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Title:

MANOVA

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Title: Name of presentation Author: Numchai Last modified by: Numchai Supparerkc haisakul Created Date: 4/20/2007 1:34:09 PM Document presentation format – PowerPoint PPT presentation

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Title: MANOVA


1
  • ?????????????????????????????????
  • MANOVA

??.????? ??????????????
????????????????????????? ????????????????????????
??
2
???????????????
  • ??????????????????????????????????? (ANOVA)
  • ?????????????????????????????????????????????
    (MANOVA)
  • ???????????????? (Assumptions)
  • ????????????????????

3
t-test for independent samples
4
t-test for independent samples
5
Logic of ANOVA
6
Logic of ANOVA
Sum of Square
Degree of Freedom
7
Partition of Variance
8
Partition of Variance
9
Partition of Variance
10
Partition of Variance
11
Partition of Variance
12
F Distribution
  • Expected 1
  • Positively Skewed
  • Lower Limit 0

13
MANOVA
  • ????????????? Multivariate Analysis of Variance
  • ?????????????????? ANOVA ?????????????????????????
    ?????
  • ??????????????????????????????????????????????????
    ???????????????????????????
  • ????????????????????????????????????????
  • ??????????????????????????????????????????????????
    ????????
  • ??????????????????????????????????????????????????
    ???????? ???????? ????????????????????????????????
    ????
  • ??????????????????? ??????????????????????????????
    ??????????????????????????? ??????????????????????
    ???????????????????????????????????????????

14
MANOVA
  • ?????????? ANOVA ??????????????????????
  • ???????? Alpha ???? Type I Error
    ?????????????????????????
  • ??????????????????????????????????????????????????
    ???????????
  • ???????????? (Power) ??????? ?????????????????????
    ???????????????????????????????????? ?????????
    MANOVA ???? ??????????????????????????????????????
    ??????????
  • ???????? Cancelling Out Effect ???????????????????
    ??????????????????????????????????????????
    ??????????????????????????????????????????????????
    ?? ?????????????????????????? ANOVA

15
??????????????????
  • ?????????????????????????????????? Alpha
    ??????????????????? Alpha ??????????
  • ??????????????????????????????? 1 ????? ???????
    Alpha ??????????????????????????????????????????
    Pairwise Error (PE) ??????????? Alpha
    ?????????????
  • PE Alpha ??????????

16
??????????????????
  • ???????????????????????? 1 ?????
    ???????????????????????????????????????? ????????
    Familywise Error (FE)
  • ????? C ??????????????????
  • ??????????????????????????????????????

17
??????????????????
  • ???????????? ????? 2 ????????? ?????????????? 3
    ????? ????????????????????????????????????????????
    ?????? 3 ?????

18
MANOVA
  • MANOVA ??????????????
  • ???????????????????????????????????????
  • ??????????????????????????????????????????
    (Multicollinearity)
  • ?????????????????????????

19
??????????????????? ANOVA
  • ??????????????????????????? (Univariate Normality
    Distribution)
  • ?????????????????????????????? (Homogeneity of
    Variance)
  • ????????????????????????????????? (Independent
    Observation)

20
??????????????????? MANOVA
  • ?????????????????????????? (Multivariate
    Normality Distribution)
  • ????????????????????????????????????????
    (Homogeneity of Covariance Matrix)
  • ????????????????????????????????? (Independent
    Observation)

21
Assumptions of MANOVA
  • Multivariate Normality Distribution
  • Univariate Normality Test
  • Mardia Statistics, Mahalanobis Distance Plot with
    Chi-square
  • Homogeneity of Covariance Matrix
  • Boxs M Test
  • Independence Observation
  • Intraclass Correlation

22
Univariate Normality
  • ?????????????? Central Limit Theorem
    ?????????????????????? F ?????????????????????????
    ??????????????? ????????????????????????????
  • ??????????
  • ????? Normal Q-Q Plot
  • ????????????? ???? Kolmogorov-Smirnov, Shapiro
    Wilk
  • ????????????????? Univariate Normality ??????????
    ????????????????????????????????? Multivariate
    Normality ???????????????????????????????
    Univariate Normality ??????

23
Univariate Normality
24
Multivariate Normality
25
Multivariate Normality
  • ?????????????? Central Limit Theorem
    ?????????????????????? F ?????????????????????????
    ??????????????? ????????????????????????????
  • ??????????
  • ?????? Mahalanobis Distance (D2) ???????? N p ?
    25 ????? p ???????????

26
Multivariate Normality
  • ??????????????????????????????????????????? (i -
    .5) / n ??? df p
  • ??????????????????????????????????????????????????
    ???????????????????

27
Normality Assumption
  • ????????????????
  • ???????????????????? ??????????????????????
  • ????????????????????????????????????
    ????????????? a ????????????????????????????????
  • ??????????????????????????????????
    ????????????????????????????????? (Power)
    ????????
  • ??????????????????????????????????????????????????
    ???
  • ???????????????????????????????????????

28
Homogeneity of Variance
  • ????? F ????????????????????????????????????
    ??????????????????????????????????????????
  • ????????????????????????????????? ???????
    Homogeneity of Variance ??????????? Levene Test
  • ??????????????????????????? ??????? Homogeneity
    of covariance matrices ??????????? Boxs M Test

29
Homogeneity of Variance
  • ????????????????
  • ??????????????????????????????????????????????????
    ???? ??? a ??????????????????????????????
  • ??????????????????????????????????????????????????
    ????? ??? a ??????????????????????????????
  • ???????????????????????????????????????

30
Independent Observation
  • ???????????????????????????????????????????????
  • ?????????????????????????????????????????????????
  • ???? ???????????????????????????????????????
  • ???????????????????????? ???????????????????????
  • ?????????????????????????????????????????
  • ???? ?????????????????????????????????????
    ??????????????????????????
  • ??????????????????????????????????????????

31
Independent Observation
  • ??????????
  • ???????? Intraclass Correlation (ICC)

32
Independent Observation
  • ????????????????????
  • ???????? ? ????????????????????????????????????
  • ????????? Type I Error ???????
  • ??????????????????????????
  • ??????????????????????????????????????
  • ???????? HLM

33
??????????????????????????????? ???? 1 ?????
  • ??????????????????????????
  • ?????????????????????????

34
??????????????????????????????? ???? 2 ?????
  • ??????????????????????????
  • ?????????????????????????

35
??????????????????????????????? ???? gt 2 ?????
  • ??????????????????????????
  • ?????????????????????????

36
??????????????????????????????? ???? 2 ?????
37
MANOVA
38
MANOVA
  • ????????????????????? (ANOVA)
  • ??????????????????????? (MANOVA)

39
MANOVA ??????????
40
MANOVA ??????????
  • Wilks Lambda

41
??????????? Post Hoc ????????????????
  • ??????????????????????????????????????? ????
    ANOVA ????????????? ???? Multiple Comparison
    ?????
  • ??????????????? Descriptive Discriminant Analysis
    (DDA)

42
????????????????????
  • ??????????? ?????? ?????????? (2542) ????????????
    3 ????? ??????????? 1 ????? ??????? 4 ?????
    ??????????????????????????????????????????????????
    ?????????????????????????????????????????? ?????
    1 ???????????????????????????????????????????????
    ?????? ????? 2 ??????????????????????????????????
    ????? 3 ????????????????????????? ????? 4
    ?????????????? ???????????????????????????????????
    ?????? 2 ??? ??? ???????????????????? (social)
    ??????????????? (family)

43
????????????????????
44
????????????????????
45
????????????????????
46
????????????????????
47
????????????????????
48
????????????????????
49
????????????????????
50
????????????????????
51
???????????
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