1 / 33

Pertemuan 13

Pertemuan 13. Analisis Ragam Peubah Ganda (MANOVA I). Matakuliah : I0214 / Statistika Multivariat Tahun : 2005 Versi : V1 / R1. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :

truman
Télécharger la présentation

Pertemuan 13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pertemuan 13 Analisis Ragam Peubah Ganda(MANOVA I) Matakuliah : I0214 / Statistika Multivariat Tahun : 2005 Versi : V1 / R1

  2. Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : • Mahasiswa dapat menerangkan konsep dasar analisis ragam peubah ganda (manova)  C2 • Mahasiswa dapat menghitung manova satu klasifikasi  C3

  3. Outline Materi • Konsep dasar analisis ragam peubah ganda (manova) • Analisis ragam peubah ganda satu klasifikasi

  4. <<ISI>> MANOVA ~ the history • Developed as a theoretical construct by S.S. Wilks in 1932 • Published in Biometrika • Wide availability of computers made these methods practical for researchers

  5. <<ISI>> MANOVA ~ the definition • Technique for assessing group differences across multiple metric dependent variables (DV’s) simultaneously, based on a set of categorical (non-metric) variables acting as independent variables (IV’s)

  6. <<ISI>> ANOVA vs MANOVA • ANOVA ~ only 1 dependent variable • MANOVA ~ 2 or more dependent variables • Both are used with experimental designs in which researchers manipulate or control one or more independent variables to determine the effect on one (ANOVA) or more (MANOVA) dependent variables

  7. <<ISI>> Equations • ANOVA Y1 = X1 + X2 + X3 +...+ Xn (metric DV) (non-metric IV’s) • MANOVA Y1 + Y2 + ... + Yn = X1 + X2 + X3 +...+ Xn (metric DV’s) (non-metric IV’s)

  8. <<ISI>> MANOVA and Regression • Note the different terminology • In multiple regression, univariate and multivariate/multiple refer to the number of IV’s • In ANOVA and MANOVA discussions, univariate and multivariate refer to the number of DV’s

  9. <<ISI>> Univariate Research Example • Subjects shown different advertising messages • Emotional or Informational or ?? • Viewers rate appeal of the message using scores from 1 to 10 Ad appeal?

  10. <<ISI>> Univariate Review ~ t Test • Two commercials shown (emotional~informational) • Single treatment/factor with two levels • Use a t Test: One IV’s, one DV, two treatment groups M1 - M2 • The t statistic = ---------------------- SEM1 M2

  11. <<ISI>> Univariate Review ~ ANOVA • Two or more commercials (emotional~informational~funny~etc) • Single treatment/factor with two or more levels • Use ANOVA : Multiple IV’s, one DV, two or more treatment groups MSB • F statistic = ------ MSW

  12. <<ISI>> Univariate Hypothesis Testing • Null Hypothesis (H0) ~ That there is no difference between the DV means of the treatment groups • Alternate Hypothesis (HA) ~ That there is a statistically significant difference between the DV means of the treatment groups

  13. <<ISI>> Multivariate Research Example • Subjects shown different advertising messages • Emotional or Informational or ?? • Viewers rate appeal of the message using scores from 1 to 10 Ad appeal? Will I buy?

  14. <<ISI>> Multivariate Procedures • Hotelling’s T2 One IV, multiple DV’s, two groups • The k Group Case: MANOVA Multiple IV’s, multiple DV’s, more than two treatment groups • Null Hypothesis ~ that there is no difference between vectors of means of multiple DV’s across the treatment groups

  15. ANOVA H0: M1 = M2 =...Mk H0: All the group means are equal, that is, they come from the same populations MANOVA <<ISI>> Null Hypothesis Testing M11 M21 Mp1 M12 M22 Mp2 M1k M2k Mpk =...= = • H0: All the group mean vectors are equal, that is, they come from the same populations

  16. <<ISI>> Hotelling’s T2 • Direct extension of the t test, used when there are only two groups, but multiple DV’s to be measured • Accounts for the fact that DV’s may be related to one another (correlated) • Provides a statistical test of the variate, formed from the DV’s, that produces the greatest group difference

  17. <<ISI>> Hotelling’s T2 ~ how it works • Maximize group differences, using the equation below: C = W1Y1 + W2Y2 +...+ WnYn where C = composite or variate score for a respondent Wi = weight for dependent variable i Yi = dependent variable I • Square the obtained t statistic to get T2 and check statistical significance

  18. <<ISI>> MANOVA • Extension of ANOVA • Extension of Hotelling’s T2 • Establish dependent variable weights to produce a variate for each respondent • Adjust weights to maximize F statistic computed on variate scores of all groups

  19. <<ISI>> MANOVA ~ how it works • The first variate (called a discriminate function) maximizes differences between groups and therefore also the F value • With maximum F, calculate greatest characteristic root (grc) and check its significance to reject null hypothesis (or not) • Subsequent discriminant functions are orthogonal and seek to explain remaining variance

  20. <<ISI>> When to use MANOVA • When you have multiple dependent variables • Control of Experimentwide Error Rate • Repeated univariate procedures can dramatically increase Type I errors • DV’s that are not highly correlated with one another will cause the most trouble • Differences among a Combination of Dependent Variables • Multiple univariate procedures do not equal a multivariate procedure • Multicollinearity is ignored

  21. <<ISI>> Discriminant Analysis • MANOVA ~ sort of a mirror image of discriminant analysis • DV’s in MANOVA become IV’s of DA • DV of DA becomes IV of MANOVA

  22. <<ISI>> Decision Process for MANOVA • Powerful analytic tool suitable to a wide array of research questions • Six step process • Logical progression through all six will yield best results

  23. <<ISI>> Step #1: Objectives of MANOVA • Determine research question • Multiple Univariate Questions ~ MANOVA used to control experimentwide error rate before further univariate analysis • Structured Multivariate Questions ~ MANOVA used to address multiple DV’s with known relationships • Intrinsically Multivariate Questions ~ MANOVA used with multiple DV’s where the principal concern is how they differ/change as a whole...or how they remain consistent across time

  24. <<ISI>> Step #1: continued • Select Dependent Variables carefully • There is a danger of including too many DV’s and a tendency to do so...simply because you can • One bad variable can skew all results • Ordering of variables can also be important and can lead to sequential effects • MANOVA step-down analysis can help here • Researcher responsibility to use tools properly

  25. <<ISI>> Stage #2: Research Design • MANOVA requires greater sample sizes than ANOVA ~ overall and by group (must exceed specific thresholds in each cell) • Factorial Designs ~ two or more IV’s or treatments in the design • Sometimes treatments are added post hoc • Blocking factors (example: gender)

  26. <<ISI>> ANOVA Cereal Example • Three colors (red, blue, green) • Three shapes (stars, cubes, balls) • 3 x 3 factorial design • With ANOVA, you would evaluate main effect for color, main effect for shape, and interaction effect of color and shape • Each would be tested with an F statistic

  27. <<ISI>> Ordinal and Disordinal • With MANOVA, we can establish the nature of the interaction between two treatments • No interaction • Ordinal Interaction ~ effects of treatment are not equal across all levels of another treatment...but magnitude is in the same direction • Disordinal Interaction ~ Effects of one treatment are positive for some levels and negative for other levels of the other treatment

  28. <<ISI>> MANOVA Interaction • If significant interactions are ordinal, researcher must interpret the interaction term carefully • If significant interaction is disordinal however, main effects of the treatments cannot be interpreted and study must be redesigned (treatments do not represent a consistent effect)

  29. <<ISI>> Covariates • Metric independent variables, called covariates can be used to eliminate systemic errors • ANOVA becomes ANCOVA • MANOVA becomes MANCOVA • Procedures similar to linear regression are used to remove variation in the DV associated with covariates and then standard ANOVA and MANOVA can be used • Ideal covariate is highly correlated with DV and not correlated with the IV

  30. <<ISI>>

  31. <<ISI>>

  32. <<ISI>>

  33. << CLOSING>> • Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis ragam peubah ganda, dan manova satu klasifikasi • Untuk dapat lebih memahami konsep dasar analisis ragam peubah ganda dan manova satu klasifikasi tersebut, cobalah Anda pelajari materi penunjang, website/internet dan mengerjakan latihan

More Related