We Have Pre-Intervention and Post-Intervention Data for Four Variables

Pre-Post MANOVA

We have pre-intervention and post-intervention data for four variables:

• AUDIT – a screening test for problem drinking (of ethanol)
• BMI – body mass index
• SUD – a measure of subjective distress
• Weight – body weight

We wish to analyze all four of these variables simultaneously. First I conduct a Doubly Multivariate Repeated Measures ANOVA using SPSS. Here is the code:

manovaAUDIT_BaselineAUDIT_PostBMI_BaselineBMI_PostSUD_BaselineSUD_PostWeight_BaselineWeight_Post

/ wsfactors = time(2) /

measure = AUDIT BMI SUD Weight /

print=transform signif(univhypoth) error(sscp) / design .

Here are selected parts of the output:

EFFECT .. TIME

Multivariate Tests of Significance (S = 1, M = 1 , N = 6 )

Test Name Value Exact F Hypoth. DF Error DF Sig. of F

Pillais .88970 28.23142 4.00 14.00 .000

Hotellings 8.06612 28.23142 4.00 14.00 .000

Wilks .11030 28.23142 4.00 14.00 .000

Roys .88970 [This value is incorrect, it should be the same as Hotelling’s trace]

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The multivariate tests here show that there is a significant change from pre to post on a weighted linear combination of the four outcome variables.

EFFECT .. TIME (Cont.)

Univariate F-tests with (1,17) D. F.

Variable Hypoth. SS Error SS Hypoth. MS Error MS F Sig. of F

T2 9.00000 17.00000 9.00000 1.00000 9.00000 .008

T4 .34517 .47444 .34517 .02791 12.36802 .003

T6 96.69444 20.80556 96.69444 1.22386 79.00801 .000

T8 15.08028 22.32472 15.08028 1.31322 11.48345 .003

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Since the multivariate test is significant, I am comfortable conducting univariate analyses, one on each outcome variable. The results here are significant for each outcome variable. These F tests are absolutely equivalent to correlated samples t tests.

Note that the values of t here are, when squared, exactly equal to the values of F above, and the values of p also identical to those from the F tests above.

I computed, for each outcome variable, a difference score, Pre minus Post. One-sample t tests (null is  = 0) are identical to the correlated t tests.

Technically, the analysis done first here is not a doubly multivariate analysis. There are only two levels for the repeated measures dimension, and thus only one contrast to define it. We could have simply done a standard MANOVA on the difference scores:

GLM AUDIT_DiffBMI_DiffSUD_DiffWeight_Diff

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/CRITERIA=ALPHA(.05).

Notice that the multivariate tests here are identical to those produced in the first analysis.

SAS. To do this analysis with SAS, you need to create a difference score for each outcome variable and then test an intercept-only model. Here is the code to test the intercept-only model:

ProcGLM; ModelAUDIT_DiffBMI_DiffSUD_DiffWeight_Diff = / SS1;

manova h=intercept; run; quit;

The output is the same as with SPSS, just formatted differently. First come the univariate tests, which are identical to correlated t-tests.

Dependent Variable: AUDIT_Diff

Dependent Variable: BMI_Diff

Dependent Variable: SUD_Diff

Dependent Variable: Weight_Diff

Then comes the multivariate test:

Doubly Multivariate Analysis of Repeated Measures Designs

The Data

Karl L. Wuensch, June, 2018