How to Perform a MANOVA in SPSS

8/3/2019 How to Perform a MANOVA in SPSS

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A dialog box will appear. It should look very similar to the dialog box that we’ve 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 morethan one DV, so you can select many DVsand put them into this box together. In thiscase, we have three different memory testsand we want to test for an effect of the IV onall three of them at once.

In the “fixed factor” box, put the predictorthat we’re looking at: experimental groupmembership.



Here’s 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.



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

Multivariate TestsEffect Value F Hypothesis

df Error df Sig.

Intercept Pillai's Trace .947 249.681 3.000 42.000 .000Wilks' Lambda .053 249.681 3.000 42.000 .000

Hotelling's Trace 17.834 249.681 3.000 42.000 .000Roy's Largest Root 17.834 249.681 3.000 42.000 .000

GROUP Pillai's Trace .464 2.683 9.000 132.000 .007Wilks' Lambda .592 2.737 9.000 102.368 .007

Hotelling's Trace .597 2.698 9.000 122.000 .007Roy's Largest Root .326 4.777 3.000 44.000 .006

a Exact statisticb The statistic is an upper bound on F that yields a lower bound on the significance level.c Design: Intercept+GROUP

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

These four numbers give you the p-values for the four different multivariate tests. Theseresults 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 multivariatetests for your conclusion.

Remember that there’s no one single multivariate test; there are four different ones. Inthis case they’re all significant ( p < .05), so we can conclude that Group Membership did have a significant effect on the three different memory variables.



Here’s the second part of the results section. This gives univariate tests for the effects of Group Membership on each of the different DVs. Think of this table as several F -testtables, 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 EffectsSource Dependent Variable Type III Sum of

Squaresdf Mean Square F Sig.

CorrectedModel

Recognition Test 26000.229 3 8666.743 3.739 .018

Cued Recall Test 17136.396 3 5712.132 3.343 .028Free Recall Test 8305.583 3 2768.528 3.687 .019

Intercept Recognition Test 827662.687 1 827662.687 357.080 .000Cued Recall Test 708831.021 1 708831.021 414.865 .000Free Recall Test 572470.083 1 572470.083 762.408 .000

GROUP Recognition Test 26000.229 3 8666.743 3.739 .018Cued Recall Test 17136.396 3 5712.132 3.343 .028Free Recall Test 8305.583 3 2768.528 3.687 .019

Error Recognition Test 101986.083 44 2317.866Cued Recall Test 75177.583 44 1708.581Free Recall Test 33038.333 44 750.871

Total Recognition Test 955649.000 48Cued Recall Test 801145.000 48Free Recall Test 613814.000 48

Corrected Total Recognition Test 127986.313 47Cued Recall Test 92313.979 47Free Recall Test 41343.917 47

a R Squared = .203 (Adjusted R Squared = .149)b R Squared = .186 (Adjusted R Squared = .130)c R Squared = .201 (Adjusted R Squared = .146)

These cells (the shaded ones) are the ones we’re most interested in. These p-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 FreeRecall Test ( p = .019).

Please note that the results in this table are not the results of a MANOVA . They are theresults of three separate univariate ANOVAs that are done as a “step down analysis” after you ran the MANOVA. This is something like doing post-hoc tests after a significantone-way F -test. The univariate results together do not add up to the multivariate test. If the multivariate test is really what you are interested in, look at the first table of theoutput instead. If the univariate tests are really what you’re interested in, skip theMANOVA 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 multipletests!



MANCOVA in SPSS Now let’s go back to the main dialog box for the multivariate analysis, and add acovariate to the model. The question here is “does the effect of experimental groupmembership on the three memory variables remain significant after controlling for theitem difficulty of the memory tasks?” To do this test, enter “test item difficulty” as a

covariate.



Here’s 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 for the effects of the others. (But that’s thedefault setting, so you don’t actually need to do anything here).

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



Here are the results —again, 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 TestsEffect Value F Hypothesis

df Error df Sig.

Intercept Pillai's Trace .308 6.083 3.000 41.000 .002Wilks' Lambda .692 6.083 3.000 41.000 .002


GROUP Pillai's Trace .472 2.675 9.000 129.000 .007Wilks' Lambda .585 2.732 9.000 99.934 .007


DIFFICLT Pillai's Trace .016 .224 3.000 41.000 .879Wilks' Lambda .984 .224 3.000 41.000 .879

Hotelling's Trace .016 .224 3.000 41.000 .879Roy's Largest Root .016 .224 3.000 41.000 .879

a Exact statistic

b The statistic is an upper bound on F that yields a lower bound on the significance level.c Design: Intercept+GROUP+DIFFICLT

You can see that “difficulty” has been included in this model as a covariate. Again, look at 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 membershipon the three memory tasks are still significant, even after controlling for the effects of test item difficulty on people’s performance on the three memory tasks.

Congratulations! You have now completed a one-way multivariate analysis of covariance , 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)

How to Perform a MANOVA in SPSS

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