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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