ways to describe the MANOVA effect

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ways to describe the MANOVA effect

pji
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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Re: ways to describe the MANOVA effect

Bruce Weaver
Administrator
Disclaimer:  I'm no expert in multivariate models, but I think the usual
approach would be to look at a plot showing the centroids for the 3 groups.
Here's some SPSS syntax that might be close to what you want (using Jim
Frost's CSV data file from that site).   HTH.


PRESERVE.
SET DECIMAL DOT.

GET DATA  /TYPE=TXT
  /FILE="C:\bw\SPSS\data\MANOVA_example.csv"
  /ENCODING='UTF8'
  /DELIMITERS=","
  /QUALIFIER='"'
  /ARRANGEMENT=DELIMITED
  /FIRSTCASE=2
  /DATATYPEMIN PERCENTAGE=95.0
  /VARIABLES=
  Method AUTO
  Test AUTO
  Satisfaction AUTO
  /MAP.
RESTORE.
CACHE.

GRAPH
  /SCATTERPLOT(BIVAR)=Satisfaction WITH Test BY Method
  /MISSING=LISTWISE
  /TITLE='Scatterplot of Test vs Satisfaction'.

CORRELATIONS Satisfaction with Test.

* The MANOVA model.
GLM Test Satisfaction BY Method
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /PRINT=DESCRIPTIVE
  /CRITERIA=ALPHA(.05)
  /DESIGN= Method.

* Use DISCRIMINANT to plot the centroids.
DISCRIMINANT Groups=Method(1,3)
 /VARIABLES=Satisfaction Test
 /PLOT=COMBINED.

* Alternative approach:  ANCOVA with Y=Test, Covariate = Satisfaction.

UNIANOVA Test BY Method WITH Satisfaction
  /METHOD=SSTYPE(3)
  /INTERCEPT=INCLUDE
  /EMMEANS=TABLES(Method) WITH(Satisfaction=MEAN) COMPARE ADJ(LSD)
  /CRITERIA=ALPHA(0.05)
  /DESIGN=Satisfaction Method.



pji wrote

> 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
>
>
> =====================
> To manage your subscription to SPSSX-L, send a message to

> LISTSERV@.UGA

>  (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
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-----
--
Bruce Weaver
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"When all else fails, RTFM."

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=====================
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Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.
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Re: ways to describe the MANOVA effect

Rich Ulrich
In reply to this post by pji
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


From: SPSSX(r) Discussion <[hidden email]> on behalf of Ji, Peter <[hidden email]>
Sent: Tuesday, January 14, 2020 2:06 AM
To: [hidden email] <[hidden email]>
Subject: ways to describe the MANOVA effect
 
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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[hidden email] (not to SPSSX-L), with no body text except the
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Re: ways to describe the MANOVA effect

Bruce Weaver
Administrator
I like that advice.  My own observations suggest that more often than not,
people use MANOVA as a precursor to multiple ANOVAs.  They seem to believe
that a significant MANOVA buys protection against Type I error in the
subsequent ANOVAs in the same way that a significant omnibus F-test buys
protection for the subsequent t-tests when one uses Fisher's LSD (with 3
groups).  But as Huberty & Morris clearly say, it just ain't so!  For them,
it boils down to this:  If you have a multivariate question, use MANOVA; but
if you have a series of univariate questions, use a series of ANOVAs.  (In
the latter case, you might consider some kind of adjustment for
multiplicity--but that's another can of worms!)

https://pdfs.semanticscholar.org/ee6c/77c99c8e4530d0cccaedf85ed525fb22a02d.pdf



Rich Ulrich wrote
> As an expert in Manova, my advice has always been,
> "Avoid it when you can."  
>
> --- snip ---





-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
Sent from: http://spssx-discussion.1045642.n5.nabble.com/

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD
--
Bruce Weaver
bweaver@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.