MANOVAHowTo

7/30/2019 MANOVAHowTo

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How to Perform a MANOVA in SPSS

In this example, we will look at a multivariate analysis of variance. The difference

between univariate and multivariate analyses is that a univariate analysis has only

one dependent variable (with any number of independent variables / predictors). Amultivariate analysis, on the other hand, has many dependent variables (again, with any

number of IVs). The goal of our analysis is to look for an effect of one or more IVs onseveral DVs at the same time. Therefore, were going to use the familiar general linearmodel command in SPSS, but choose a multivariate analysis.

This dataset has information about whether a person is in one of several differentexperimental groups (group), and their scores on three different types of memory tests

(recognition, free recall, and cued recall). The difficulty level of each memory task is

also rated.

We will treat the three different memory tasks as different examples of a single

phenomenon (memory). Therefore, we will look at all three togetheras dependentvariables in our analysis.


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A dialog box will appear. It should look very similar to the dialog box that weve beenusing for the past two weeks (except that it says multivariate up here, instead).

Now, hit the Options button to go on.

In a multivariate analysis, you have more

than one DV, so you can select many DVs

and put them into this box together. In this

case, we have three different memory tests

and we want to test for an effect of the IV on

all three of them at once.

In the fixed factor box, put the predictorthat were looking at: experimental group

membership.


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Again, this options dialog is very similar to the used in the univariate analyses.

Hit Continue, and then, back in the main dialog box, hit the Model button to goon.

Click on the observed power butto

to get the statistical power of the

multivariate tests.


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Heres the model dialog box, again very similar to the one for univariate analyses.

As usual, you can use the default value of full factorial, or you can select just certain

variables to be included in the model.

Go back to the main dialog box, and hit OK to run the analysis.


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The output has two segments. The first part gives you the results of the multivariate

tests.

Multivariate Testsd

Effect

Value F Hypothesis df Error df Sig.

Noncent.

Parameter

Observed

Powerb

Intercept Pil lai's Trace .947 249.681a

3.000 42.000 .000 749.044 1.000

Wilks' Lambda .053 249.681a

3.000 42.000 .000 749.044 1.000

Hotelling's Trace 17.834 249.681a

3.000 42.000 .000 749.044 1.000

Roy's Largest Root 17.834 249.681a

3.000 42.000 .000 749.044 1.000

group Pillai's Trace .464 2.683 9.000 132.000 .007 24.147 .940

Wilks' Lambda .592 2.737 9.000 102.368 .007 19.567 .864

Hotelling's Trace .597 2.698 9.000 122.000 .007 24.282 .941

Roy's Largest Root .326 4.777c

3.000 44.000 .006 14.330 .874

a. Exact statistic

b. Computed using alpha = .05

c. The statistic is an upper bound on F that yields a lower bound on the significance level.

d. Design: Intercept + group

As usual for these F-test results, ignore the section labeled Intercept.

These four numbers give you thep-values for the four different multivariate tests. These

results tell you if there is a significant effect of the IVs on all of the DVs, considered as a

group. If you are asked overall, is there a significant effect of something on some set of

variables, as a group, then you would run a MANOVA and look at these multivariate

tests for your conclusion.

Remember that theres no one single multivariate test; there are four different ones. Inthis case theyre all significant (p < .05), so we can conclude that Group Membership did

have a significant effect on the three different memory variables.


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Heres the second part of the results section. This gives univariate tests for the effects ofGroup Membership on each of the different DVs. Think of this table as several F-test

tables, all stacked on top of one another. For instance, if you look at all of the rows with

blue print, you could put them all back together into a single F-table. You could dosimilar re-arranging to get the individual F-tables for the other two variables.

Tests of Between-Subjects Effects

Source Dependent Variable Type III Sum of

Squares df Mean Square F Sig.

Noncent.

Parameter

Observed

Powerb

Corrected Modeldime

nsion

1

Recognition Test 26000.229a

3 8666.743 3.739 .018 11.217 .7

Cued Recall Test 17136.396c

3 5712.132 3.343 .028 10.030 .7

Free Recall Test 8305.583d

3 2768.528 3.687 .019 11.061 .7

Interceptdime

nsion

1

Recognition Test 827662.688 1 827662.688 357.080 .000 357.080 1.0

Cued Recall Test 708831.021 1 708831.021 414.865 .000 414.865 1.0

Free Recall Test 572470.083 1 572470.083 762.408 .000 762.408 1.0

groupdime

nsion

1

Recognition Test 26000.229 3 8666.743 3.739 .018 11.217 .7

Cued Recall Test 17136.396 3 5712.132 3.343 .028 10.030 .7

Free Recall Test 8305.583 3 2768.528 3.687 .019 11.061 .7

Errordime

nsion

1

Recognition Test 101986.083 44 2317.866

Cued Recall Test 75177.583 44 1708.581

Free Recall Test 33038.333 44 750.871

Totaldime

nsion

1

Recognition Test 955649.000 48

Cued Recall Test 801145.000 48

Free Recall Test 613814.000 48

Corrected Totaldime

nsion

1

Recognition Test 127986.313 47

Cued Recall Test 92313.979 47

Free Recall Test 41343.917 47

a. R Squared = .203 (Adjusted R Squared = .149)


c. R Squared = .186 (Adjusted R Squared = .130)

d. R Squared = .201 (Adjusted R Squared = .146)

These cells (the shaded ones) are the ones were most interested in. Thesep-values tellyou that Group Membership had a significant effect on the results of the Recognition Test

(p = .018), the results of the Cued Recall Test (p = .028), and the results of the Free

Recall Test (p = .019).

Please note that the results in this tableare not the results of a MANOVA. They are the

results of three separate univariate ANOVAs that are done as a step down analysis afteryou ran the MANOVA. This is something like doing post-hoc tests after a significant


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one-way F-test. The univariate results together do not add up to the multivariate test. Ifthe multivariate test is really what you are interested in, look at the first table of the

output instead. If the univariate tests are really what youre interested in, skip the

MANOVA and just do the three different univariate tests but you will need to do acorrection to your alpha level to control for inflated Type I error when doing multiple

tests!

MANCOVA in SPSS

Now lets go back to the main dialog box for the multivariate analysis, and add a

covariate to the model. The question here is does the effect of experimental group

membership on the three memory variables remain significant after controlling fortheitem difficulty of the memory tasks? To do this test, enter test item difficulty as a

covariate.


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Heres what the model dialog looks like. (Again, you can get the same result byleaving the model on its default setting, full factorial).

You do have to leave the Sums of Squares setting on Type III, in order to get a test of

the effects of each variable after controlling forthe effects of the others. (But thats the

default setting, so you dont actually need to do anything here).

Hit Continue, and then in the main dialog box, hit OK to run the test.


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Here are the resultsagain, the first section shows you the results of the multivariatetests (i.e., the effect of the various predictors on all of the memory tasks).

Multivariate Testsd

Effect

Value F Hypothesis df Error df Sig.

Noncent.

Parameter

Observed

Powerb

Intercept Pil la i's Trace .308 6.083a

3.000 41.000 .002 18.250 .942

Wilks' Lambda .692 6.083a

3.000 41.000 .002 18.250 .942

Hotelling's Trace .445 6.083a

3.000 41.000 .002 18.250 .942

Roy's Largest Root .445 6.083a

3.000 41.000 .002 18.250 .942

group Pillai's Trace .472 2.675 9.000 129.000 .007 24.078 .939

Wilks' Lambda .585 2.732 9.000 99.934 .007 19.523 .862

Hotelling's Trace .611 2.694 9.000 119.000 .007 24.242 .940

Roy's Largest Root .334 4.785c

3.000 43.000 .006 14.354 .873

difficlt Pillai's Trace .016 .224a

3.000 41.000 .879 .673 .089

Wilks' Lambda .984 .224a

3.000 41.000 .879 .673 .089

Hotelling's Trace .016 .224a

3.000 41.000 .879 .673 .089

Roy's Largest Root .016 .224a

3.000 41.000 .879 .673 .089

a. Exact statistic


c. The statistic is an upper bound on F that yields a lower bound on the significance level.

d. Design: Intercept + group + difficlt

You can see that difficulty has been included in this model as a covariate. Again, lookat the multivariate test results, just in the rows for the IV called Group. Again, all four

multivariate tests are significant, so we can conclude that the effects of group membership

on the three memory tasks are still significant, even after controlling for the effects of test

item difficulty on peoples performance on the three memory tasks.

Congratulations! You have now completed a one-waymultivariate analysis ofcovariance, or MANCOVA. We use this term because we have:

--one nominal-level predictor (or fixed factor)

--many I/R-level DVs--and an I/R-level predictor (as a covariate)

Paul F. Cook, University of Colorado Denver, Center for Nursing Research

Updated 1/10 with SPSS (PASW) version 18

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