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???????? (MANOVA)

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(manova) * anova vs. manova * t-test ( anova ) (anova) ... – PowerPoint PPT presentation

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Title: ???????? (MANOVA)


1
????????(MANOVA)
  • ??????
  • ??????? ??
  • 2013?10?31????

2
ANOVA vs. MANOVA
T-test (?ANOVA???) ????? (ANOVA) ??? ????? (MANOVA)
?? ???????????? ?????????????? ????k??????????????(centroid)?????
??? ??(????)? ?????(??????)? ??????
??? ??? ??? ???
?? ????,????? ?????????,????????? ????(???)???(A?B?C),???????? ?????????,???????????? ?????????????,??????????????
3
1. MANOVA????? (p.281)
  1. ?????????????????????,???????????????(????????)?
  2. ???????????????????,???????????????????

4
2 MANOVA????? (p.282)
  1. ????????????????
  2. ????????
  3. ??????????? (multivariate normal distribution) ?
  4. k????????????????,???????????????????????,???????
    ??,ANOVA ???????????????,???????????k?????????

5
3. MANOVA????? (p.282)
  • MANOVA????????ANOVA ,?????????

6
3. MANOVA????? (p.282)
  • ???????MANOVA
  • Wilks ????
  • Pillai-Bartlett trace???(v)
  • Roy???(GCR)???
  • Hotelling-Lawley trace (T)???
  • ???????,???????

?? df SSCP ?
?? k ? 1 H
?? N ? k E
?? N ? 1 T ? H ? E
7
3. MANOVA?????
Wilks Lambda ???????,???? ??1??????,??????,????
?????? ????????
8
3. MANOVA????? (p.283)
  • ???????MANOVA
  • ???????
  • ????????????,??????????????
  • ??????????????????
  • ???????,??????? (p.285)

?? df SSCP ?
??A a ? 1 HA
??B B ? 1 HB
????(AB) (a ? 1)(B ? 1) HAB
??(e) ab(n ? 1) HE
?? N ? 1 T ? HA ? HB ? HAB ? HE
9
3. MANOVA????? (p.287)
???F??
???
?Bonferroni????????,????F????????? /
p(p??????) Borgen?Seling (1978)??,?????????????(?
???)??????????????? ??????????
MANOVA??????,????? ??????????,????? ?????????????
??,???????????????????????
???????????,??????????,????????? ????????????????
?,????????????????
????
?????
10
???F??
?????????????????? ???????? / p (p??????),.05 /
2 .025,?????.025????????????????,???? ??2?????
,?????????
11
3. MANOVA????? (p.288)
?????
???
???????????????p??????????????????????????????? ?
???????Hotelling T2 ? ?????,?????????????,???????
?,??????????????? / g(g?????)?
??????????p?????,??????????????? Bird (1975)
??,?????????????,????????,??????????????? /
gp(g?????,p?????)?
??????Roy-Bose??????????????,????,???????Bonferron
i????? ?WILKS?ROY?PILLAI?BONFER?HOTELLING????????
????????????0,??????????????
?????
??????
12
Bonferroni????
??????,??????,???????????????????0??????,???0?????
?????? ??3?????,?????1?42?33?4?,????????
13
3. MANOVA????? (p.289)
???? ????
?? ???? ????
???? ?????????????? ??????????
?? ??????????,???? ??????????,???
(????????)? C0 ?(???) C0 ? t a,
(N-k)(C0?t??????)? ????3?,????30?,?t .05 (30-3) ?
2.05183
14
3. MANOVA????? (p.290)
  • ????2????????,??????????
  • ??1 ? ???Wilks ? ?
    ,???????????????????
  • 1 ? ?1/s??s??0??????

15
??????2
?2(Pillai) ? V / s ? .516 / 2 ? .258 ?2(Wilks) ?
1 ? ?1/s ? 1 ? .5021/2? .291 ?2(Hotelling) ?
? ? .323 ?2(Roy) ? ?1 / (1 ?
?1) ? .914 / (1 ? .914) ? .478
16
???
  • ??????????????????????,???12??????????????????????
    ???????????????????????

17
???
  • ?????????????????????????????a
    .05????????(1)????????????????(2)???????????????
    ?????????(3)?????????????????????????

??? ??? ??? ??? ??? ??? ??? ??? ???
?? ?? ?? ?? ?? ?? ?? ?? ??
9 10 20 3 4 10 2 7 9
8 12 21 4 4 19 2 9 11
9 11 25 5 5 18 3 9 10
6 9 17 7 3 15 1 8 7
18
??? ?????
?5-8 ???????????????
?? df SSCP ?
?? 2 .014
?? 9
?? 11
plt.05 plt.01
19
??? ?????
?5-9 ???????????????????
??? ?? ?? ??? ?? ??? 95 ?? 95 ?? ????
?? ??-?? 3.25 0.965 1.068 5.432 ??gt??
?? ??-?? 2.75 0.965 0.568 4.932 ??gt??
?? ??-?? 6.50 0.736 4.835 8.165 ??gt??
?? ??-?? -4.25 0.736 -5.915 -2.585 ??lt??
?? ??-?? 5.25 2.242 0.178 10.322 ??gt??
?? ??-?? 6.25 2.242 1.178 11.322 ??gt??
20
??? ?????
?5-10 ???????????????????
??? ???? ??? ?? ??? 95 ?? 95 ??
?? ??-?? 3.25 0.965 -2.487 8.977
?? ??-?? 2.75 0.965 -2.987 8.487
?? ??-?? 6.00 0.965 0.263 11.737
?? ??-?? 6.50 0.736 2.123 10.877
?? ??-?? -4.25 0.736 -8.627 0.127
?? ??-?? 2.25 0.736 -2.127 6.627
?? ??-?? 5.25 2.242 -8.086 18.586
?? ??-?? 6.25 2.242 -7.086 19.586
?? ??-?? 11.50 2.242 -1.836 24.836
21
???
  • ???????12?,???????????????????????????????????????
    ????????????????????? a .05 ???????????

??? ??? ??? ??? ??? ???
?? ?? ?? ?? ?? ??
? ? 11 10 10 9 10 9
? ? 12 12 10 10 9 9
? ? 10 11 12 9 9 10
? ? 11 10 14 11 11 9
? ? 10 13 11 10 12 11
? ? 10 13 10 13 11 10
? ? 9 12 9 11 10 10
? ? 9 10 10 13 12 11
22
??? ?????
?5-11 ???????????????



?? df SSCP ?
??(A) 2 .621
??(B) 1 .509
????(AB) 2 .581
??(e) 18
?? 23
Qa


Qb

Qab
Qe
Qt
plt.05
23
?5-12 ??????????????????????
?? df SSCP ?
??(A)
???(b1) 2 .646
???(b2) 2 .555
??(B)
???(a1) 1 .657
???(a2) 1 .537
???(a3) 1 .780
?? 18
Qa at b1
Qa at b2
Qb at a1
Qb at a2
Qb at a3
Qe
plt.05
24
????!
  • PS. ?????????????????,???
  • ???????(2002)? SPSS?SAS?BMDP ????????????????(???)
    ??????
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