Home >Documents >Pertemuan 15

Pertemuan 15

Date post:11-Jan-2016
Category:
View:41 times
Download:0 times
Share this document with a friend
Description:
Pertemuan 15. Analisis Ragam Peubah Ganda (MANOVA III). Matakuliah: I0214 / Statistika Multivariat Tahun: 2005 Versi: V1 / R1. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : - PowerPoint PPT Presentation
Transcript:
  • Pertemuan 15Matakuliah: I0214 / Statistika MultivariatTahun: 2005Versi: V1 / R1

    Analisis Ragam Peubah Ganda(MANOVA III)

  • Learning OutcomesPada 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

    Mahasiswa dapat melakukan uji Fisher dan uji Bartlette C3

  • Outline Materi

    Konsep dasar analisis ragam peubah ganda (manova)

    Analisis ragam peubah ganda satu klasifikasi

    Uji Fisher

    Uji Bartlette

  • Null Hypothesis

    Univariate t-test:

    H0 : (1 = (2 (population means are equal)

    Multivariate case (2-group MANOVA):

    H0 :

    (population mean vectors are equal)

    Main assumptions: normally distributed DVs, equal covariance matrices across groups

    _1065350985.unknown

  • Test Statistic for 2-group MANOVA

    Hotellings T2 : T2 =

    n1 : sample size in first group

    n2 : sample size in second group

    : vector of means of DVs in first group

    : vector of means of DVs in second group

    S : pooled within-group covariance matrix

    _1065351488.unknown

    _1065351533.unknown

    _1065351304.unknown

  • Hotellings T2 measures the between-group difference

    , which is weighted by the within-group covariance matrix S-1. The test works as follows: From Hotellings T2, form

    F =

    F is the test statistic for testing whether there is a significant group difference with respect to the whole vector y of dependent variables. F-distributed with p and (n1+n2p1) degress of freedom

    _1065351834.unknown

    _1065351950.unknown

  • Rao's F Approximation

    degrees of Freedom

    Special Note Concerning s

    If either the numerator or the deminator of s = 0 set s = 1

  • Hotelling's Trace Criterion

    Roy's Largest Latent Root

    Pillai's Trace Criterion

  • Which of these is "best? Schatzoff (1966) Roy's largest-latent root was the most sensitive when population centroids differed along a single dimension, but was otherwise least sensative. Under most conditions it was a toss-up between Wilks' and Hotelling's criteria.

    Olson (1976) Pillai's criteria was the most robust to violations of assumptions concerning homogeneity of the covariance matrix. Under diffuse noncentrality the ordering was Pillai, Wilks, Hotelling and Roy. Under concentrated noncentrality the ordering is Roy, Hotelling, Wilks and Pillai.

    Final "Best" When sample sizes are very large the Wilks, Hotelling and Pillai become asymptotically equivalent

  • Tabel Manova

    Sumber Variasi

    Matriks Jumlah Kuadrat

    dan Hasil Kali Silang

    Derajat Bebas

    Perlakuan

    Residual

    Total

    (terkoreksi)

    _1153723774.unknown

    _1153723983.unknown

    _1160224633.unknown

    _1166436750.unknown

    _1153723793.unknown

    _1153723738.unknown

  • Uji hipotesa

    menyangkut generalized variance.

    ditolak bila generalized variance

    kecil

    (

    ditemukan oleh Wilks).

    Distribusi yang eksak untuk

    diberikan dalam tabel

    _1153724194.unknown

    _1153724291.unknown

    _1168343889.unknown

    _1153724268.unknown

    _1153724171.unknown

  • Tabel Distribusi Wilks Lamda

    Jumlah Variabel

    Jumlah Grup

    Distribusi sampling data multivariat

    _1153725142.unknown

    _1154421775.unknown

    _1166436701.unknown

    _1166436719.unknown

    _1168343988.unknown

    _1166436694.unknown

    _1153725289.unknown

    _1153725298.unknown

    _1153725230.unknown

    _1153724950.unknown

    _1153724958.unknown

    _1153724866.unknown

  • Bila

    benar dan

    besar:

    berdistribusi mendekati Khi kuadrat dengan derajat bebas

    .

    Jadi, untuk

    besar,

    ditolak pada tingkat signifikansi bila:

    _1153725632.unknown

    _1156230956.unknown

    _1166435794.unknown

    _1166436677.unknown

    _1156230990.unknown

    _1153725683.unknown

    _1153725414.unknown

  • >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

    Developed a while backTough to tackle without a fairly sophisticated computer.Definition always a good place to start.

Embed Size (px)
Recommended