Multivariate powerpoint

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Introduction to Multivariate AnalysisMPU2263

Zairul Nor Deana Md Desa, Ph.D.

Department of Educational Foundations and Social SciencesUniversiti Teknologi Malaysia

Email: [email protected]

Lecture 3: Multivariate ANOVA (MANOVA)

7/9/20131

mailto:[email protected]

mailto:[email protected]



Outline

Multivariate Analysis of Variance (MANOVA)

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Purpose of Multivariate ANOVA

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It is a generalization of ANOVA with several DVs.

IV can be different treatments or groups.

To discover whether behavior (i.e. the DVs) is

changed by manipulation of the IVs.

Sometimes the treatment (or groups) shown nodifference in separate ANOVA but when responses

to more than one DV group differences become

apparent.



Research Questions in MANOVA

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What is it the changes in composite DV as a result of different treatments (or groups) and their interaction.

Is a combination of DVs varies as a function of IVs?

Is there any difference between the means and,

thus, is there any statistically difference among

groups?



Research Questions in MANOVA

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Overall Model What is the proportion of the composite DV explained by each IV?

Main Effect

Separate test for each IV

Are there mean differences in composite DV associated with

differences in treatment (or group)? - without covariate Are there differences in composite DV associated with IV, after

adjustment for covariate prior to treatment (or condition)? - withcovariate (for next week)

Interaction Effect

Does change in the DV over levels of one IV depend on the levelof another IV?

Is the pattern of responses to the different types (or levels) of oneIV the same for different levels of another IV?

Given different types of treatment, does one treatment works

better than the other?



Theoretical Issues

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How to choose IVs and/or DVs? Logic and research design!

Skills and area of study

A set of continuous DVs

Start from looking at more important DVs than others

Categorical IVs

How to choose covariates (CVs)? CVs are need to be controlled for or removed.

Identify a set of CVs that are uncorrelated with each other

Select CVs that adjust the DV for predictable butunwanted sources of variability.

Based on theoretical ground and literature.

Can look at CV with highest correlation with DV.



Fundamental Interpretation in MANOVA

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See Example



Example

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A study on proficiency assessment among Englishlanguage leaners.

See SPSS output

Data file: data3MANOVA.sav

Output file: outData3.spv



Example

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How-to-SPSS Please refer to SPSS hand-out!

Analyze>Generalized Linear Model>Multivariate

Select the DVs (e.g. listen, read, speak, write)

Select the IVs (e.g. Nation)

In Options button:

Choose all IVs to Display Means for

Check Descriptive Statistics, Estimate of Effect Size, Homogeneity

test

In Post Hoc button: Choose pairwise comparison adjustment method (optional for this

example)

Use LSD for <4 pairwise comparisons, and use sequential

Bonferroni for more than 4 comparisons. Note.

# = −

2



Example – One-way MANOVA

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Steps in interpreting MANOVA results in SPSS1. Examine the Box’s M Test (i.e. test for the assumption of

homogeneity variance-covariance of DVs across IVs)

We want non significant result (Why?) at α = .001 (why

conservative significance level?) – followed up with Wilks’

Lambda.

If the test is non-significant the follow-up analysis must use Pillai’s

Trace in order to use MANOVA!

2. Examine multivariate model (Omnibus Multivariate Test)

For each IV, examine its multivariate test at .001 level. Significant result Multivariate test is more powerful than

univariate in examine the DV as a composite (i.e. combination of

DVs)

It provide information about the proportion of generalized variance

in the DVs that is accounted for by the IVs.



Example - One-way MANOVA

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Steps in interpreting MANOVA results in SPSS3. Levene’s Test

Test for the equality of error variances in each DV

Want significant results reject null hypothesis that variancesacross groups are unequal.

If significant for some DVs proceed with nonparametric or univariate ANOVA. We can also use MANOVA and assuming for unequal variances across groups!

4. Examine Test of Between Subjects Effects

We want to look at an individual effect of IV (one-way ANOVA)

We want to look at main and interaction effects (two- or three-way ANOVA).

We want significant results to support researcher’s hypotheses!

Note. Bonferroni adjustment of the significant level must be used!

=.5

#



Example - One-way MANOVA

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Steps in interpreting MANOVA results in SPSS5. Follow-up Tests with LMATRIX (Pairwise comparisons)

LSD or Bonferroni (in Post Hoc button) or contrast in Contrast

button in default SPSS won’t provide F value and degree of

freedom for the pairwise comparisons.

LMATRIX will use contrast for the comparison which will testeach individual level of IV appropriately

Use the same procedure in Slide 9 then click Paste to use

Syntax for LMATRIX procedure.

Completed follow-up tests can be found in Contrast Results (K

Matrix)a andUnivariate Test Results tables.



Example - Two-way MANOVA

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Now, consider two IVs in the model fromprevious example. Data file: data3MANOVA.sav

Output file: outData3-2.spv

We need to examine significant interaction, main

effect, and simple main effect.

Use sequential Bonferroni adjustment for follow-up

test with more than 4 pairs of comparison.



Next Week

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Multivariate ANCOVA (MANCOVA)

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