We'll be drawing heavily from the following article, which contains worked-out examples and many helpful tips:
Grice, J. W., & Iwasaki, M. (2007). A truly multivariate approach to MANOVA. Applied Multivariate Research, 12, 199-226.
Grice and Iwasaki's example involves one independent variable (culture/nationality: European-Americans; Asian-Americans; Asian-Internationals) and the "Big Five" personality traits as multiple dependent variables (neuroticism, extraversion, openness, agreeableness, and conscientiousness).
MANOVA takes the multiple DV's and adds them up in a linear-weighted combination (see "Step 2" on p. 206, the grey box on p. 207, and the equations toward the bottom of p. 209). According to Grice and Iwasaki, "MANOVA maximizes the differences between group means on linear combinations of the dependent variables" (p. 216). See also the paragraph beginning "Reasoning multivariately..." on p. 202.
There are four different MANOVA significance tests in most outputs (Pillai, Wilks, Hotelling, Roy).
Bryan Manly (Multivariate Statistical Methods: A Primer, 3rd edition, 2005) writes that, "Generally, the four tests... can be expected to give similar significance levels, so there is no real need to choose between them... They are all also considered to be fairly robust [to violations of assumptions] if the sample sizes are equal or nearly so for the [cells]" (p. 49). Manly also notes that Pillai's Trace appears to be most robust to violations of assumptions.
If the overall MANOVA is significant, it has been customary to follow up with a series of "regular" univariate ANOVA's to see which one or more of the multiple DV's in the set differs across the IV groups (e.g., running one ANOVA with just the personality trait of neuroticism as the DV, running another ANOVA with just the trait of extraversion as the DV, etc.). However, this routine has come into question by many statisticians (see Grice and Iwasaki, p. 203, paragraph beginning with "Second, many researchers...").
In fact, under some circumstances, one might want to skip the MANOVA altogether and just run a separate ANOVA on each DV. Write Grice and Iwasaki:
Are we truly interested in examining the multivariate, linear combinations of Big Five traits, or are we content with considering each trait separately? ... if we have no intention of interpreting the multivariate composites (that is, the linear combinations of traits -- the dependent variables), then the univariate analyses... are perfectly sufficient. There is certainly no shame in conducting multiple ANOVAs and separately interpreting the results for each dependent variable. It is more than a methodological faux pas, however, to conduct a MANOVA with no intent of interpreting the multivariate combination of variables (p. 202-203; red highlight by Dr. Reifman, other emphases in original).
(See also the discussion on p. 203 of controlling the error-rate of significance levels when performing multiple tests, as well as this webpage.)
In order to get everything you need from MANOVA, you need to run your analysis twice in SPSS, once in the Windows version and once via syntax (to get the weighting coefficients). See the link in the right-hand column "Getting More Extensive Output in SPSS" (especially pages 29 and 33).
MANOVA anticipates Discriminant Analysis, which we'll cover later in the course, and even Structural Equation Modeling, which is the subject matter of QM IV.
Let's conclude with a song:
It’s a MANOVA
Lyrics by Alan Reifman
(May be sung to the tune of “Maneater,” Hall/Oates/Allen; for audio of a performed version, click here)
You have your, IV’s set up,
Sometimes, as a 2 X 4,
You look for effects, on the dependent variable, yes you do,
Multiple measures,
Aren’t what you’re used to seeing, just a single outcome,
You study, alcohol use,
By gender and, by student groups,
You can measure drinking, different ways, to get a broader view,
Multiple measures,
Volume, times drunk, and bingeing days, just to name a few,
(Slow) Mul-ti-ple DV’s,
Analyze ’em, all at once,
Doing so’s, a breeze,
It’s a MANOVA,
(Slow) Mul-ti-ple DV’s,
Analyze ’em, all at once,
Doing so’s, a breeze,
It’s a MANOVA,
(Brief interlude)
The DV’s are, given weights,
To create, a composite,
The IV groups, are then compared, on these composite scores,
Multiple results,
Are printed out, on which you can, follow through,
(Slow) Mul-ti-ple DV’s,
Analyze ’em, all at once,
Doing so’s, a breeze,
It’s a MANOVA,
(Slow) Mul-ti-ple DV’s,
Analyze ’em, all at once,
Doing so’s, a breeze,
It’s a MANOVA
