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Question about SPSS MANOVA output

Jeff Miller

My question concerns two separate tables of "Multivariate" tests produced by the GLM command. As an example, I will use a design with two groups (e.g., males/females). Each individual was measured at each of three time points (time1/time2/time3) on each of four dependent variables (dv1/dv2/dv3/dv4).

(At the end of this question is a syntax file that will generate sample data and run the analysis, allowing me to ask the question with reference to specific values.)

The first "Multivariate Tests^a" output table appears early in the output, and it includes one section for "Between Subjects" effects (i.e., intercept & group, in this design) and another section for "Within Subjects" effects (i.e., Time and Time*group).

The second "Multivariate^a,b" table appears later in the output (after Mauchley's test) under the major heading "Tests of Within-Subjects Effects".

Each of these two tables displays the results of multivariate tests (eg Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources (i.e., Time and Time*group), but the two tables give different values.

My question is simply, "what is the difference between these two tables?"  For example, what are the models and null hypotheses in each case? Why are the error df's different?   What would it mean if the first table's test of Time was significant and the second table's was not, or vice versa?

Any insight would be greatly appreciated.  Thanks for your time.

-----  Syntax file follows: Just copy, paste, and run all to see a specific data set and analysis illustrating my question.

* Here is a syntax file to generate and analyze an example data set,
* so that the question can be posed in terms of specific values.

* For this example, there are 2 groups of randomly-selected individuals (cases).
* Each case is measured at 3 time points on 4 different DVs.

* Set the RNG seed so that the results are reproduced exactly.
set RNG=MT MTINDEX=121314.15.

new file.
input program.

compute #SampleSize = 50.

loop #i = 1 to #SampleSize.
   compute group = 1.
   compute dv1time1 = rv.normal(0,1).
   compute dv1time2 = rv.normal(0,1).
   compute dv1time3 = rv.normal(0,1).
   compute dv2time1 = rv.normal(0,1).
   compute dv2time2 = rv.normal(0,1).
   compute dv2time3 = rv.normal(0,1).
   compute dv3time1 = rv.normal(0,1).
   compute dv3time2 = rv.normal(0,1).
   compute dv3time3 = rv.normal(0,1).
   compute dv4time1 = rv.normal(0,1).
   compute dv4time2 = rv.normal(0,1).
   compute dv4time3 = rv.normal(0,1).
   end case.
end loop.
loop #i = 1 to #SampleSize.
   compute group = 2.
   compute dv1time1 = rv.normal(0,1).
   compute dv1time2 = rv.normal(0,1).
   compute dv1time3 = rv.normal(0,1).
   compute dv2time1 = rv.normal(0,1).
   compute dv2time2 = rv.normal(0,1).
   compute dv2time3 = rv.normal(0,1).
   compute dv3time1 = rv.normal(0,1).
   compute dv3time2 = rv.normal(0,1).
   compute dv3time3 = rv.normal(0,1).
   compute dv4time1 = rv.normal(0,1).
   compute dv4time2 = rv.normal(0,1).
   compute dv4time3 = rv.normal(0,1).
   end case.
end loop.

end file.
end input program.
execute.

GLM
  dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
  dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
  /WSFACTOR = Time 3 Polynomial
  /MEASURE = DV1 DV2 DV3 DV4
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(group)
  /EMMEANS = TABLES(Time)
  /EMMEANS = TABLES(group*Time)
  /PRINT = DESCRIPTIVE HOMOGENEITY
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = Time
  /DESIGN = group .

* Here is a more specific version of my question.
*
* An earlier "Multivariate Tests^a" output table includes the line:
*    Within Subjects           Time        Pillai's Trace       0.145   1.935^b       8.000   91.000    0.064
*
* Two tables farther along is a  "Multivariate^a,b" table that includes the line:
*    Within Subjects           Time        Pillai's Trace       0.068   1.712         8.000  388.000    0.094
*
* These two tables include the same sources (i.e., Time and Time*group),
*   but they give different values and different error df's.
*
* What is the difference between these two tables?
* (My question pertains to both of the sources, Time and Time*group).

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Re: Question about SPSS MANOVA output

Kirill Orlov
The first table represents Multivariate approach results to RM-ANOVA.
The second table (Tests of within-subject effects) represents Univariate approach results to RM-ANOVA.
SPSS Help for RM GLM clearly outlines the distinction.
See also e.g. here http://stats.stackexchange.com/a/15212/3277 with some further links.

05.09.2016 5:12, Jeff Miller пишет:
My question concerns two separate tables of "Multivariate" tests produced by
the GLM command. As an example, I will use a design with two groups (e.g.,
males/females). Each individual was measured at each of three time points
(time1/time2/time3) on each of four dependent variables (dv1/dv2/dv3/dv4).

(At the end of this question is a syntax file that will generate sample data
and run the analysis, allowing me to ask the question with reference to
specific values.)

The first "Multivariate Tests^a" output table appears early in the output,
and it includes one section for "Between Subjects" effects (i.e., intercept
& group, in this design) and another section for "Within Subjects" effects
(i.e., Time and Time*group).

The second "Multivariate^a,b" table appears later in the output (after
Mauchley's test) under the major heading "Tests of Within-Subjects Effects".

Each of these two tables displays the results of multivariate tests (eg
Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources (i.e.,
Time and Time*group), but the two tables give different values.

My question is simply, "what is the difference between these two tables?" 
For example, what are the models and null hypotheses in each case? Why are
the error df's different?   What would it mean if the first table's test of
Time was significant and the second table's was not, or vice versa?

Any insight would be greatly appreciated.  Thanks for your time.

-----  Syntax file follows: Just copy, paste, and run all to see a specific
data set and analysis illustrating my question.

* Here is a syntax file to generate and analyze an example data set,
* so that the question can be posed in terms of specific values.

* For this example, there are 2 groups of randomly-selected individuals
(cases).
* Each case is measured at 3 time points on 4 different DVs.

* Set the RNG seed so that the results are reproduced exactly.
set RNG=MT MTINDEX=121314.15.

new file.
input program.

compute #SampleSize = 50.

loop #i = 1 to #SampleSize.
   compute group = 1.
   compute dv1time1 = rv.normal(0,1).
   compute dv1time2 = rv.normal(0,1).
   compute dv1time3 = rv.normal(0,1).
   compute dv2time1 = rv.normal(0,1).
   compute dv2time2 = rv.normal(0,1).
   compute dv2time3 = rv.normal(0,1).
   compute dv3time1 = rv.normal(0,1).
   compute dv3time2 = rv.normal(0,1).
   compute dv3time3 = rv.normal(0,1).
   compute dv4time1 = rv.normal(0,1).
   compute dv4time2 = rv.normal(0,1).
   compute dv4time3 = rv.normal(0,1).
   end case.
end loop.
loop #i = 1 to #SampleSize.
   compute group = 2.
   compute dv1time1 = rv.normal(0,1).
   compute dv1time2 = rv.normal(0,1).
   compute dv1time3 = rv.normal(0,1).
   compute dv2time1 = rv.normal(0,1).
   compute dv2time2 = rv.normal(0,1).
   compute dv2time3 = rv.normal(0,1).
   compute dv3time1 = rv.normal(0,1).
   compute dv3time2 = rv.normal(0,1).
   compute dv3time3 = rv.normal(0,1).
   compute dv4time1 = rv.normal(0,1).
   compute dv4time2 = rv.normal(0,1).
   compute dv4time3 = rv.normal(0,1).
   end case.
end loop.

end file.
end input program.
execute.

GLM
  dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
  dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
  /WSFACTOR = Time 3 Polynomial
  /MEASURE = DV1 DV2 DV3 DV4
  /METHOD = SSTYPE(3)
  /EMMEANS = TABLES(group)
  /EMMEANS = TABLES(Time)
  /EMMEANS = TABLES(group*Time)
  /PRINT = DESCRIPTIVE HOMOGENEITY
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = Time
  /DESIGN = group .

* Here is a more specific version of my question.
*
* An earlier "Multivariate Tests^a" output table includes the line:
*    Within Subjects           Time        Pillai's Trace       0.145  
1.935^b       8.000   91.000    0.064
*
* Two tables farther along is a  "Multivariate^a,b" table that includes the
line:
*    Within Subjects           Time        Pillai's Trace       0.068  
1.712         8.000  388.000    0.094
*
* These two tables include the same sources (i.e., Time and Time*group),
*   but they give different values and different error df's.
*
* What is the difference between these two tables?
* (My question pertains to both of the sources, Time and Time*group).





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Re: Question about SPSS MANOVA output

Bruce Weaver
Administrator
That doesn't sound right to me, Kirill.  As the attached Excel file shows, both tables Jeff refers to are showing multivariate test results for the Time and Time*Group terms (with no separation by DV1 through DV4).

Members who do not use Nabble can download the attached Excel file here:

http://spssx-discussion.1045642.n5.nabble.com/Question-about-SPSS-MANOVA-output-td5733053.html

Miller_example.xls

Kirill Orlov wrote
The first table represents Multivariate approach results to RM-ANOVA.
The second table (Tests of within-subject effects) represents Univariate
approach results to RM-ANOVA.
SPSS Help for RM GLM clearly outlines the distinction.
See also e.g. here http://stats.stackexchange.com/a/15212/3277 with some
further links.

05.09.2016 5:12, Jeff Miller пишет:
> My question concerns two separate tables of "Multivariate" tests produced by
> the GLM command. As an example, I will use a design with two groups (e.g.,
> males/females). Each individual was measured at each of three time points
> (time1/time2/time3) on each of four dependent variables (dv1/dv2/dv3/dv4).
>
> (At the end of this question is a syntax file that will generate sample data
> and run the analysis, allowing me to ask the question with reference to
> specific values.)
>
> The first "Multivariate Tests^a" output table appears early in the output,
> and it includes one section for "Between Subjects" effects (i.e., intercept
> & group, in this design) and another section for "Within Subjects" effects
> (i.e., Time and Time*group).
>
> The second "Multivariate^a,b" table appears later in the output (after
> Mauchley's test) under the major heading "Tests of Within-Subjects Effects".
>
> Each of these two tables displays the results of multivariate tests (eg
> Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources (i.e.,
> Time and Time*group), but the two tables give different values.
>
> My question is simply, "what is the difference between these two tables?"
> For example, what are the models and null hypotheses in each case? Why are
> the error df's different?   What would it mean if the first table's test of
> Time was significant and the second table's was not, or vice versa?
>
> Any insight would be greatly appreciated.  Thanks for your time.
>
> -----  Syntax file follows: Just copy, paste, and run all to see a specific
> data set and analysis illustrating my question.
>
> * Here is a syntax file to generate and analyze an example data set,
> * so that the question can be posed in terms of specific values.
>
> * For this example, there are 2 groups of randomly-selected individuals
> (cases).
> * Each case is measured at 3 time points on 4 different DVs.
>
> * Set the RNG seed so that the results are reproduced exactly.
> set RNG=MT MTINDEX=121314.15.
>
> new file.
> input program.
>
> compute #SampleSize = 50.
>
> loop #i = 1 to #SampleSize.
>     compute group = 1.
>     compute dv1time1 = rv.normal(0,1).
>     compute dv1time2 = rv.normal(0,1).
>     compute dv1time3 = rv.normal(0,1).
>     compute dv2time1 = rv.normal(0,1).
>     compute dv2time2 = rv.normal(0,1).
>     compute dv2time3 = rv.normal(0,1).
>     compute dv3time1 = rv.normal(0,1).
>     compute dv3time2 = rv.normal(0,1).
>     compute dv3time3 = rv.normal(0,1).
>     compute dv4time1 = rv.normal(0,1).
>     compute dv4time2 = rv.normal(0,1).
>     compute dv4time3 = rv.normal(0,1).
>     end case.
> end loop.
> loop #i = 1 to #SampleSize.
>     compute group = 2.
>     compute dv1time1 = rv.normal(0,1).
>     compute dv1time2 = rv.normal(0,1).
>     compute dv1time3 = rv.normal(0,1).
>     compute dv2time1 = rv.normal(0,1).
>     compute dv2time2 = rv.normal(0,1).
>     compute dv2time3 = rv.normal(0,1).
>     compute dv3time1 = rv.normal(0,1).
>     compute dv3time2 = rv.normal(0,1).
>     compute dv3time3 = rv.normal(0,1).
>     compute dv4time1 = rv.normal(0,1).
>     compute dv4time2 = rv.normal(0,1).
>     compute dv4time3 = rv.normal(0,1).
>     end case.
> end loop.
>
> end file.
> end input program.
> execute.
>
> GLM
>    dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
>    dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
>    /WSFACTOR = Time 3 Polynomial
>    /MEASURE = DV1 DV2 DV3 DV4
>    /METHOD = SSTYPE(3)
>    /EMMEANS = TABLES(group)
>    /EMMEANS = TABLES(Time)
>    /EMMEANS = TABLES(group*Time)
>    /PRINT = DESCRIPTIVE HOMOGENEITY
>    /CRITERIA = ALPHA(.05)
>    /WSDESIGN = Time
>    /DESIGN = group .
>
> * Here is a more specific version of my question.
> *
> * An earlier "Multivariate Tests^a" output table includes the line:
> *    Within Subjects           Time        Pillai's Trace       0.145
> 1.935^b       8.000   91.000    0.064
> *
> * Two tables farther along is a  "Multivariate^a,b" table that includes the
> line:
> *    Within Subjects           Time        Pillai's Trace       0.068
> 1.712         8.000  388.000    0.094
> *
> * These two tables include the same sources (i.e., Time and Time*group),
> *   but they give different values and different error df's.
> *
> * What is the difference between these two tables?
> * (My question pertains to both of the sources, Time and Time*group).
>
>
>
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Question-about-SPSS-MANOVA-output-tp5733053.html
> Sent from the SPSSX Discussion mailing list archive at 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
>




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http://sites.google.com/a/lakeheadu.ca/bweaver/

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Re: Question about SPSS MANOVA output

Mike
Okay, believe it or not, this question has been asked previously
(on the Usenet spss group and the answer is on the IBM SPSS
website).  The key thing to notice is that the second table has
the footnote:

b. Tests based on averaged variables

This is makes the second Multivariate results different from
the first table which uses the original variables.  For more on this
point see:
https://groups.google.com/forum/#!topic/comp.soft-sys.stat.spss/UeqpN6ISxy8

and

http://www-01.ibm.com/support/docview.wss?uid=swg21476707

If the within-subject factor has only two levels, both multivariate
results
would be the same.  The following quote is from the IBM website
in describing why the two multivariate results differ when W-S
levels > 2 (and more than one dependent variable is used):

|       The first table entitled Multivariate Tests carries the true
|doubly-multivariate test statistics. The averaged results appear
|in the table entitled Multivariate that is listed under the heading
|Tests of Within-Subjects Effects. Averaged results are like those
|you would have obtained had you set up a multivariate model with
|a data set that is configured for the univariate approach to repeated
|measures (e.g., a split-plot approach).

The IBM SPSS webiste provides three GLM syntax programs that
shows how one would do the doubly-multivariate analysis (first syntax)
and how to do the univariate or split-plot analysis (3rd syntax; NOTE:
"Subject" is included as a factor for the example used -- for the OP's
situation, he doesn't really have a doubly multivariate situation but a
"straight" univariate withn-subject design requiring a repeated measures
ANOVA).  The split-plot analysis assumes a form of multivariate
sphericity
that SPSS does not text for, hence, one wouldn't know if the analysis
appropriate or the degree of the violation.  The doubly multivariate
analysis does not make this assumption, hence one would focus on
the first set of Multivariate results if that is of concern/interest.

Now, I assume that that the OP just wants an old-fashioned G-ddamned
repeated measues ANOVA and is not really interested in the Multivariate
or MANOVA (not to be confused with the SPSS procedure MANOVA)
results.  If printing the Multivariate results were left up to the
programmer
instead of being automatically presented, the confusion that invariably
shows up (NOTE: the Usenet group post is from 2009 and it references
older posts asking the question "Why oh why do the Multivariate results
tables disagree?!?").

It would be helpful if (a) the distinction provided on IBM  SPSS webpage
was clearly provided in the SPSS manual (I looked but didn't find it;
I'm
open to correction on this point) and/or (b) provided a brief
explanation
in the output after the second Multivariate table.

Or maybe they could build in a command or keyword "repeated" into GLM
that it should *only* be treated as a repeated measures design instead
of
some kind of multivariate analysis.  This would save having to delete
the
multivariate results especially if one does a one-way repeated measures
ANOVA.

But what do I know, right?

-Mike Palij
New York University
[hidden email]


----- Original Message -----
From: "Bruce Weaver" <[hidden email]>
To: <[hidden email]>
Sent: Tuesday, September 06, 2016 9:12 AM
Subject: Re: Question about SPSS MANOVA output


That doesn't sound right to me, Kirill.  As the attached Excel file
shows,
*both* tables Jeff refers to are showing multivariate test results for
the
Time and Time*Group terms (with no separation by DV1 through DV4).

Members who do not use Nabble can download the attached Excel file here:

http://spssx-discussion.1045642.n5.nabble.com/Question-about-SPSS-MANOVA-output-td5733053.html

Miller_example.xls
<http://spssx-discussion.1045642.n5.nabble.com/file/n5733058/Miller_example.xls>


Kirill Orlov wrote

> The first table represents Multivariate approach results to RM-ANOVA.
> The second table (Tests of within-subject effects) represents
> Univariate
> approach results to RM-ANOVA.
> SPSS Help for RM GLM clearly outlines the distinction.
> See also e.g. here http://stats.stackexchange.com/a/15212/3277 with
> some
> further links.
>
> 05.09.2016 5:12, Jeff Miller пишет:
>> My question concerns two separate tables of "Multivariate" tests
>> produced
>> by
>> the GLM command. As an example, I will use a design with two groups
>> (e.g.,
>> males/females). Each individual was measured at each of three time
>> points
>> (time1/time2/time3) on each of four dependent variables
>> (dv1/dv2/dv3/dv4).
>>
>> (At the end of this question is a syntax file that will generate
>> sample
>> data
>> and run the analysis, allowing me to ask the question with reference
>> to
>> specific values.)
>>
>> The first "Multivariate Tests^a" output table appears early in the
>> output,
>> and it includes one section for "Between Subjects" effects (i.e.,
>> intercept
>> & group, in this design) and another section for "Within Subjects"
>> effects
>> (i.e., Time and Time*group).
>>
>> The second "Multivariate^a,b" table appears later in the output
>> (after
>> Mauchley's test) under the major heading "Tests of Within-Subjects
>> Effects".
>>
>> Each of these two tables displays the results of multivariate tests
>> (eg
>> Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources
>> (i.e.,
>> Time and Time*group), but the two tables give different values.
>>
>> My question is simply, "what is the difference between these two
>> tables?"
>> For example, what are the models and null hypotheses in each case?
>> Why
>> are
>> the error df's different?   What would it mean if the first table's
>> test
>> of
>> Time was significant and the second table's was not, or vice versa?
>>
>> Any insight would be greatly appreciated.  Thanks for your time.
>>
>> -----  Syntax file follows: Just copy, paste, and run all to see a
>> specific
>> data set and analysis illustrating my question.
>>
>> * Here is a syntax file to generate and analyze an example data set,
>> * so that the question can be posed in terms of specific values.
>>
>> * For this example, there are 2 groups of randomly-selected
>> individuals
>> (cases).
>> * Each case is measured at 3 time points on 4 different DVs.
>>
>> * Set the RNG seed so that the results are reproduced exactly.
>> set RNG=MT MTINDEX=121314.15.
>>
>> new file.
>> input program.
>>
>> compute #SampleSize = 50.
>>
>> loop #i = 1 to #SampleSize.
>>     compute group = 1.
>>     compute dv1time1 = rv.normal(0,1).
>>     compute dv1time2 = rv.normal(0,1).
>>     compute dv1time3 = rv.normal(0,1).
>>     compute dv2time1 = rv.normal(0,1).
>>     compute dv2time2 = rv.normal(0,1).
>>     compute dv2time3 = rv.normal(0,1).
>>     compute dv3time1 = rv.normal(0,1).
>>     compute dv3time2 = rv.normal(0,1).
>>     compute dv3time3 = rv.normal(0,1).
>>     compute dv4time1 = rv.normal(0,1).
>>     compute dv4time2 = rv.normal(0,1).
>>     compute dv4time3 = rv.normal(0,1).
>>     end case.
>> end loop.
>> loop #i = 1 to #SampleSize.
>>     compute group = 2.
>>     compute dv1time1 = rv.normal(0,1).
>>     compute dv1time2 = rv.normal(0,1).
>>     compute dv1time3 = rv.normal(0,1).
>>     compute dv2time1 = rv.normal(0,1).
>>     compute dv2time2 = rv.normal(0,1).
>>     compute dv2time3 = rv.normal(0,1).
>>     compute dv3time1 = rv.normal(0,1).
>>     compute dv3time2 = rv.normal(0,1).
>>     compute dv3time3 = rv.normal(0,1).
>>     compute dv4time1 = rv.normal(0,1).
>>     compute dv4time2 = rv.normal(0,1).
>>     compute dv4time3 = rv.normal(0,1).
>>     end case.
>> end loop.
>>
>> end file.
>> end input program.
>> execute.
>>
>> GLM
>>    dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
>>    dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
>>    /WSFACTOR = Time 3 Polynomial
>>    /MEASURE = DV1 DV2 DV3 DV4
>>    /METHOD = SSTYPE(3)
>>    /EMMEANS = TABLES(group)
>>    /EMMEANS = TABLES(Time)
>>    /EMMEANS = TABLES(group*Time)
>>    /PRINT = DESCRIPTIVE HOMOGENEITY
>>    /CRITERIA = ALPHA(.05)
>>    /WSDESIGN = Time
>>    /DESIGN = group .
>>
>> * Here is a more specific version of my question.
>> *
>> * An earlier "Multivariate Tests^a" output table includes the line:
>> *    Within Subjects           Time        Pillai's Trace       0.145
>> 1.935^b       8.000   91.000    0.064
>> *
>> * Two tables farther along is a  "Multivariate^a,b" table that
>> includes
>> the
>> line:
>> *    Within Subjects           Time        Pillai's Trace       0.068
>> 1.712         8.000  388.000    0.094
>> *
>> * These two tables include the same sources (i.e., Time and
>> Time*group),
>> *   but they give different values and different error df's.
>> *
>> * What is the difference between these two tables?
>> * (My question pertains to both of the sources, Time and Time*group).
>>
>>
>>
>>
>>
>> --
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Re: Question about SPSS MANOVA output

Kornbrot, Diana
In reply to this post by Jeff Miller
1st output table is the one to use
it makes full use of the correlation matrix between repeated measures, i.e different correlation between t1, t2 and t2,t3
2nd table ASSUMES all pairwise correlation same and estimates a mean correlation and then makes various corrections for correlation differences
it was rocket science when SPSS launched some decades ago when the truly multivariate method was computationally expensive
why it is still there I have no idea, but spss does not like to drop anything

the Maunchley test is testing whether all the pairwise correlations ARE the same. In my view it is better to use full correlation matrix even if Maunchley is ns [power is low anyway]

best
Diana

On 5 Sep 2016, at 03:12, Jeff Miller <[hidden email]> wrote:

My question concerns two separate tables of "Multivariate" tests produced by
the GLM command. As an example, I will use a design with two groups (e.g.,
males/females). Each individual was measured at each of three time points
(time1/time2/time3) on each of four dependent variables (dv1/dv2/dv3/dv4).

(At the end of this question is a syntax file that will generate sample data
and run the analysis, allowing me to ask the question with reference to
specific values.)

The first "Multivariate Tests^a" output table appears early in the output,
and it includes one section for "Between Subjects" effects (i.e., intercept
& group, in this design) and another section for "Within Subjects" effects
(i.e., Time and Time*group).

The second "Multivariate^a,b" table appears later in the output (after
Mauchley's test) under the major heading "Tests of Within-Subjects Effects".

Each of these two tables displays the results of multivariate tests (eg
Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources (i.e.,
Time and Time*group), but the two tables give different values.

My question is simply, "what is the difference between these two tables?"
For example, what are the models and null hypotheses in each case? Why are
the error df's different?   What would it mean if the first table's test of
Time was significant and the second table's was not, or vice versa?

Any insight would be greatly appreciated.  Thanks for your time.

-----  Syntax file follows: Just copy, paste, and run all to see a specific
data set and analysis illustrating my question.

* Here is a syntax file to generate and analyze an example data set,
* so that the question can be posed in terms of specific values.

* For this example, there are 2 groups of randomly-selected individuals
(cases).
* Each case is measured at 3 time points on 4 different DVs.

* Set the RNG seed so that the results are reproduced exactly.
set RNG=MT MTINDEX=121314.15.

new file.
input program.

compute #SampleSize = 50.

loop #i = 1 to #SampleSize.
 compute group = 1.
 compute dv1time1 = rv.normal(0,1).
 compute dv1time2 = rv.normal(0,1).
 compute dv1time3 = rv.normal(0,1).
 compute dv2time1 = rv.normal(0,1).
 compute dv2time2 = rv.normal(0,1).
 compute dv2time3 = rv.normal(0,1).
 compute dv3time1 = rv.normal(0,1).
 compute dv3time2 = rv.normal(0,1).
 compute dv3time3 = rv.normal(0,1).
 compute dv4time1 = rv.normal(0,1).
 compute dv4time2 = rv.normal(0,1).
 compute dv4time3 = rv.normal(0,1).
 end case.
end loop.
loop #i = 1 to #SampleSize.
 compute group = 2.
 compute dv1time1 = rv.normal(0,1).
 compute dv1time2 = rv.normal(0,1).
 compute dv1time3 = rv.normal(0,1).
 compute dv2time1 = rv.normal(0,1).
 compute dv2time2 = rv.normal(0,1).
 compute dv2time3 = rv.normal(0,1).
 compute dv3time1 = rv.normal(0,1).
 compute dv3time2 = rv.normal(0,1).
 compute dv3time3 = rv.normal(0,1).
 compute dv4time1 = rv.normal(0,1).
 compute dv4time2 = rv.normal(0,1).
 compute dv4time3 = rv.normal(0,1).
 end case.
end loop.

end file.
end input program.
execute.

GLM
dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
/WSFACTOR = Time 3 Polynomial
/MEASURE = DV1 DV2 DV3 DV4
/METHOD = SSTYPE(3)
/EMMEANS = TABLES(group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(group*Time)
/PRINT = DESCRIPTIVE HOMOGENEITY
/CRITERIA = ALPHA(.05)
/WSDESIGN = Time
/DESIGN = group .

* Here is a more specific version of my question.
*
* An earlier "Multivariate Tests^a" output table includes the line:
*    Within Subjects           Time        Pillai's Trace       0.145  
1.935^b       8.000   91.000    0.064
*
* Two tables farther along is a  "Multivariate^a,b" table that includes the
line:
*    Within Subjects           Time        Pillai's Trace       0.068  
1.712         8.000  388.000    0.094
*
* These two tables include the same sources (i.e., Time and Time*group),
*   but they give different values and different error df's.
*
* What is the difference between these two tables?
* (My question pertains to both of the sources, Time and Time*group).





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Work
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College Lane, Hatfield, Hertfordshire AL10 9AB, UK
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Home
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London N2 0LT, UK
+44 (0) 208 444 2081                                                    



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Re: Question about SPSS MANOVA output

Mike
After doing some more searching of the literature and the web,
let me say that Diana is correct, that is, if one is going to use a
multivariate analysis instead of traditional repeated measures ANOVA,
the approach SPSS calls "doubly-multivariate results" should be
used.  But a few more points need to be made:

(1) The question about the two sets of multivariate results was
original asked on the SPSS Usenet group back in 1998 and
David Nichols (Hi David!) gave a response. His post can be
read here:
https://groups.google.com/forum/#!topic/comp.soft-sys.stat.spss/857xHuoXDYw

And his response is reproduced here:

|I already answered these questions individually, but in
|case others are interested, the tests mentioned are
|indeed the same as those labeled averaged multivariate
|tests in MANOVA.

NOTE to those still using the SPSS MANOVA procedure:
check to see whether only the average multivariate results
are still provided.

|They ignore the parts of the SSCP matrices that involve
|covariation among transformed variables within the same
|measure, but incorporate covariation among transformed
|variables in different measures to produce multivariate tests. I
|'ve seen them referred to as Scheffe's multivariate mixed
|model tests in an article by Robert Boik (I don't have the full
|reference handy). Unfortunately, SPSS does not at the
|current time have a test for the condition of multisample
|sphericity that is required for them to be valid. To get corrected
|averaged univariate tests printed in Release 7.5, double
|click on the table with the averaged tests, then choose
|Pivot->Move Layers to Rows, or activate the pivoting trays
|and move the Epsilon corrections icons from the Layers
|area to the Rows area. In Release 8.0, the table is presented
|with these tests displayed.

(2) I don't know which Boik article David is referring to but
one that explicitly refers to the second method is covered in
the following reference:

Boik, R. J. (1991). Scheffés mixed model for multivariate
repeated measures: a relative efficiency evaluation. Communications
in Statistics-Theory and Methods, 20(4), 1233-1255.

At the end of the article's abstract Boik writes:

|Based on relative efficiency evaluations, the adjusted MMM
|[NOTE: MMM = Scheffe's multivatiate mixed model] analyses
|described in this paper can be recommended only when sample
|sizes are very small or there is reason to believe that multivariate
|sphericity is nearly satisfied. Neither the €-adjusted analysis
|suggested in the SPSS MANOVA output (release 4.0) nor the
|adjusted analysis suggested by Boik (1988) can be recommended
|at all.

NOTE: Yes, Boik refers to good old version 4.0 of SPSS.
I Don't think SPSS has changed MANOVA or the multivariate
analysis much since back then (except GLM came after
version 4.0).

(3) An old reference that argues strongly for the Multivariate
approach to repeated measures analysis is the following
reference:

O'Brien, R. G., & Kaiser, M. K. (1985). MANOVA method for
analyzing repeated measures designs: an extensive primer.
Psychological bulletin, 97(2), 316.

The authors use the term MANOVA to refer to both the statistical
procedure and the SPSSX (what it was called back then) procedure.

(4) Given the issues above, one wonders why SPSS has not
provided the multivariate sphericity test that would show whether
the second set of multivariate (Scheffe) results are valid. Without
it, one has to try to work it out on one's own or see if some other
package provides it (or do the analysis in a SEM package).
And does the MANOVA procedure (still available via syntax)
still only give the Scheffe results?  If so, warnings about whether
to use it or not should be more widely communicated.

If anyone has more up-to-date knowledge about this situation,
either in SPSS or in other programs (e.g., SAS, Stata, etc.),
I think it would be of benefit to the user community if it were
provided here.

-Mike Palij
New York University
[hidden email]



----- Original Message -----
From: Kornbrot, Diana
To: [hidden email]
Sent: Tuesday, September 06, 2016 11:27 AM
Subject: Re: Question about SPSS MANOVA output


1st output table is the one to use
it makes full use of the correlation matrix between repeated measures,
i.e different correlation between t1, t2 and t2,t3
2nd table ASSUMES all pairwise correlation same and estimates a mean
correlation and then makes various corrections for correlation
differences
it was rocket science when SPSS launched some decades ago when the truly
multivariate method was computationally expensive
why it is still there I have no idea, but spss does not like to drop
anything

the Maunchley test is testing whether all the pairwise correlations ARE
the same. In my view it is better to use full correlation matrix even if
Maunchley is ns [power is low anyway]

best
Diana


On 5 Sep 2016, at 03:12, Jeff Miller <[hidden email]> wrote:

My question concerns two separate tables of "Multivariate" tests
produced by
the GLM command. As an example, I will use a design with two groups
(e.g.,
males/females). Each individual was measured at each of three time
points
(time1/time2/time3) on each of four dependent variables
(dv1/dv2/dv3/dv4).

(At the end of this question is a syntax file that will generate sample
data
and run the analysis, allowing me to ask the question with reference to
specific values.)

The first "Multivariate Tests^a" output table appears early in the
output,
and it includes one section for "Between Subjects" effects (i.e.,
intercept
& group, in this design) and another section for "Within Subjects"
effects
(i.e., Time and Time*group).

The second "Multivariate^a,b" table appears later in the output (after
Mauchley's test) under the major heading "Tests of Within-Subjects
Effects".

Each of these two tables displays the results of multivariate tests (eg
Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources
(i.e.,
Time and Time*group), but the two tables give different values.

My question is simply, "what is the difference between these two
tables?"
For example, what are the models and null hypotheses in each case? Why
are
the error df's different?   What would it mean if the first table's test
of
Time was significant and the second table's was not, or vice versa?

Any insight would be greatly appreciated.  Thanks for your time.

-----  Syntax file follows: Just copy, paste, and run all to see a
specific
data set and analysis illustrating my question.

* Here is a syntax file to generate and analyze an example data set,
* so that the question can be posed in terms of specific values.

* For this example, there are 2 groups of randomly-selected individuals
(cases).
* Each case is measured at 3 time points on 4 different DVs.

* Set the RNG seed so that the results are reproduced exactly.
set RNG=MT MTINDEX=121314.15.

new file.
input program.

compute #SampleSize = 50.

loop #i = 1 to #SampleSize.
 compute group = 1.
 compute dv1time1 = rv.normal(0,1).
 compute dv1time2 = rv.normal(0,1).
 compute dv1time3 = rv.normal(0,1).
 compute dv2time1 = rv.normal(0,1).
 compute dv2time2 = rv.normal(0,1).
 compute dv2time3 = rv.normal(0,1).
 compute dv3time1 = rv.normal(0,1).
 compute dv3time2 = rv.normal(0,1).
 compute dv3time3 = rv.normal(0,1).
 compute dv4time1 = rv.normal(0,1).
 compute dv4time2 = rv.normal(0,1).
 compute dv4time3 = rv.normal(0,1).
 end case.
end loop.
loop #i = 1 to #SampleSize.
 compute group = 2.
 compute dv1time1 = rv.normal(0,1).
 compute dv1time2 = rv.normal(0,1).
 compute dv1time3 = rv.normal(0,1).
 compute dv2time1 = rv.normal(0,1).
 compute dv2time2 = rv.normal(0,1).
 compute dv2time3 = rv.normal(0,1).
 compute dv3time1 = rv.normal(0,1).
 compute dv3time2 = rv.normal(0,1).
 compute dv3time3 = rv.normal(0,1).
 compute dv4time1 = rv.normal(0,1).
 compute dv4time2 = rv.normal(0,1).
 compute dv4time3 = rv.normal(0,1).
 end case.
end loop.

end file.
end input program.
execute.

GLM
dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY  group
/WSFACTOR = Time 3 Polynomial
/MEASURE = DV1 DV2 DV3 DV4
/METHOD = SSTYPE(3)
/EMMEANS = TABLES(group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(group*Time)
/PRINT = DESCRIPTIVE HOMOGENEITY
/CRITERIA = ALPHA(.05)
/WSDESIGN = Time
/DESIGN = group .

* Here is a more specific version of my question.
*
* An earlier "Multivariate Tests^a" output table includes the line:
*    Within Subjects           Time        Pillai's Trace       0.145
1.935^b       8.000   91.000    0.064
*
* Two tables farther along is a  "Multivariate^a,b" table that includes
the
line:
*    Within Subjects           Time        Pillai's Trace       0.068
1.712         8.000  388.000    0.094
*
* These two tables include the same sources (i.e., Time and Time*group),
*   but they give different values and different error df's.
*
* What is the difference between these two tables?
* (My question pertains to both of the sources, Time and Time*group).





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________________________________________
Professor Diana Kornbrot
Work
University of Hertfordshire
College Lane, Hatfield, Hertfordshire AL10 9AB, UK
+44 (0) 170 728 4626
[hidden email]
http://dianakornbrot.wordpress.com/
http://go.herts.ac.uk/Diana_Kornbrot
skype: kornbrotme
Home
19 Elmhurst Avenue
London N2 0LT, UK
+44 (0) 208 444 2081




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REFCARD

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Re: Question about SPSS MANOVA output

Bruce Weaver
Administrator
The following MANOVA syntax appears to produce the same results as Jeff's GLM command:

MANOVA
 dv1time1 dv1time2 dv1time3
 dv2time1 dv2time2 dv2time3
 dv3time1 dv3time2 dv3time3
 dv4time1 dv4time2 dv4time3 BY group(1,2)
 /WSFACTORS=Time(3)
 /MEASURE = DV1 DV2 DV3 DV4 /* /WSDESIGN=Time, Time BY Group */
 /PRINT=SIGNIF(HYPOTH AVERF)
 /DESIGN=GROUP
.

I commented out the WSDESIGN sub-command, because it was causing the syntax to fail.  While exploring that, I pasted the following example from the FM into my syntax editor, and key words MANOVA and WSDESIGN appeared in red (rather than blue & green respectively), indicating that SPSS didn't like the command syntax.  

Example from the FM:
MANOVA TEMP1 TO TEMP6, WEIGHT1 TO WEIGHT6 BY GROUP(1,2)
 /WSFACTORS=DAY(3) AMPM(2)
 /MEASURE=TEMP WEIGHT
 /WSDESIGN=DAY, AMPM, DAY BY AMPM
 /PRINT=SIGNIF(HYPOTH AVERF)
 /DESIGN.

Anyway, the output from my MANOVA syntax above can be viewed in the attached text file.  (Non-nabble users will have to visit this thread in Nabble to get it.)  For convenience, I pasted results from GLM right below the corresponding results from MANOVA.  Inside the text file, search for <FROM GLM:> to find those pasted results.  As you will see, the MANOVA command above has produced all the same multivariate tests.

HTH.

Miller_example_via_MANOVA.txt


p.s. - Jon or Rick, or anyone else who might know:  Is the WSDESIGN sub-command for MANOVA no longer supported?  


Mike wrote
--- snip ---

NOTE to those still using the SPSS MANOVA procedure:
check to see whether only the average multivariate results
are still provided.

--- snip ---
--
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: Question about SPSS MANOVA output

Kirill Orlov
In reply to this post by Bruce Weaver
Bruce, that might be. I didn't open (didn't notice) the files provided by the OP and probably assumed about the question incorrectly.


06.09.2016 16:12, Bruce Weaver пишет:
That doesn't sound right to me, Kirill.  As the attached Excel file shows,
*both* tables Jeff refers to are showing multivariate test results for the
Time and Time*Group terms (with no separation by DV1 through DV4).

Members who do not use Nabble can download the attached Excel file here:

http://spssx-discussion.1045642.n5.nabble.com/Question-about-SPSS-MANOVA-output-td5733053.html

Miller_example.xls
<http://spssx-discussion.1045642.n5.nabble.com/file/n5733058/Miller_example.xls>  





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Re: Question about SPSS MANOVA output

Jeff Miller
[This is a follow-up from the OP.]

First, thanks to everyone who replied.  I greatly appreciate your time.  The responses gave me several new links and pointers that look helpful, and I will definitely follow those up.

Perhaps I should say that I am asking this question mostly to inform myself so that I can better teach MANOVA to some PhD students—not because I want to analyze an actual data set.  As we go through this SPSS output, students often ask seemingly obvious questions that I can’t answer.

For example, students want to know what, exactly, is meant by the table note “b. Tests are based on averaged variables”?  One naive interpretation of this note is that this table is based on an analysis of a “dvavg” that one could compute (in my example) with these statements:
compute dvavgtime1=(dv1time1+dv2time1+dv3time1+dv4time1)/4.
compute dvavgtime2=(dv1time2+dv2time2+dv3time2+dv4time2)/4.
compute dvavgtime3=(dv1time3+dv2time3+dv3time3+dv4time3)/4.
execute.

If this interpretation were correct, then surely some GLM of the dvavgtimeN scores would give the same results shown in the earlier table marked with note b, but I can find no such analysis.  Evidently, the variables are being averaged in some other way, and it would be nice to know how.

Students also ask about the error df’s in the different tables.  Why are these values on the order of 380 for the table marked with note b, as compared with error df’s of 91 for the same sources in the original multivariate table? And what is going on with Roy’s largest root, which has the same hypothesis & error df’s as the other tests in the original table but has only half as many df’s for hypothesis and error in the table marked with note b? These students have a good grasp of how df’s relate to observations and model terms.   It would be great to be able to give them some conceptual feeling for the models from which these dfs emerge—something more concrete than my current vague mumbling about “univariate approach” versus “multivariate approach”.

Finally, I notice that Mike Palij suggested that I don't really have a doubly multivariate situation but a "straight" univariate within-subject design requiring a repeated measures ANOVA.  I’m not sure how I gave that impression.  If it was that I used rv.normal(0,1) for all four dv’s then I apologize for being unclear—probably I should have used very distinct mu’s and sigma’s for the four dv’s so that it would be obvious that they were incommensurable quantities—i.e., that I really had a doubly multivariate design.
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Re: Question about SPSS MANOVA output

David Marso
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Go to Help Algorithms.
Should address all of these questions and more.
---
Jeff Miller wrote
[This is a follow-up from the OP.]

First, thanks to everyone who replied.  I greatly appreciate your time.  The responses gave me several new links and pointers that look helpful, and I will definitely follow those up.

Perhaps I should say that I am asking this question mostly to inform myself so that I can better teach MANOVA to some PhD students—not because I want to analyze an actual data set.  As we go through this SPSS output, students often ask seemingly obvious questions that I can’t answer.

For example, students want to know what, exactly, is meant by the table note “b. Tests are based on averaged variables”?  One naive interpretation of this note is that this table is based on an analysis of a “dvavg” that one could compute (in my example) with these statements:
compute dvavgtime1=(dv1time1+dv2time1+dv3time1+dv4time1)/4.
compute dvavgtime2=(dv1time2+dv2time2+dv3time2+dv4time2)/4.
compute dvavgtime3=(dv1time3+dv2time3+dv3time3+dv4time3)/4.
execute.

If this interpretation were correct, then surely some GLM of the dvavgtimeN scores would give the same results shown in the earlier table marked with note b, but I can find no such analysis.  Evidently, the variables are being averaged in some other way, and it would be nice to know how.

Students also ask about the error df’s in the different tables.  Why are these values on the order of 380 for the table marked with note b, as compared with error df’s of 91 for the same sources in the original multivariate table? And what is going on with Roy’s largest root, which has the same hypothesis & error df’s as the other tests in the original table but has only half as many df’s for hypothesis and error in the table marked with note b? These students have a good grasp of how df’s relate to observations and model terms.   It would be great to be able to give them some conceptual feeling for the models from which these dfs emerge—something more concrete than my current vague mumbling about “univariate approach” versus “multivariate approach”.

Finally, I notice that Mike Palij suggested that I don't really have a doubly multivariate situation but a "straight" univariate within-subject design requiring a repeated measures ANOVA.  I’m not sure how I gave that impression.  If it was that I used rv.normal(0,1) for all four dv’s then I apologize for being unclear—probably I should have used very distinct mu’s and sigma’s for the four dv’s so that it would be obvious that they were incommensurable quantities—i.e., that I really had a doubly multivariate design.
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Re: Question about SPSS MANOVA output

Jeff Miller
> Go to Help Algorithms.
> Should address all of these questions and more.
---
Thanks for the tip, but unfortunately this material doesn't help me at all.  A big problem is that I can't see how to connect the algorithms described in the Help to the two output tables that I am trying to understand.  For example, a single general model is specified under "Model (GLM algorithms)".  I guess both tables are computed using versions of this model, but there is no indication understandable by me (yes, I realize this may be the problem) of how that model is applied differently in these two tables (e.g., constrained in one table).
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Re: Question about SPSS MANOVA output

Jon Peck
The What's This help might provide useful information here, though I haven't looked at the specific text.  To see it, double click the table and then right click on a column header.

On Tue, Sep 13, 2016 at 10:17 PM, Jeff Miller <[hidden email]> wrote:
> Go to Help Algorithms.
> Should address all of these questions and more.
---
Thanks for the tip, but unfortunately this material doesn't help me at all.
A big problem is that I can't see how to connect the algorithms described in
the Help to the two output tables that I am trying to understand.  For
example, a single general model is specified under "Model (GLM algorithms)".
I guess both tables are computed using versions of this model, but there is
no indication understandable by me (yes, I realize this may be the problem)
of how that model is applied differently in these two tables (e.g.,
constrained in one table).



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Re: Question about SPSS MANOVA output

Mike
In reply to this post by Jeff Miller
Previously Dave Marso wrote:
>> Go to Help Algorithms.
>> Should address all of these questions and more.
>
On Wednesday, September 14, 2016 12:17 AM, Jeff Miller wrote:
> Thanks for the tip, but unfortunately this material doesn't help
>me at all. A big problem is that I can't see how to connect the
>algorithms described in the Help to the two output tables that I
>am trying to understand.

It is not clear what it is that you don't understand.  Let's be more
specific: I don't know what version of SPSS you're using but
since I'm using ver 23, let's work with that. Let me suggest that
you use the PDF for the Algorithms (it should be located in the
directiory for IBM SPSS); if you can't find on your machine,
go to the IBM SPSS webiste and download a copy; go to:
http://www-01.ibm.com/support/docview.wss?uid=swg27043946#en

If you go to page 492, it will put you on a page for GLM algorithms.
for the two version of the multivariate tests.

The top part of the page describing the calculationss for the
Multivariate
tests for Wihtin-Subjects without the assumption of multivariate
sphericity -- Steps 2 and 3 specifies how the S matrice (for Hypothesis
and Error matrices) are computefd for each of the multivariate tests
(see page 482-484 for the multivariate test calculations). This is done
for each level of the between-subjects variable.

The bottom of the page covers the "Averaged Tests on the Within-
Subjects Effects" (aka Scheffe's Mixed Multivariate Model). Steps
1 to 6 identifies the specific calculations used and you can compare
them to the calculations used in steps 2 and 3 in the Multivariate
tests above.

Is the problem you can't follow the matrix operations specified in
the two sections or is it something else?

You may want to look at the following references:

The original article by Scheffe describing his mixed model analysis:
Scheffe, H. (1956). A" mixed model" for the analysis of variance.
The Annals of Mathematical Statistics, 23-36.
A PDF copy is available on the Project Euclid website; see:
http://projecteuclid.org/euclid.aoms/1177728348

I believe I previously mentioned the following article by Boik but
repeat it here for completeness sake:
Boik, R. J. (1991). Scheffés mixed model for multivariate
repeated measures: a relative efficiency evaluation.
Communications in Statistics-Theory and Methods,
20(4), 1233-1255.
Availabe at:
http://www.tandfonline.com/doi/pdf/10.1080/03610929108830562?needAccess=true

And you might want to look at the following article by Davidson
that compares the univariate repeated measures ANOVA to the
Averaged Multivariate/Scheffe MMM analysis (when the assumptions
for the Average Multivariate test are met, it is more powerful than
the univariate ANOVA and the non-average MANOVA -- the
problem is that SPSS does not provide a test for multivariate
sphericity, etc.); see:
Davidson, M. L. (1972). Univariate versus multivariate tests
in repeated-measures experiments. Psychological Bulletin,
77(6), 446.

It seems to me that SPSS promotes the use of the non-averaged
MANOVA for within-subject variables even when they are all
the same (e.g., reaction times under different conditions).  If you
have a copy of Tabachnick & Fidell (6th Edition), see pages 310-311
for details on doing MANOVA/MANCOVA in SPSS using
either the procedure MANOVA or GLM -- they differ in what
they provide and depending upon one's need, one might prefer
one over the other or use both.

>For example, a single general model is specified under "Model (GLM
>algorithms)".
> I guess both tables are computed using versions of this model, but
> there is
> no indication understandable by me (yes, I realize this may be the
> problem)
> of how that model is applied differently in these two tables (e.g.,
> constrained in one table).

-Mike Palij
New York University
[hidden email]

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Re: Question about SPSS MANOVA output

Jeff Miller
Thanks very much, Mike.  The detailed road map you provided should help me a lot.

> Is the problem you can't follow the matrix operations specified in the two sections

Well, yes and no.  I believe that I could reproduce the algorithm (say, in MATLAB),
so I can follow it in that sense.  At this point I would be very hard pressed to say
what was going on, though.  I find step 5 under the Averaged Tests to be the
most mysterious.  It appears to me that the averaging takes place here, but I
am not sure.  Maybe this will become clear when I work through some examples.

I will check out all of the references you suggested; so far, I’ve only looked at this one:

> Davidson, M. L. (1972). Univariate versus multivariate tests in repeated-measures experiments.

Initially, this only seems to compare the G-G adjusted univariate versus multivariate tests
in cases where there is only one DV (e.g., RT in a variety of conditions tested within Ss)—not
the doubly repeated-measures case.  But I believe the regular multivariate versus “averaged tests"
multivariate analyses that I am struggling with are most distinct in the doubly repeated-measures
case.  I’ll have to study the article a bit more—maybe I am just overlooking the “averaged tests” bit.

> It is not clear what it is that you don't understand.

Such a broad topic…For starters, I would like to be able to explain to students:

1) What is the difference between the conclusions that would be appropriate from significant
effects in the regular multivariate versus “averaged tests” multivariate?

2) Under what circumstances* would one test have more power than the other?  (*For example,
it would be nice to be able to generate simulated data favoring one test or the other.)
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