Multivariate comparison (Hotelling's T?)

[torvon]

Hello.

I have the following two problems, and I think I might need Hotelling's T test for that.

(1) I want to test whether my 9 dependent variables (9 symptoms) are equally high or not (equally
high = Null Hypothesis). I can run a couple of t-tests to compare them, but would like to do this in
one step. Is Hotelling's T the correct test for this? I googled for Hotelling's T, but the results are very
different from each other, and although Hotelling's T pops up under various options, I have not found
any way to test against the Null Hypothesis of equal severity.
The dependent variables are ordinal (0,1,2,3) and pretty skewed, but I guess I could treat them as
metric for this.

(2) I want to compare 9 dependent variables at time 1 to the same variables at time 2. I want to know
whether the profile of severity changes or not. How would I do this? Also Hotelling's T? If so, what
option exactly? Again google wasn't helpful, people say "MANOVA" or "SCALE", and yes, I do find an
output option, but nowhere does SPSS allow me to put down 2 measurement points.

Thank you!

=====================
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

[David Marso]

Look at GLM with REPEATED subcommand.

torvon wrote

Hello.

I have the following two problems, and I think I might need Hotelling's T test for that.

(1) I want to test whether my 9 dependent variables (9 symptoms) are equally high or not (equally
high = Null Hypothesis). I can run a couple of t-tests to compare them, but would like to do this in
one step. Is Hotelling's T the correct test for this? I googled for Hotelling's T, but the results are very
different from each other, and although Hotelling's T pops up under various options, I have not found
any way to test against the Null Hypothesis of equal severity.
The dependent variables are ordinal (0,1,2,3) and pretty skewed, but I guess I could treat them as
metric for this.

(2) I want to compare 9 dependent variables at time 1 to the same variables at time 2. I want to know
whether the profile of severity changes or not. How would I do this? Also Hotelling's T? If so, what
option exactly? Again google wasn't helpful, people say "MANOVA" or "SCALE", and yes, I do find an
output option, but nowhere does SPSS allow me to put down 2 measurement points.

Thank you!

=====================
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

[Swank, Paul R]

Question 1 sounds like a repeated measures design assuming the 9 dependent variables are all in the same scale. This can be done with a univariate repeated measures design or a multivariate design. However, Hotelling's T squared is the multivariate extension of the t test for two correlated measures or two independent groups. There are several multivariate tests available but I have always liked  Wilks' Lambda since 1 minus Wilks' lambda is a nice measure of effect size. The second question is what I would call doubly repeated measures since you have 9 dependent variables and two times. This could be handled as a multivariate repeated measures as well, using time for the repeated factor and DV for the multivariate test. As David suggests, see the GLM procedure.

 Dr. Paul R. Swank, Professor
Health Promotion and Behavioral Sciences
School of Public Health
University of Texas Health Science Center Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of David Marso
Sent: Monday, November 12, 2012 7:04 PM
To: [hidden email]
Subject: Re: Multivariate comparison (Hotelling's T?)

Look at GLM with REPEATED subcommand.


torvon wrote

> Hello.
>
> I have the following two problems, and I think I might need
> Hotelling's T test for that.
>
> (1) I want to test whether my 9 dependent variables (9 symptoms) are
> equally high or not (equally high = Null Hypothesis). I can run a
> couple of t-tests to compare them, but would like to do this in one
> step. Is Hotelling's T the correct test for this? I googled for
> Hotelling's T, but the results are very different from each other, and
> although Hotelling's T pops up under various options, I have not found
> any way to test against the Null Hypothesis of equal severity.
> The dependent variables are ordinal (0,1,2,3) and pretty skewed, but I
> guess I could treat them as metric for this.
>
> (2) I want to compare 9 dependent variables at time 1 to the same
> variables at time 2. I want to know whether the profile of severity
> changes or not. How would I do this? Also Hotelling's T? If so, what
> option exactly? Again google wasn't helpful, people say "MANOVA" or
> "SCALE", and yes, I do find an output option, but nowhere does SPSS
> allow me to put down 2 measurement points.
>
> Thank you!
>
> =====================
> 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 SIGNOFF SPSSX-L For a list of commands to
> manage subscriptions, send the command INFO REFCARD





-----
Please reply to the list and not to my personal email.
Those desiring my consulting or training services please feel free to email me.
--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Multivariate-comparison-Hotelling-s-T-tp5716159p5716160.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

=====================
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

[Rich Ulrich]

Yes, the first one looks like a univariate repeated measures test that
assumes the same scale.  Unless there is a very large N, I would expect
that  there is small power -- There are 9 items, and the separate items are
ordinal, 4-point items, which I (usually) would prefer to examine in the
form of composite scores.  Further, if there is an effect, I wonder if anyone
will be surprised that the 9 items do not have the same means.  That is,
it takes an effort to select items (and their wording) to achieve "equal
difficulty" or "equal pathology" or whatever.  For one population, or several.

Especially if there is strong stability for scores across time, the simple
and most effective way to test for "change of profile" might be to compute
the 9 change scores and to a simple one-way repeated measures test on
that set of scores. 

If you want to know if there is "improvement" from time 1 to 2, you do
compute the composite (average) pathology score for each period and
use a paired t-test.

--
Rich Ulrich

> Date: Tue, 13 Nov 2012 11:45:19 -0600
> From: [hidden email]
> Subject: Re: Multivariate comparison (Hotelling's T?)
> To: [hidden email]
>
> Question 1 sounds like a repeated measures design assuming the 9 dependent variables are all in the same scale. This can be done with a univariate repeated measures design or a multivariate design. However, Hotelling's T squared is the multivariate extension of the t test for two correlated measures or two independent groups. There are several multivariate tests available but I have always liked Wilks' Lambda since 1 minus Wilks' lambda is a nice measure of effect size. The second question is what I would call doubly repeated measures since you have 9 dependent variables and two times. This could be handled as a multivariate repeated measures as well, using time for the repeated factor and DV for the multivariate test. As David suggests, see the GLM procedure.
> ...

[Swank, Paul R]

I would agree as long as the nine items are basically measuring the same thing. Then it would be more powerful to combine them into a scale for analysis. If they do not measure the same thing, then that would not be the best way to go. The power for the first question is a function of the sample size and the degree of correlation between the measures.

 

Dr. Paul R. Swank, Professor

Health Promotion and Behavioral Sciences

School of Public Health

University of Texas Health Science Center Houston

 

From: Rich Ulrich [mailto:[hidden email]]
Sent: Tuesday, November 13, 2012 2:20 PM
To: Swank, Paul R; SPSS list
Subject: RE: Multivariate comparison (Hotelling's T?)

 

Yes, the first one looks like a univariate repeated measures test that
assumes the same scale.  Unless there is a very large N, I would expect
that  there is small power -- There are 9 items, and the separate items are
ordinal, 4-point items, which I (usually) would prefer to examine in the
form of composite scores.  Further, if there is an effect, I wonder if anyone
will be surprised that the 9 items do not have the same means.  That is,
it takes an effort to select items (and their wording) to achieve "equal
difficulty" or "equal pathology" or whatever.  For one population, or several.

Especially if there is strong stability for scores across time, the simple
and most effective way to test for "change of profile" might be to compute
the 9 change scores and to a simple one-way repeated measures test on
that set of scores. 

If you want to know if there is "improvement" from time 1 to 2, you do
compute the composite (average) pathology score for each period and
use a paired t-test.

--
Rich Ulrich

> Date: Tue, 13 Nov 2012 11:45:19 -0600
> From: [hidden email]
> Subject: Re: Multivariate comparison (Hotelling's T?)
> To: [hidden email]
>
> Question 1 sounds like a repeated measures design assuming the 9 dependent variables are all in the same scale. This can be done with a univariate repeated measures design or a multivariate design. However, Hotelling's T squared is the multivariate extension of the t test for two correlated measures or two independent groups. There are several multivariate tests available but I have always liked Wilks' Lambda since 1 minus Wilks' lambda is a nice measure of effect size. The second question is what I would call doubly repeated measures since you have 9 dependent variables and two times. This could be handled as a multivariate repeated measures as well, using time for the repeated factor and DV for the multivariate test. As David suggests, see the GLM procedure.
> ...

[torvon]

Please excuse the late answer! For some reason my Gmail account marked your very helpful responses as spam, which had never happened before.

The point of my investigation is to how that symptoms differ from each other on various dimensions. Severity at time 1, and change from time 1 to time 2 are just two dimensions of many reported in the paper, but the ones I did not know how to investigate statistically. I absolutely want to avoid to use a sum score for "general psychopathology".

For test 1 (do symptoms at time 1 have equal severity): Rich, you are correct with your statement:
"It takes an effort to select items (and their wording) to achieve "equal difficulty" or "equal pathology" or whatever.  For one population, or several."
No one will be surprised indeed by a ridiculous Hotelling' T^2 test (I have about 150 zeros after the decimal point), but some symptoms are more than 20 times as severe as others, and I simply need a statistical test to report this fact (although it is absolutely obvious from looking at the mean scores).

For test 2, comparing whether symptoms increase differentially from each other:
"Especially if there is strong stability for scores across time, the simple
and most effective way to test for "change of profile" might be to compute
the 9 change scores and to a simple one-way repeated measures test on
that set of scores."
I don't understand what you mean. If I compute change scores, I lose repeated measures by definition because the information of 2 measurement points is merged into 1 (change). What procedure would you recommend?

If I would not use change scores, and simply want to compare s1_t0 to s1_t1, s2_t0 to t2_t1, s3_t0 to s3_t1 in a multivariate way, which procedure do I use? I found Hotelling's T in the Scale -> Reliability section as test statistic, but there is no way to specify 2 measurement points.

Thanks
T

[torvon]

"This could be handled as a multivariate repeated measures as well, using time for the repeated factor and DV for the multivariate test. As David suggests, see the GLM procedure."

I do not find Hotelling's T in the repeated measures section. I did find Hotelling's Trace in the multivariate GLM section (not repeated). Could I "trick" SPSS by defining my 9 variables as DVs, and time as factor (using a long version of the data)? And what exactly is Hotelling's Trace? Can I report this as statistic in a paper: "Hotelling's Trace = xxx, P<.001. This means that the means of all items differed from t1 to t2."?

Thank you