? ?A?B?A?B?A?BA1+A2+?+An=?Ai? ?A?B? ABA1A2?An=?Ai? ?A?B?AB? ?A?B? A+B? AB?B=? ?A1,A2,?,An? ?A?B?A?B?A?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ?A? ?A? ?p?(?n?)?n?f ?p?naAf=)()()(=npAPna?2010Sichuan University of Science & Engineering

14、? ? ? ? ? ? ? ? ? P(A)=0?A? ?P(A)?P(A)?0.05 ?P(A)?0.01?A?P(A)=P(V)?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?x? ?x?x? ?x?a, b, (ab)?x?f(x)?x?x?)(+xxfdxxfbxapba)()(=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering

15、? ? ? ? ? ? ? ? ?1?n?0?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ?x?2?x?x?222)(21)(=xexf?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2 2? ?x=?x=?f (x)? ?-?f (?-?)?+?f (?+?)? ? ?x?-?+?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?00.9

16、-4 -3 -2 -101234?=0.5?=1.0?=1.5?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3 3? ?x? ?x?u? ?=xu2221)(ueuf=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?=0?2=1?u?u?N?0?1?u?N?0?1?u?y?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4 4?(1) ?1?u?, u

17、?u?=uxudxedxxfuuP2221)()()(uuP?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?P?-1?u?1?=0.6826P?-2?u?2?=0.9545P?-3?u?3?=0.9973P?-1.96?u?1.96?=0.95P?-2.58?u?2.58?=0.99?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?(2) ?N(0, 1)? ?x N(30?102)?X 40? ? ?u?1030=xu7158.

18、 03841. 01) 1(1) 1()103040()40(=uPuPuPxP?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?3-8 ?P36? ? ?u?2100=xu3413. 05 . 03841. 0) 10()21001022100100()102100(=5?nq5?n?=np?2=npq?x?npq=pnnpx=22nnpqx=npqx=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?n?p?2010Sichua

19、n University of Science & Engineering? ? ? ? ? ? ? ? ?3 3?3-1?P29?p=0.85?n=6?k=5?3993. 0)15. 0()85. 0()15. 0()85. 0()5(15)!56( !5!615566=?CP?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3-2?P30?p=0.85?n=6?k=4?4?9525. 03771. 03993. 01761. 015. 085. 015. 085. 015. 085. 0)4()(0666155

20、624466415=+=+=?CCCqpCxPqpCkxPxxnxxnnkxxn?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3-3?P30?p=0.85?n=6?k=4?4?22352. 017618. 004145. 000549. 000039. 000001. 015. 085. 015. 085. 015. 085. 015. 085. 015. 085. 0)4(2446333642265116600640=+=+=?CCCCCqpCxPxxnxxn?2010Sichuan University o

21、f Science & Engineering? ? ? ? ? ? ? ? ?n?p?0?x?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1 1? ?x(x=m)?0?1?2?m=0?1?n ? ?0?e=2.7182?(?)?x?(Poisson?s distribution)?x?P(?)? ? ?=emmxPm!)(?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2 2? ?=np?2?=?=?2? ?1?P(x0)?1?

22、2?P(x=1)?2?3?P(x=2)?=20?=50?20? =?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3 3?3-4?P32?x?1008. 0! 53!)5(P35=ekexk916. 0!)5(P50=kkkex084. 0)5(1!)5(P5=xPkexk?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?=0.51?S2=0.52?=0.51?(k=0,1,2,?)?e-0.51=0.6005?P(x=0)= (0.

23、510?0! )0.6005=0.6005P(x=1)= (0.511?1! )0.6005=0.3063P(x=2)= (0.512?2! )0.6005=0.0781P(x=3)= (0.513?3! )0.6005=0.0133P(x=4)= (0.514?4! )0.6005=0.0017x51.0!51.0)(=emmxPm0001. 09999. 01)(1)4(40=kmxpxP?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?=0.51?=0.51? k 0 1 2 3 ?4 ? ? ? 120 6

24、2 15 2 1 200 ? ? 0.6000 0.3100 0.0750 0.0100 0.0050 1.00 ? ? 0.6005 0.3063 0.0781 0.0133 0.0018 1.00 ? 120.12 61.26 15.62 2.66 0.34 200 ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?S2?2? ?2? ? ?

25、xx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1? ?N?n?Nn? ?ixixix?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?standard error?Se? ?xxxxx=xnx=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?N=3?x1=2?x2=4?x3=6?=4?n=2?9?9?Nn=32=9?N?633. 1383485

26、62)(2=NxNx=+=49369632xnNNxxx=2383499)36(156)(222?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2 2?2?S2?S?S2?S?()?x?N(?2)? ?N(?)?x?n?xxxnx22=?dfSS2=n2xn2x?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3 3? ? ? ?Sd?Se?xnx=xxxxxx?2010Sichuan University of Science &

27、Engineering? ? ? ? ? ? ? ? ? ?1?N1?1?1?2?N2?2?2? ?n1?n2? ?n1?30?n2?30?1x2x11nN22nN21xx 2121nnNN21xx 221xx ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ?2121=xx2221212222121nnxxxx+=+=221xx 21xx 21xx 22221=)11(212221nnxx+=nnn=21nxx22221=?2010Sichuan University of Science & Eng

28、ineering? ? ? ? ? ? ? ? ?1.? ?n?n?xxnx=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2.? ?S?S?xxSxnSSx22=nSSx=xxSx xxSx xSx ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3. ?1-?2 ?1-?xxxuxux+xuxxux+xu xu ?2010Sichuan University of Science & Engineering? ? ? ? ?

29、? ? ? ?t t ?1? ?2?2?n?30?S2?2?t ? t ?Gosset?1908?student?Fisher?1926?t ?2122xSxt=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? t ?t ?y? t ? t ?0 (df1)?(df2)212)1()2/(2/)1(1)(+=dfdftdfdfdftf)2/(=dfdft?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?t?2010Sichuan Un

30、iversity of Science & Engineering? ? ? ? ? ? ? ? ?2 2?t t ? t ?t = 0?t = 0?t ? ?df ?t ?n 30?t ?n 100?t?n?t ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?F F ?1?F ? ?2?df1=n1-1?df2=n2-1? ?2?F ?1x2x21S22S221121) 1(Sn =222222) 1(Sn =22212222221211222121) 1() 1() 1() 1() 1() 1(SSnSnnS

31、nnnF=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?F?df1?df2?F?F?F F?df1, df2? F?222122121122122211)(2()2()2()(dfdfdfdfdfdfdfdfFdfdfdfFdfdfFf+=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?F?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2 2?F

32、 F ?F?df1?df2?df1?df2?F?0?+?=1?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?64?8-10?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ?hypothesis test?parametric estimate? ? ?point estimate?(interva

33、l estimate)?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ? ? ?0?9.75?5.30?30?11.99?= 11.99?9.75?=2.24%? ?2.24%?x0 x?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?1?2? ?1x2x21xx ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?xi ?xi=?+?i?i=1?

34、2?n? ?+=+=+=ninininnxnx1111)(11)()()()(2121221121+=+= xx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?(u-test)? ? ?1. ?2. ?3. ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1.?H0: ?=?0? H0: ?=?0=9.75? HA: ?0?HA: ?0=9.75?2010Sichuan University of Science & Enginee

35、ring? ? ? ? ? ? ? ? ?2. ?0? ?H0?0=2.24%?0=2.24%?u-? ?H0?H0?H0?HA?5%? 1%xxxxx96. 131. 2009676. 0%75. 9%99.1105. 00=uxuxxxx96. 196. 100+xxx58. 258. 200+?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?3?0?5%?5%?1%?0=11.99?9.75?=2.24%?0.010.05?xx?2010Sichuan University of Science & Engi

36、neering? ? ? ? ? ? ? ? ?H0?H0?H0?H0?1-? u?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?HA:?0? ?HA:? ?2?1-?2?0?-?1- ?2?0?1x2x1x2x1x2x?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?n? ?n?0? ?=0.05?2? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ?

37、 ? ? ?2?u ?u ? ?2?S2?2?t ?t ?t ?xxu=xSxt=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?u?u ?u ?nx=xxu=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?4-1?P53?N(500?64)(?g)?10?505?512?497?493?508?515

38、?502?495?490?5l 0?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?1?H0?=?0?500g?HA?0?2?u ?3?P?0.05?7 .50210510512505=+=nxx530. 2108=nx96. 1067. 1530. 25007 .50205. 0=tSxtx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-3?P54?H0?=?0?5.5%?HA?0?P?0.05?001. 08003. 0=

39、nSSx895. 11001. 0055. 0056. 0)7(05. 00=uSxxuxx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2. ?=?t-?u?=?t-?2122212221222)()() 1() 1()()() 1() 1() 1() 1(212222212121212222112122221121222211212+=+=+=+=nnnxxnxxnnxxxxnnSnSndfdfdfSdfdfdfSS?2010Sichuan University of Science & Engineeri

40、ng? ? ? ? ? ? ? ? ?n1=n2=n?)11(2)()()11(2121222221212121211nnnnnxxnxxnnSSxx+=+=) 1()()(2222221212222121+=+=nnnxxnxxSSnSSxxxx?nSSSxx222121+=2121xxSxxt=2) 1() 1(2121+=+=nnnndf?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-5?P56?P?0.01?2350. 5S65.1323267. 847.98222211=?xSx5034. 1623

41、50. 53267. 8222121=+=+=nSSSxx169. 3735.225034. 196.13247.98)10(01. 02121=tSxxtxx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-6?P57?P?0.05?61.2815.2821=xx?3332. 0)5161(256505.14390.409369 .16802.4756)11(2)()(222121222221212121=+=+=?nnnnnxxnxxSxx262. 2381. 13332. 061.2815.28)9(05

42、. 02121=?H0?HA?222121S22S2221SSF =2221=),(21dfdfFF22212221?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2?Cochran-cox?22212121nSnSSxx+=2121xxSxxt=221212)(221)(21221SnSntSntSntdfdf+=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-7?P58?P?0.05?3578. 0511. 01006. 1

43、22212121=+=+=nSnSSxx838. 03578. 062. 732. 72121=xxSxxt35. 211. 01006. 15776. 211. 010262. 206. 15221212)(221)(21221=+=+=SnSntSntSntdfdf35. 2838. 005. 0=tt?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?u-?u0.05=1.96?u0.

44、01=2.58?nppp)1 (00=pppu0? =?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-9?P60?P?0.05?014. 05007?=nxp00445. 0500)01. 01 (01. 0=p1.64899. 000445. 001. 0014. 0)(05. 0=?uu?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?x?)1 (00pnpp=)1 (00pnpnpxxuxx=?2010Sichuan U

45、niversity of Science & Engineering? ? ? ? ? ? ? ? ?+=+=212121212121?11)1 ( 11121nnppnnnnxxnnxxSpp21?21?ppSppu=?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?4-10?P61?1.96u2.58 ?0.01P0.05?0649. 038525?111=nxp0334. 059820?222=nxp?0458. 059838520252121=+=+=nnxxp0137. 059813851)0458. 0

46、1 (0458. 021?=+=ppS299. 20137. 00334. 00649. 0=u?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?u-?n25?np5?u?u-?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1?2?nppnppuppc)1 (5 . 0?=?+=+=2121212121?2211111)5 . 0?()5 . 0?(2121nnnnxxnnxxSSnpnpuppppc?2010Sichuan Univ

47、ersity of Science & Engineering? ? ? ? ? ? ? ? ? ?4-11?P62?u=0.2450?02468101214051015XY(C) ?ryyxx0)(yyxx0)(=yyxx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?SPxy? ?3?1?2? ?x?y?)(yyxx?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?22)()()( )(11yxyxyxyxyyxxyxyxyxNy

48、xN=?yxxyyxxyyxyxSSCoVSSSSSPyyxxyyxxSSyyxxnSyySxxnr=22)()()( )(1111?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?SPxy?x?y?r?nyxyxyyxxSPiiiiiixy=)(xyCoV1)(=nyyxxCoVxy)()()()()()(222222 =nyynxxnyxxyyyxxyyxxr?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?6- 4?P167?

49、 ?6- 5?P167?9987. 00343.842143.537857.66=yxxySSSSSPr8517. 06583.2928048.2376967.224=yxxySSSSSPr?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?1?r?0?r =1?r?0?r =-1?r =0?0?2?r?-1?1?r?x?y?r?x?y?r r?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? ?r2?x?y?1-r2?n-2?r? ?r

50、?8?rrSrSrt=?21S2=nrr?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?r? ?r? ?x?y? ? ?x?y?r?r?r?-1-0.67-0.3300.330.671?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ?2010Sichuan University of Science & Engineering? ? ? ? ? ? ? ? ? x?y ?y?x?y?y?y?x?xi? ?a?y?x=0?b?b?y?x


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