Posted by
Rich Ulrich on
Jan 14, 2020; 5:06pm
URL: http://spssx-discussion.165.s1.nabble.com/ways-to-describe-the-MANOVA-effect-tp5738769p5738773.html
As an expert in Manova, my advice has always been,
"Avoid it when you can." Not only is interpretation
difficult, but there is a loss of power when compared
to direct tests of the relevant hypotheses.
For the example cited: Can /you/ give an easy statement of
what that finding is, in the scattergram?
Manova provides two or more "canonical factors" - it
is rather like a factor analysis on two sets of variables
at once, with the condition that there will be a maximum
amount of "prediction" (association) between the corresponding
factors of the two sets - #1 with #1, #2 with #2, etc.
With just two variables, there are only two simple factors,
the sum and the difference (with weightings attached).
When you see two /highly/ correlated variables like those
two in the example, the Difference between the two scores
/should be/ an obvious thing to test, though many people
don't recognize that. Their Sum is also a more "reliable" and
thus more powerful hypothesis to test, compared to testing
the two separately; however, for this example I'm not sure
that the Sum does make better sense than two univariate tests.
For two variables that are this highly correlated, you could
construct a new composite score which reflects the difference.
That could be tested as a single variable for the single hypothesis.
(To equalize the variances for any composite, I usually start with
z-scores; after a first pass to get the mean and standard deviation
of a new composite, which is most often a sum, I re-score the
composite to a "T-score" - mean of 50, SD of 10. That gives me
a somewhat-interpretible value without looking past the decimal.)
The part of the MANOVA output that shows you what is being
tested will be the canonical regressions for the two roots/solutions.
Each equation has a left side (dependent vars) and a right side
(independent vars). The example's equation that is significant is
the one which defines a difference.
The famous example of a practical use for the Manova result with
a Difference is: the scoring of IQ or Achievement Tests or SAT.
Testing may suggest that "reading speed" be subtracted from the
crude, summed score to improve the fit to other measures of
"competency". I forget what test actually does (or did) this.
--
Rich Ulrich
Hello,
I came across this blog post on this website:
https://statisticsbyjim.com/anova/multivariate-anova-manova-benefits-use/.
I am curious about the figure with the Scatterplot of Test vs. Satisfaction, with satisfaction on the X axis, test on the Y axis, and the three Methods as separate plot points on the graph.
My question is, in SPSS, what part of the output do I examine to determine the nature of the multi-variate effect? Based on the example and explanation on the website, it would seem that to arrive at the conclusion that there is a multi-variate effect, you
have to plot the effect by using a scatterplot. To arrive at the conclusion about the multivariate effect of the teaching method on both satisfaction and test score, you have to heuristically examine the scatterplot. Is there any section in the SPSS MANOVA
output that serves as an indicator to support the description about the nature of the multi-variate effect? Or do I just obtain the MANOVA test (e.g., Wilks' test) that indicates that there is a multivariate effect, and then to describe the actual multivariate
effect, I would have to construct a scatterplot and base my description on a heuristic examination of the scatterplot? If so, then it seems archaic to describe the multivariate effect simply based on a heuristic examination. It would be better if there was
a section of the MANOVA output that I could reference that would provide the statistical results that I could cite to describe the nature of the multivariate effect.
Thanks in advance.
Peter Ji
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