ANOVA

[haytham siala]

Is the homogoneity of variance-covariance prerequisite to ANOVA a
requirement?

If yes, if my data failed the homogoneity of variance-covariance test,
should I use a non-parametric test instead or is ANOVA robust enough to be
conducted even if the data fails the homogoneity of variance-covariance
test?

HAIDER.




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ANOVA

[haytham siala]

Can I perform an ANOVA on standardized variables?





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Re: ANOVA

[Rich Ulrich]

On Sat, 5 Feb 2000 16:46:38 -, "haytham siala"
<[EMAIL PROTECTED]> wrote:

> Is the homogoneity of variance-covariance prerequisite to ANOVA a
> requirement?

No, it is a warning that your model might be inappropriate, in any of
several ways.  A single EXTREME outlier could make any average
meaningless, regardless of N.  If your averages all seem useful, then
the ANOVA is probably robust.

If your groups have equal Ns, the tests are quite good in terms of
comparing the means.

> If yes, if my data failed the homogoneity of variance-covariance test,
> should I use a non-parametric test instead or is ANOVA robust enough to be
> conducted even if the data fails the homogoneity of variance-covariance
> test?

The proper response, if the failure is an important one, is to further
review your assumptions.   Which specific transformation or
non-parametric test might test what you want to test?

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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ANOVA/ MANOVA

[sofyan2000]

I have conducted a repeated measure mixed two-factor ANOVA on one sample
consisting of 2 groups (conservatives and liberals). The dependent variables
where ATTA (attitude towards policy A) and ATTB (attitude towardfs B). I
have a few questions:

1. What statistical ANOVA test can reveal an outlier in my data?

2. If my test failed the 'homogeneity of variance/ covariance' test, should
I conduct a MANOVA ( learnt that this test does not require a homogeneity of
variance/ covariance test)?

3. Which part of the SPSS results (which heading?) afer running an MANOVA
shows the interaction between the between groups IV (political category
conservative vs. liberals) and the within-groups DV (ATTA & ATTB).

Thanks.






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ANOVA data

[haytham siala]

Can I perform an ANOVA on standardized variables?







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ANOVA problem

[Asst Professor]

I have data from a 24 item (1-4 likert scale) survey for 5 groups with varying
Ns (9,16,23,34,43). According to the Levene homogeniety of variance test, I
also have varying means for some questions and not others.

I find conflicting sources about which ANOVA/post hoc to run...

My questions:
Can I run an ANOVA and post hoc...if so, which one?




-- 
Posted from vo39155.valdosta.peachnet.edu [168.18.159.128] 
via Mailgate.ORG Server - http://www.Mailgate.ORG


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ANOVA = Regression

[Wuensch, Karl L]

For a demonstration of the equivalence of regression and traditional ANOVA,
just point your browser to
http://core.ecu.edu/psyc/wuenschk/StatHelp/ANOVA=reg.rtf.

-Original Message-
From:   Stephen Levine [mailto:[EMAIL PROTECTED]] 
Sent:   Tuesday, December 11, 2001 3:47 AM
To: Karl L. Wuensch
Subject:Re: When does correlation imply causation?

Hi
You wrote
>>Several times I have I had to explain to my colleagues that two-group t
tests and ANOVA are just special cases of correlation/regression analysis.
I can see what you mean - could you please proof it - I read, in a pretty
good text, that the results are not necessarily the same!
Cheers
S.




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ANOVA with proportions

[Wouter Duyck]

Hi to all...

i have a question. I have n subjects. for each subject, i have a
proportion. i wanna test if there are some differences in that
proportion, depending on some independent variables (e.g. sexe) on wich
the subjects differ.

Can i use those proportions as a dependent variable in an ANOVA?

tanx.
-- 
Wouter Duyck
Philips Research Laboratories 

Building:   Room WAE 1.07
Prof. Holstlaan 4
5656 AA Eindhoven   
The Netherlands
Phone:  +31-40-27 42895 

---
E-mail: [EMAIL PROTECTED]
[EMAIL PROTECTED]
Personal Homepage:  http://studwww.rug.ac.be/~wduyck
---

GLM vs. ANOVA

[sean_flanigan]

Will someone please enlighten me as to the general differences between
GLM and ANOVA. In my short journey through graduate statistics, I
somehow assumed they were the same.

Thanks.


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GLM vs. ANOVA

[Alan Zaslavsky]

Unfortunately there is potential for confusion of terminology, or at least
of acronyms.  SAS uses the name GLM (for "General Linear Model") for their
most general procdedure for linear models.  However, the term 
"generalized linear model", also abbreviated GLM, is now widely used for 
a class of models that are not necessarily linear, of the form

f(E(Y))= X'beta

where E(Y) is the expectation of Y, f is any monotone function (the "link"
function), and X'beta is a linear predictor.  This includes the logistic
or probit models for binomial data, the Poisson model for count data, and
many others.  It most nearly corresponds to PROC GENMOD in SAS.  

See McCullagh & Nelder, Generalized Linear Models, or other texts for
a general(ized) discussion of this class of models.

Alan Zaslavsky
[EMAIL PROTECTED]

ANOVA and normality

[Greg Hooper]

Hi, I want to use a one-way random effects anova intraclass correlation on
the following data. 70 subjects, each with 30 measurements of the one
property - their EEG alpha frequency - taken across a 5 minute interval.
I'm looking at both single and average measures for reliability. When
assessing normality of the distribution do I look at the entire data set ie
70*30 measures, or do I look at the single columns of alpha ie 30
distributions of 70 measures each. Is the within subject distribution
important, ie 70 distributions of 30 measures each. Thankyou for your time,
I understand this is trivial but I find the statistic texts i have consulted
quite opaque on this point.
Greg Hooper

Re: ANOVA/ MANOVA

[Elliot Cramer]

In sci.stat.consult sofyan2000 <[EMAIL PROTECTED]> wrote:

: I have conducted a repeated measure mixed two-factor ANOVA on one sample
you shouldn't have

: 1. What statistical ANOVA test can reveal an outlier in my data?
none

: 2. If my test failed the 'homogeneity of variance/ covariance' test, should
: I conduct a MANOVA ( learnt that this test does not require a homogeneity of
: variance/ covariance test)?
it does but this is what you should use






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Re: ANOVA/ MANOVA

[Thom Baguley]

sofyan2000 wrote:
> 
> I have conducted a repeated measure mixed two-factor ANOVA on one sample
> consisting of 2 groups (conservatives and liberals). The dependent variables
> where ATTA (attitude towards policy A) and ATTB (attitude towardfs B). I
> have a few questions:
> 
> 1. What statistical ANOVA test can reveal an outlier in my data?

No statistical test can. If an outlier is defined as an observation from
outside the population you are interested in, the decision can only be made
with reference to the aims and context of the experiment. Statistical tests or
information can be use to help flag potential outliers, but that isn't the
same thing. If an outlier is defined as an unusually extreme observation which
may be distorting your test in some way you are better of use graphs and
diagnostic info to identify possible problematic observations. (In either case
running tests with and without potential outliers can be informative about how
they influence your analysis).

> 2. If my test failed the 'homogeneity of variance/ covariance' test, should
> I conduct a MANOVA ( learnt that this test does not require a homogeneity of
> variance/ covariance test)?

If you have a 2x2 mixed ANOVA homogeneity of covariance can not be violated
(and tests of sphericity can not be performed). Homogeniety of variance may be
violated, but better to look at graphs and descriptive statistics than rely on
tests (which may be radically over- or uner-powered). A common error is to
assume homogeneity of covariance/sphericity is violated if Mauchley's
sphericity test can not be computed (SPSS prints sig as "." when d.f. = 0).

> 3. Which part of the SPSS results (which heading?) afer running an MANOVA
> shows the interaction between the between groups IV (political category
> conservative vs. liberals) and the within-groups DV (ATTA & ATTB).

Tests of within-subjects effects, I believe.

Thom


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Re: ANOVA/ MANOVA

[Rich Ulrich]

On Mon, 7 Feb 2000 18:42:03 -, "sofyan2000"
<[EMAIL PROTECTED]> wrote:

> 3. Which part of the SPSS results (which heading?) afer running an MANOVA
> shows the interaction between the between groups IV (political category
> conservative vs. liberals) and the within-groups DV (ATTA & ATTB).

Wouldn't that be the "interaction" term, which tests the difference of
att_a  and att_b?  (Or, is this what inspires the question?), finding
that in a MANOVA listing is not always the simple thing.

The simple and non-confusing way to test that is to avoid MANOVA; to
compute the difference and put it into a new preference-variable, 
   pref_a = (att_a - att_b) ;
and test that variable with a t-test.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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Re: ANOVA data

[Zina Taran]

hmmm. what is variance-between groups when all of them are standardized?
am I missing something?

- Original Message - 
From: haytham siala <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, February 09, 2000 5:12 PM
Subject: ANOVA data


> Can I perform an ANOVA on standardized variables?
> 




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Re: ANOVA data

[David A. Heiser]

- Original Message -
From: haytham siala <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, February 09, 2000 2:12 PM
Subject: ANOVA data


> Can I perform an ANOVA on standardized variables?
>---
If you standardize the complete data set based on the overall mean of the
complete data set and the standarad deviation of the whole data set, then
there would be no effect on the conclusions as to significance. What you are
doing is arriving at a total sum of squares of unity.

The magnetude of the effects of each variable and variable interaction as
derived from the basic experimental design will be different It may be
difficult to work back to the original scales.

Standardization with respect to the mean should be done when you are doing
the ANOVA in EXCEL (or other canned programs), since the accuracy of results
is much improved. (EXCEL algorithms are very sensitive to the overall mean
value.)

Standardization with respect to the variance is not necessary, except in
regression.

The canned software, if it is good should do the standardization internally,
and back calculate values to the scales of the input variables. In that case
there would be no difference in the results.

DAH





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ANOVA causal direction

[sofyan2000]

Is there a statistical test in ANOVA / MANOVA that can show the causal
direction between 2 variables (Independent and Dependent).




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ANOVA: planned comparisons

[A. Murias Santos]

Hello everybody!

Sorry for the long post. I'm not sure if this is the right 
place to ask such a question, but here it goes. I've got some 
doubts in the use of appropriate planned comparisons. 
The problem is that the topic is quite new for me and the 
literature does not help a lot (I could not get a copy of
Rosenthal & Rosnow, 1985...)

I've got two possible models of ANOVA to test for differences 
in space occupancy between periods. 

Lets assume population A as a dominant space occupier. It
outcompete other species, growing over them, but never 
monopolizes space (Density < 100%, and is usually below 60%). 
The hypothesis is that external disturbance events prevent 
it from reaching 100% of space occupancy. 

Disturbance events are seasonal. Lets assume W as a winter
disturbance, beginning in November--December and ending
in March--April; S is a summer disturbance, beginning in
June--July and ending in November--December; P stands for
spring season, begins in April--March and ends in June--July,
and no disturbance occurs between these periods.

In each of the above months I have 3 sampling dates (which 
are actually 3 different years) and in each date I have
10 estimates of A density.

The hypothesis states that there should be a decrease in
density in winter, an increase in spring (growing season)
and a possible decrease in summer (summer disturbance is 
not supposed to be as effective as the winter one).

First model:
 
Factors are locations (4, random), periods (6, fixed) 
and sampling dates (3, nested, random) with 10 replicates 
per combination. Periods are:

March (end of winter), 
April (beginning of spring), 
June(end of spring), 
July (beginning of summer), 
November (end of summer),
December (beginning of winter)

The model goes like this

Source of Variation DF Test against
--
Periods   5  P*L
   Between winter months   1  P*L  
   Between spring months   1  P*L   
   Between summer months   1  P*L   
   Winter vs Others1  P*L 
   Summer vs Spring1  P*L   
Locations 3  D(P*L)
Periods*Locations15  D(P*L)
Dates(Periods*Locations) 48  Residual
Residual648 
---
TOTAL   719 

There is no point in using "unplanned comparisons" because
the interesting contrasts are known before the experiment.
As you see, there is a number of planned comparisons, but
I'm really interested only in the first 3... the others are
there just because they sum up to the SS of "Periods"
They could have been Spring vs Others and Summer vs Winter
or Summer vs Others and Spring vs Winter... whatever...

First question: is it fair to omit these last two
contrasts, since they measure averages between periods
rather than differences within periods? If I omit them
the sums of squares will not add up to "SS Periods" and
the same applies to the dfs. But I read somewhere that
this was valid (was it in Cochran and Cox?)

The second model:

I came out with another simpler model. It is slightly
different from first, because only three periods are 
considered. The model goes like this: locations (4, random), 
periods (3, fixed) and sampling dates (3, nested, random) 
with 10 replicates per combination. Periods are::

November (beginning of winter and end of summer)
March (end of winter and beginning of spring)
June (end of spring and beginning of summer)

Source of Variation DF Test against
--
Periods   2  P*L
   Between winter months   1  P*L  
   Between spring months   1  P*L   
   Between summer months   1  P*L
Locations 3  D(P*L)
Periods*Locations 6  D(P*L)
Dates(Periods*Locations) 24  Residual
Residual324 
---
TOTAL   359 

Now the planned comparisons are not orthogonal, because each
period is used in two tests. The dfs of the comparisons add up 
to more than the df of "Periods". I use the Dunn-Sidak method
to correct the critical value of alpha, because the comparisons
are not independent. 

I guess both analyses are correct, the latter being simpler
but less "elegant" than the former. Is there any reason to prefer
one analysis against the other? 

Thanks in advance

Antonio


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Repeated Measures ANOVA

[alfseet]

Hi.

I have conducted an experiment with 4 within subject variables.
1) Colour
2) Shape
3) Pattern
4) Movement

Each of these 4 factors have 2 levels so each subject would be exposed
to 16 conditions in total. However, I have made each subject do 10
replications per condition and I have 10 subjects so I have a total of
1600 data points.

I have tried using SPSS repeated measures in GLM to analyse my data but
I don't know how to include my replications. SPSS requires that I
select 16 columns of dependant variables each representing a
combination of my factors. However, I am only allowed one row per
subject, so how do I input the 10 replications that each subject
performed for each combination?

Thanks !

Alfred





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Regression vs ANOVA

[Alexander Tsyplakov]

An interesting problem have arised during discussion of the
origins of "eigenvalue".

My own point of view is that ANOVA is just a particular case
of regression analysis with dummy (1/0) regressors and
either fixed or random effects. Block orthogonality of
regression matrix in the special case of ANOVA makes it
possible to decompose the sum of squared residuals (and
variance) into several components.

If people misuse the term ANOVA then what is it's correct
meaning? Is it a statistical model which is different from
regression model y=Xb+e? Then there must be some clear
formal discription.

-
Alexander Tsyplakov
Novosibirsk State University
http://www.nsu.ru/ef/tsy/

Elliot Cramer wrote...
> Werner Wittmann <[EMAIL PROTECTED]>
wrote:
> : inverting the
> : correlation matrix to get the effects was too
complicated to compute by
> : hand, so Sir Ronald developed the ANOVA shortcut.
>
> hardly.  They do have some mathematics in common (through
use of dummy
> variables which some of us think is for dummies).  they
are comceptually
> completely different/  Unfortunately many people misuse
ANOVA because they
> think of it as regression analysis.

> : I'm always teasing my colleagues and students, if you
spent one year
> : learning ANOVA and one year multiple regression you've
wasted almost one
> : year of your life.

> you can learn the mathematics of regression analysis in 10
minutes but
> you're still a long way from understanding either it or
ANOVA





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ANOVA and regression

[Alfred Barron]

The relation between ANOVA and regression goes
to the heart of the linear model; they are, at
once, both inter-connected aspects of the linear 
model. In fact, one could interpret ANOVA as
regression on indicator variables. If you want 
to go further, one could contrast linear modeling 
ingeneral with experimental design as well. Again,
both are inter-connected.

This perspective is outlined well in the Kutner,
Neter, & Wasserman books on linear models. There 
there are 2 or 3 versions on the market, in 
various editions. The current one is called
"Applied Linear Statistical Models".

A more theoretical approach can be found in 
Searle's Linear Models. 

No false placebo effect here !

Al

===
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NonClinical Biostatistics
R. W. Johnson Pharmaceutical Research Institute
1000 Route 202, OMP Rm. G-35
Raritan, NJ 08869

[908] 704-4102
[EMAIL PROTECTED]
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Re: ANOVA problem

[Rich Ulrich]

On Fri, 14 Sep 2001 16:44:11 + (UTC), "Asst Professor"
<[EMAIL PROTECTED]> wrote:

> I have data from a 24 item (1-4 likert scale) survey for 5 groups with varying
> Ns (9,16,23,34,43). According to the Levene homogeniety of variance test, I
> also have varying means for some questions and not others.
> 
> I find conflicting sources about which ANOVA/post hoc to run...
> 
> My questions:
> Can I run an ANOVA and post hoc...if so, which one?

You have a 24 item total.  You have 5 groups to compare, which
do have unequal Ns.  Do you have specific hypotheses about the
groups?  Do you have specific hypotheses about the 24 variables, 
or is that a second level of fishing expedition?

With Likert items, your homogeneity of variance is a *relatively*
innocuous diagnosis -- you can't have a distant outlier messing
up the variance when the score runs just 1-4 as integers.  

However, chasing after  *items*  tends to (always) be an 
exploratory activity.  And  post-hoc-tests-with-names are 
about 100%  in accord, in assuming that the Ns are equal;
and then telling you to use the harmonic mean of N  in 
comparing groups.  That always gives you an approximation,
with Ns as varied as 9 and 43.

So:  If you have some hypothesis or two, spell it out and test it.
THEN:  Admit that you are frankly exploratory in whatever else
you do.

You say you have conflicting sources:  I have seen a lot 
of indeterminate stuff, that would be hard to figure out.
Do you have anything that really conflicts with the 
advice that I just gave?

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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Re: ANOVA problem

[Glen]

Rich Ulrich <[EMAIL PROTECTED]> wrote in message 
news:<[EMAIL PROTECTED]>...
> On Fri, 14 Sep 2001 16:44:11 + (UTC), "Asst Professor"
> <[EMAIL PROTECTED]> wrote:
> 
> > I have data from a 24 item (1-4 likert scale) survey for 5 groups with varying
> > Ns (9,16,23,34,43). According to the Levene homogeniety of variance test, I
> > also have varying means for some questions and not others.
> > 
> > I find conflicting sources about which ANOVA/post hoc to run...
> > 
> > My questions:
> > Can I run an ANOVA and post hoc...if so, which one?
> 
> You have a 24 item total.  You have 5 groups to compare, which
> do have unequal Ns.  Do you have specific hypotheses about the
> groups?  Do you have specific hypotheses about the 24 variables, 
> or is that a second level of fishing expedition?
> 
> With Likert items, your homogeneity of variance is a *relatively*
> innocuous diagnosis -- you can't have a distant outlier messing
> up the variance when the score runs just 1-4 as integers.  

With 4 items, differences in spread are probably just  reflecting
differences  in  mean -- it's a bit hard to shift  the mean up or
down much without running into the ends.

How does the size of the Levene test change with such discreteness?

Glen


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ANOVA by items

[Wouter Duyck]

Dear all :-)

Suppose i have a factorial design with two between-subject factors (one
factor A of 3 levels and one factor B of 2 levels) en two within-subject
factors (one factor C of 2 levels and one factor D of 5 levels). Of course,
to perform an ANOVA on this data, my matrix should like :

Subj. ABC1D1C1D2 ...C1D5...C2D1...
C2D5
111
222
331

Every cell is the number of correct responses (0 through 8) to a given task
under certain conditions (factors C en D)

But if I want to do an ANOVA with items instead of subjects as a random
factor, how should my data matrix look like? I am pretty sure i did it
correct, but i would very much like to see that confirmed by anybody...

Tanx alot!







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Re: ANOVA = Regression

[Dennis Roberts]

of course, the typical software program, when doing regression analysis ... 
prints out a summary ANOVA table ... so, there is one place to start ...


At 10:52 AM 12/11/01 -0500, Wuensch, Karl L wrote:
>For a demonstration of the equivalence of regression and traditional ANOVA,
>just point your browser to
>http://core.ecu.edu/psyc/wuenschk/StatHelp/ANOVA=reg.rtf.
>
>-Original Message-
>From:   Stephen Levine [mailto:[EMAIL PROTECTED]]
>Sent:   Tuesday, December 11, 2001 3:47 AM
>To: Karl L. Wuensch
>Subject:Re: When does correlation imply causation?
>
>Hi
>You wrote
> >>Several times I have I had to explain to my colleagues that two-group t
>tests and ANOVA are just special cases of correlation/regression analysis.
>I can see what you mean - could you please proof it - I read, in a pretty
>good text, that the results are not necessarily the same!
>Cheers
>S.
>
>
>
>
>=
>Instructions for joining and leaving this list and remarks about
>the problem of INAPPROPRIATE MESSAGES are available at
>   http://jse.stat.ncsu.edu/
>=

_
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm



=
Instructions for joining and leaving this list and remarks about
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Re: ANOVA = Regression

[Stan Brown]

Jerry Dallal <[EMAIL PROTECTED]> wrote in sci.stat.edu:
>It's lunch hour.  I'm browsing.  Shall I click on a link to a file
>type that has the potential to carry viruses?  OT1H, Karl is a
>regular poster.  OTOH, why run the risk?  I guess I'll download and
>look at it in WordView.

The file type was RTF. Unless I'm _VERY_ much mistaken, RTF cannot 
carry macros of any sort, let alone viruses.



Oops, there is one loophole:



Note the advice to turn on "macro virus" warning in your copy of 
Microsoft Word, which should defang this particular risk.

-- 
Stan Brown, Oak Road Systems, Cortland County, New York, USA
  http://oakroadsystems.com/
"My theory was a perfectly good one. The facts were misleading."
   -- /The Lady Vanishes/ (1938)


=
Instructions for joining and leaving this list and remarks about
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Re: ANOVA = Regression

[Jerry Dallal]

It's lunch hour.  I'm browsing.  Shall I click on a link to a file
type that has the potential to carry viruses?  OT1H, Karl is a
regular poster.  OTOH, why run the risk?  I guess I'll download and
look at it in WordView.


"Wuensch, Karl L" wrote:
> 
> For a demonstration of the equivalence of regression and traditional ANOVA,
> just point your browser to
> http://core.ecu.edu/psyc/wuenschk/StatHelp/ANOVA=reg.rtf.
> 
> -Original Message-
> From:   Stephen Levine [mailto:[EMAIL PROTECTED]]
> Sent:   Tuesday, December 11, 2001 3:47 AM
> To: Karl L. Wuensch
> Subject:Re: When does correlation imply causation?
> 
> Hi
> You wrote
> >>Several times I have I had to explain to my colleagues that two-group t
> tests and ANOVA are just special cases of correlation/regression analysis.
> I can see what you mean - could you please proof it - I read, in a pretty
> good text, that the results are not necessarily the same!
> Cheers
> S.
> 
> =
> Instructions for joining and leaving this list and remarks about
> the problem of INAPPROPRIATE MESSAGES are available at
>   http://jse.stat.ncsu.edu/
> =


=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
  http://jse.stat.ncsu.edu/
=

Re: ANOVA = Regression

[Jerry Dallal]

Stan Brown wrote:
> 
> The file type was RTF. Unless I'm _VERY_ much mistaken, RTF cannot
> carry macros of any sort, let alone viruses.

> Oops, there is one loophole:

Yes, a loophole.  In fact, one can embed a destructive program in a
pure ASCII file that can affect some machines.  (Hint: it is
possible to reprogram keyboards under some circumstances with the
proper ASCII strings.)  There aren't too many people whose machines
are set up that way, so most virus writers don't bother.

One doesn't get RTFs through web browsers too often.  I wonder how
many users know how their browser is set up to handle them.  When I
saw the link, I wasn't sure in my own case.


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Re: ANOVA with proportions

[Donald F. Burrill]

On Tue, 14 Dec 1999, Wouter Duyck wrote:

> I have a question.  I have n subjects.  For each subject, I have a
> proportion.  I want to test if there are some differences in that
> proportion, depending on some independent variables (e.g. sex) on which
> the subjects differ.
> 
> Can I use those proportions as a dependent variable in an ANOVA?

Why not?  Proportions are means, after all.  Might even be more 
interesting analyses to be pursued, if the proportions represent (or, 
perhaps, conceal?) some repeated measures on the subjects.
-- DFB.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  

Re: ANOVA with proportions

[Robert Dawson]

- Original Message -
From: Donald F. Burrill <[EMAIL PROTECTED]>
To: Wouter Duyck <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Tuesday, December 14, 1999 9:03 AM
Subject: Re: ANOVA with proportions


> On Tue, 14 Dec 1999, Wouter Duyck wrote:
>
> > I have a question.  I have n subjects.  For each subject, I have a
> > proportion.  I want to test if there are some differences in that
> > proportion, depending on some independent variables (e.g. sex) on which
> > the subjects differ.
> >
> > Can I use those proportions as a dependent variable in an ANOVA?
>
> Why not?  Proportions are means, after all.  Might even be more
> interesting analyses to be pursued, if the proportions represent (or,
> perhaps, conceal?) some repeated measures on the subjects.

    My first thought was that this seemed like a rather cavalier misuse of
ANOVA, given that the population distributions are rather far from normal,
and that Bernoulli distributions have a relation between mu and sigma that
ANOVA fails to exploit. However, out of curiosity, I ran the following
simulation twenty times:

MTB > random 10  c11;
SUBC> bernoulli 0.4.
MTB > random 10 c10;
SUBC> bernoulli 0.5.
MTB > random 10 c12;
SUBC> bernoulli 0.6.
MTB > stack c10-c12 c13;
SUBC> subs c14.
MTB > oneway c13 c14
MTB > table c13 c14;
SUBC> chisquare.

and a similar one in which the null hypothesis was true 80 times, and
discovered that the p-values obtained are actually rather close!  The main
peculiarity of the distribution of the ANOVA p (if Ho is true) is that it is
very granular at the high end: the value 1.000 appeared several times, as
did several other values. The chisquare test seemed to have slightly more
power, but not by as much as I'd expected.

I still think that chi-square is probably a better choice,and logistic
regression more flexible - but I was surprised how well the screwdriver
drove the nail...

-Robert Dawson

Re: ANOVA with proportions

[William B. Ware]

As I recall, there was an article by Lunney et al that appeared in the
Journal of Educational Measurement that examined the use of ANOVA with "1"
and "0" as the DV.  I believe that they concluded that distortion was
minimal when the distributions were within an 80/20 split... I think that
the article was in the early 70s, perhaps 1971.

As Don has noted, proportions are means... which will be symmetrically
distributed when the split is about 50/50.  Apparently, the Central Limit
Theorem applies as long as sample size is sufficiently large...

Bill

__
William B. Ware, Professor and Chair   Educational Psychology,
CB# 3500   Measurement, and Evaluation
University of North Carolina PHONE  (919)-962-7848
Chapel Hill, NC  27599-3500  FAX:   (919)-962-1533
http://www.unc.edu/~wbware/  EMAIL: [EMAIL PROTECTED]
__


On Tue, 14 Dec 1999, Robert Dawson wrote:

> 
> - Original Message -
> From: Donald F. Burrill <[EMAIL PROTECTED]>
> To: Wouter Duyck <[EMAIL PROTECTED]>
> Cc: <[EMAIL PROTECTED]>
> Sent: Tuesday, December 14, 1999 9:03 AM
> Subject: Re: ANOVA with proportions
> 
> 
> > On Tue, 14 Dec 1999, Wouter Duyck wrote:
> >
> > > I have a question.  I have n subjects.  For each subject, I have a
> > > proportion.  I want to test if there are some differences in that
> > > proportion, depending on some independent variables (e.g. sex) on which
> > > the subjects differ.
> > >
> > > Can I use those proportions as a dependent variable in an ANOVA?
> >
> > Why not?  Proportions are means, after all.  Might even be more
> > interesting analyses to be pursued, if the proportions represent (or,
> > perhaps, conceal?) some repeated measures on the subjects.
> 
> My first thought was that this seemed like a rather cavalier misuse of
> ANOVA, given that the population distributions are rather far from normal,
> and that Bernoulli distributions have a relation between mu and sigma that
> ANOVA fails to exploit. However, out of curiosity, I ran the following
> simulation twenty times:
> 
> MTB > random 10  c11;
> SUBC> bernoulli 0.4.
> MTB > random 10 c10;
> SUBC> bernoulli 0.5.
> MTB > random 10 c12;
> SUBC> bernoulli 0.6.
> MTB > stack c10-c12 c13;
> SUBC> subs c14.
> MTB > oneway c13 c14
> MTB > table c13 c14;
> SUBC> chisquare.
> 
> and a similar one in which the null hypothesis was true 80 times, and
> discovered that the p-values obtained are actually rather close!  The main
> peculiarity of the distribution of the ANOVA p (if Ho is true) is that it is
> very granular at the high end: the value 1.000 appeared several times, as
> did several other values. The chisquare test seemed to have slightly more
> power, but not by as much as I'd expected.
> 
> I still think that chi-square is probably a better choice,and logistic
> regression more flexible - but I was surprised how well the screwdriver
> drove the nail...
> 
> -Robert Dawson
> 
> 
> 

Re: ANOVA with proportions

[Dale Berger]

Just a reminder that transformations can be used on proportions as a dv to reduce
the skew, important if some values approach 0 or 1.  These include arcsine,
probit, and logit.  Each needs special treatment when p=0 or p=1.  Cohen and Cohen
(2nd ed. of Applied MR/C) has a section on transformations for proportions (pp.
265-270).

Cheers, Dale Berger


William B. Ware wrote:

> As I recall, there was an article by Lunney et al that appeared in the
> Journal of Educational Measurement that examined the use of ANOVA with "1"
> and "0" as the DV.  I believe that they concluded that distortion was
> minimal when the distributions were within an 80/20 split... I think that
> the article was in the early 70s, perhaps 1971.
>
> As Don has noted, proportions are means... which will be symmetrically
> distributed when the split is about 50/50.  Apparently, the Central Limit
> Theorem applies as long as sample size is sufficiently large...
>
> Bill
>
> __
> William B. Ware, Professor and Chair   Educational Psychology,
> CB# 3500   Measurement, and Evaluation
> University of North Carolina PHONE  (919)-962-7848
> Chapel Hill, NC  27599-3500  FAX:   (919)-962-1533
> http://www.unc.edu/~wbware/  EMAIL: [EMAIL PROTECTED]
> __
>
> On Tue, 14 Dec 1999, Robert Dawson wrote:
>
> >
> > - Original Message -
> > From: Donald F. Burrill <[EMAIL PROTECTED]>
> > To: Wouter Duyck <[EMAIL PROTECTED]>
> > Cc: <[EMAIL PROTECTED]>
> > Sent: Tuesday, December 14, 1999 9:03 AM
> > Subject: Re: ANOVA with proportions
> >
> >
> > > On Tue, 14 Dec 1999, Wouter Duyck wrote:
> > >
> > > > I have a question.  I have n subjects.  For each subject, I have a
> > > > proportion.  I want to test if there are some differences in that
> > > > proportion, depending on some independent variables (e.g. sex) on which
> > > > the subjects differ.
> > > >
> > > > Can I use those proportions as a dependent variable in an ANOVA?
> > >
> > > Why not?  Proportions are means, after all.  Might even be more
> > > interesting analyses to be pursued, if the proportions represent (or,
> > > perhaps, conceal?) some repeated measures on the subjects.
> >
> > My first thought was that this seemed like a rather cavalier misuse of
> > ANOVA, given that the population distributions are rather far from normal,
> > and that Bernoulli distributions have a relation between mu and sigma that
> > ANOVA fails to exploit. However, out of curiosity, I ran the following
> > simulation twenty times:
> >
> > MTB > random 10  c11;
> > SUBC> bernoulli 0.4.
> > MTB > random 10 c10;
> > SUBC> bernoulli 0.5.
> > MTB > random 10 c12;
> > SUBC> bernoulli 0.6.
> > MTB > stack c10-c12 c13;
> > SUBC> subs c14.
> > MTB > oneway c13 c14
> > MTB > table c13 c14;
> > SUBC> chisquare.
> >
> > and a similar one in which the null hypothesis was true 80 times, and
> > discovered that the p-values obtained are actually rather close!  The main
> > peculiarity of the distribution of the ANOVA p (if Ho is true) is that it is
> > very granular at the high end: the value 1.000 appeared several times, as
> > did several other values. The chisquare test seemed to have slightly more
> > power, but not by as much as I'd expected.
> >
> > I still think that chi-square is probably a better choice,and logistic
> > regression more flexible - but I was surprised how well the screwdriver
> > drove the nail...
> >
> > -Robert Dawson
> >
> >
> >

Re: ANOVA with proportions

[sean_flanigan]

In article <[EMAIL PROTECTED]>,
  Wouter Duyck <[EMAIL PROTECTED]> wrote:
> Hi to all...
>
> i have a question. I have n subjects. for each subject, i have a
> proportion. i wanna test if there are some differences in that
> proportion, depending on some independent variables (e.g. sexe) on
wich
> the subjects differ.
>
> Can i use those proportions as a dependent variable in an ANOVA?
>
> tanx.
> --
> Wouter Duyck


What about a z test for proportions?

> Philips Research Laboratories
>
> Building: Room WAE 1.07
>   Prof. Holstlaan 4
>   5656 AA Eindhoven
>   The Netherlands
>   Phone:  +31-40-27 42895
>
> ---
> E-mail:   [EMAIL PROTECTED]
>   [EMAIL PROTECTED]
> Personal Homepage:http://studwww.rug.ac.be/~wduyck
> ---
>


Sent via Deja.com http://www.deja.com/
Before you buy.

Re: ANOVA with proportions

[Rich Strauss]

At 12:52 PM 12/14/99 -0800, Dale Berger wrote:
>Just a reminder that transformations can be used on proportions as a dv to
reduce
>the skew, important if some values approach 0 or 1.  These include arcsine,
>probit, and logit.  Each needs special treatment when p=0 or p=1.  Cohen
and Cohen
>(2nd ed. of Applied MR/C) has a section on transformations for proportions
(pp.
>265-270).

I'll just add the usual caveat that hasn't yet been mentioned in these
responses about proportions: the transformations, use of the binomial, and
comment about proportions just being means all assume that the data really
are proportions, not ratios -- that is, that the denominator is fixed among
all values, not variable.  The problem is that many people use the terms
interchangably, talking about proportions or percentages when they're
actually dealing with ratios.

Rich Strauss



Dr Richard E Strauss
Biological Sciences  
Texas Tech University   
Lubbock TX 79409-3131

Email: [EMAIL PROTECTED]
Phone: 806-742-2719
Fax: 806-742-2963 

Re: GLM vs. ANOVA

[Donald F. Burrill]

On Wed, 15 Dec 1999 [EMAIL PROTECTED] wrote:

> Will someone please enlighten me as to the general differences between 
> GLM and ANOVA.  In my short journey through graduate statistics, I
> somehow assumed they were the same.

Parallelling your short journey, here is a short distinction in one 
sentence.  (Some might want to quibble about details.)

GLM, as its name (General Linear Models) implies, is more 
general than ANOVA (ANalysis Of VAriance), which is that subset of GLM 
whose predictors (aka independent variables, aka factors) are categorical 
(aka of nominal scale).

To elaborate:
In some contexts (e.g., for some packaged statistical programs) 
ANOVA -- which in these contexts usually means "factorial ANOVA" -- is 
further restricted to balanced designs, sometimes to balanced complete 
designs.
In other contexts (as in "the ANOVA summary table"), ANOVA is 
much more general -- as general as GLM, actually.  The phrase often 
refers to the partitioning of variance (in a response variable, aka a 
dependent variable or DV) into random ("error") and systematic 
components.  (There may be more than one of each kind, reflecting the 
structure of the design that generated the data.)  In this sense, one 
encounters analysis of variance as part of the output of a multiple 
linear regression (MLR) analysis.  (MLR is that subset of GLM whose
predictors are [treated as] "quantitative", meaning quasi-continuous, 
aka of interval scale.) 
-- DFB.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  

Re: GLM vs. ANOVA

[Alex Yu]

In SAS, ANOVA is for design of one-way and balanced multi-way 
classifications. The main point here is "balanced." ANOVA may be used for 
unbalanced data if the factors do not interact, otherwise, GLM is a 
better procedure. 


Chong-ho (Alex) Yu, Ph.D., CNE, MCSE
Instruction and Research Support
Information Technology
Arizona State University
Tempe AZ 85287-0101
Voice: (602)965-7402
Fax: (602)965-6317
Email: [EMAIL PROTECTED]
URL:http://seamonkey.ed.asu.edu/~alex/
   
  

Re: GLM vs. ANOVA

[Paige Miller]

[EMAIL PROTECTED] wrote:
> 
> Will someone please enlighten me as to the general differences between
> GLM and ANOVA. In my short journey through graduate statistics, I
> somehow assumed they were the same.

If you are referring the SAS procedures GLM And ANOVA, ANOVA works only
on balanced designs, GLM works on any design. If you are referring to
GLM and ANOVA in general, ANOVA refers to situations where your
independent variables are classification variables, while GLM can be
used for any combination of continuous or classification independent
variables.

-- 
Paige Miller
Eastman Kodak Company
[EMAIL PROTECTED]
"It's nothing until I call it!" -- Bill Klem, NL Umpire

Re: GLM vs. ANOVA

[dennis roberts]

in minitab for example ... the command ANOVA insists on equal ns in the 
cells ... glm does not ... this is not a conceptual difference as don was 
pointing out ... but, it is important IF you happen to be using minitab
--
208 Cedar Bldg., University Park, PA 16802
AC 814-863-2401Email mailto:[EMAIL PROTECTED]
WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm
FAX: AC 814-863-1002

Re: ANOVA with proportions

[Rich Ulrich]

On 14 Dec 1999 08:40:18 -0800, [EMAIL PROTECTED] (William B. Ware)
wrote:

> As I recall, there was an article by Lunney et al that appeared in the
> Journal of Educational Measurement that examined the use of ANOVA with "1"
> and "0" as the DV.  I believe that they concluded that distortion was
> minimal when the distributions were within an 80/20 split... I think that
> the article was in the early 70s, perhaps 1971.
> 
> As Don has noted, proportions are means... which will be symmetrically
> distributed when the split is about 50/50.  Apparently, the Central Limit
> Theorem applies as long as sample size is sufficiently large...
 < ... >

The problem that I am aware of has nothing to do with the Central
Limit Theorem -- and I'm not positive what that problem is supposed to
be -- and everything to do with additivity and linearity.

If you have a 2x2 table, and the four groups have means on the
dichotomous outcome, of (1%, 4%; 4%, 16%), do you decide that this is
additive and has an interaction, or do you label it a simple pair of
multiplicative main-effects? -  The interaction apparent by ANOVA
does not exist in the log-linear model.  So it may be worth using the
ANOVA computer-procedure, and ignoring the interaction, if it is a lot
simpler to use that computer program.  I am willing to use the
systematic absence of the interaction as evidence that the
multiplicative model is the better one.

The linearity-artifact does not exist  for a simple t-test, one-way
ANOVA, or regression with small effect size (low R-squared, AND low
Odds ratios).  So far as I know, you can do those ANOVA analyses with
proportions that may be beyond 20%, with very little loss of power.
Further, you should note, you have the risk of similar
linearity-artifacts  when you  analyze continuous variables that have
been re-expressed as their *rank-transformed values*.  That applies
for essentiall the same set of models -- multiway, multi-variable, or
high R-squared.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html

Re: ANOVA with proportions

[Rich Ulrich]

On 14 Dec 1999 16:38:00 -0800, [EMAIL PROTECTED] (Rich Strauss)
wrote:

< snip > 
> I'll just add the usual caveat that hasn't yet been mentioned in these
> responses about proportions: the transformations, use of the binomial, and
> comment about proportions just being means all assume that the data really
> are proportions, not ratios -- that is, that the denominator is fixed among
> all values, not variable.  The problem is that many people use the terms
> interchangably, talking about proportions or percentages when they're
> actually dealing with ratios.

Ratios are one problem.  Right -- be careful about them.

But Proportions are another problem when the denominators are not the
same.  If one subject is scored a proportion which is  none-for-one,
0/1= 0%,  that is usually a score with far less "information,"  and
bigger standard error on the response,  than if another subject rates
0/20=0%.  

I am not referring just to zero -- if subjects have data based on
vastly different Ns, it may be wasteful to lump them based on
percents.  One approach that seemed useful for some analyses of
genotypes was:  do separate analyses for different N, and then combine
those analyses.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html

Re: ANOVA and normality

[Donald F. Burrill]

On Sun, 26 Dec 1999, Greg Hooper wrote:

> I want to use a one-way random effects anova intraclass correlation on
> the following data.  70 subjects, each with 30 measurements of the one
> property - their EEG alpha frequency - taken across a 5 minute interval. 

Every ten seconds, then?  How are you proposing to model the time 
dependency(ies) across the 5 minutes?  Is it reasonable to model EEG 
alpha as constant during that time?  One would suppose not, since you 
write of "a one-way random effects anova" and the random effects in 
question are, presumably, time effects?  But then it would appear that 
you would be considering the 70 first measurements (one for each subject) 
as somehow equivalent, and possibly systematically (if randomly) 
different from the 70 second measurements, and the 70 third measurements, 
and so on.  That doesn't sound to me any more reasonable than a constant 
over the 5 minutes.  But perhaps I misapprehend your purpose...
 Presumably the 70 subjects are homogeneous with respect to possible 
between-subject variables of interest (sex or age, e.g.), else you'd have 
mentioned the design factors...

> I'm looking at both single and average measures for reliability. 
> When assessing normality of the distribution ...

You must mean "assessing non-normality"?  

> do I look at the entire data set, i.e. 70*30 measures, or do I look at 
> the single columns of alpha, i.e. 30 distributions of 70 measures each. 

By "alpha" I take it you mean the EEG alpha frequency measures, not the 
reliability coefficient alpha.  In general, the assumption associated 
with anova is that the residuals -- i.e., the departures from the model 
one is trying to fit -- be normally distributed.  In practice, it usually 
suffices if they're unimodal and not too asymmetric.  It follows that you 
cannot assess possible non-normality of residuals until after you have 
attempted to fit a model.

> Is the within subject distribution important, i.e. 70 distributions of 
> 30 measures each? 

It certainly would have some bearing, one would expect, on how you chose 
to model the time series.  If your model were too simple for the universe 
of discourse, the distributions of residuals -- and perhaps particularly 
the time-dependent distribution of residuals -- would provide some 
evidence that the model needed revision.

> Thank you for your time, I understand this is trivial but I find the 
> statistic texts i have consulted quite opaque on this point.

Not all that trivial (in the corrupt modern sense;  might well be trivial 
as a metaphor for the classical sense of "belonging to the trivium", i.e.
the first three of the seven liberal arts).  And textbooks do tend to be 
opaque, I'm afraid.
-- DFB.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  

Re: ANOVA and normality

[Rich Ulrich]

On Mon, 27 Dec 1999 17:44:51 +1000, "Greg Hooper"
<[EMAIL PROTECTED]> wrote:

> Thanks very much for that reply. The subjects are all 16 years old, right
> handed, equally split across sex etc, its a very homogenous group. 

 - From the whole post, it sounds as if you may be pretty satisfied
with your solution, and it seems fairly conventional from what I have
read.  

But I can add a couple of observations that may pertain.  Right here,
you say that it is a very homogeneous group.  Do you consider the
consequences of that?  -- every statement of reliability is a
statement about the measurement-in-that-sample.  If your sample is not
hetergeneous in what you what to look for, correlational reliability
may be directing you to the wrong variables.

For in intraclass correlation, which is effectively what you computed,
you can compute the 2-way ANOVA, Subject by Time.  The big F-test for
subjects shows that Subjects differ  (reliably) on the measure.  So,
how varied are the subjects?  If *these*  subjects are homogeneous on
what you want to detect -- when you do research later -- then what you
find to be reliable here might be something that distinguishes them
like sworls and ridges of fingerprints:  unique, but of no inherent
meaning.

>  
> The time
> effects are not significant because, due to a bunch of factors I won't go
> into, the time order of the measurements is randomised within each subject.
> ie you can't equate any order within one subject to the order of measurement
> within another subject.   < ... snip, rest >

If there is a meaning to the type of measurements, then you certainly
*could*  classify them by "Type" rather than time-period.  When Type
corresponds to Treatments, varying the order of Treatments is the
basis of Crossover designs.  Of course, you seemed to be just making a
side-comment here, so my observation might be irrelevant to your
purposes.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html

Re: ANOVA and normality

[Greg Hooper]

Thanks very much for that reply. The subjects are all 16 years old, right
handed, equally split across sex etc, its a very homogenous group. The time
effects are not significant because, due to a bunch of factors I won't go
into, the time order of the measurements is randomised within each subject.
ie you can't equate any order within one subject to the order of measurement
within another subject. There is no data on whether the alpha frequency - or
any aspect of the EEG  -  is generated by a single constant process or not.
For example, an electrode at the scalp records the spatial average of
activity from a large, 10 cm^2, area of cortex. As well, there is a temporal
window, say 2-seconds, within which analysis occurs. Many spatially and
temporally independent processes within that area can appear as one process
within the spatial and temporal window - basic experimental limitation. One
of my research questions is to examine the reliability of EEG to see if that
gives us a handle on the number and stationarity of the processes generating
the signal. Error introduced by the measuring apparatus is random and
consistent across all frequencies. Therefore alterations in reliability are
mostly due to nonstationarity in the generators. The reason for using
reliability, rather than some other measure of stationarity, is that the end
point - hopefully  - is a small group of variables for which we can find the
genetic locii. It looks as though the peak Alpha frequency and its amplitude
qualify, they have the highest reliability with the least amount of data.

Thankyou again for your time
Greg Hooper
Donald F. Burrill <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> On Sun, 26 Dec 1999, Greg Hooper wrote:
>
> > I want to use a one-way random effects anova intraclass correlation on
> > the following data.  70 subjects, each with 30 measurements of the one
> > property - their EEG alpha frequency - taken across a 5 minute interval.
>
> Every ten seconds, then?  How are you proposing to model the time
> dependency(ies) across the 5 minutes?  Is it reasonable to model EEG
> alpha as constant during that time?  One would suppose not, since you
> write of "a one-way random effects anova" and the random effects in
> question are, presumably, time effects?  But then it would appear that
> you would be considering the 70 first measurements (one for each subject)
> as somehow equivalent, and possibly systematically (if randomly)
> different from the 70 second measurements, and the 70 third measurements,
> and so on.  That doesn't sound to me any more reasonable than a constant
> over the 5 minutes.  But perhaps I misapprehend your purpose...
>  Presumably the 70 subjects are homogeneous with respect to possible
> between-subject variables of interest (sex or age, e.g.), else you'd have
> mentioned the design factors...
>
> > I'm looking at both single and average measures for reliability.
> > When assessing normality of the distribution ...
>
> You must mean "assessing non-normality"?
>
> > do I look at the entire data set, i.e. 70*30 measures, or do I look at
> > the single columns of alpha, i.e. 30 distributions of 70 measures each.
>
> By "alpha" I take it you mean the EEG alpha frequency measures, not the
> reliability coefficient alpha.  In general, the assumption associated
> with anova is that the residuals -- i.e., the departures from the model
> one is trying to fit -- be normally distributed.  In practice, it usually
> suffices if they're unimodal and not too asymmetric.  It follows that you
> cannot assess possible non-normality of residuals until after you have
> attempted to fit a model.
>
> > Is the within subject distribution important, i.e. 70 distributions of
> > 30 measures each?
>
> It certainly would have some bearing, one would expect, on how you chose
> to model the time series.  If your model were too simple for the universe
> of discourse, the distributions of residuals -- and perhaps particularly
> the time-dependent distribution of residuals -- would provide some
> evidence that the model needed revision.
>
> > Thank you for your time, I understand this is trivial but I find the
> > statistic texts i have consulted quite opaque on this point.
>
> Not all that trivial (in the corrupt modern sense;  might well be trivial
> as a metaphor for the classical sense of "belonging to the trivium", i.e.
> the first three of the seven liberal arts).  And textbooks do tend to be
> opaque, I'm afraid.
> -- DFB.
>  
>  Donald F. Burrill [EMAIL PROTECTED]
>  348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
>  MSC #29, Plymouth, NH 03264 603-535-2597
>  184 Nashua Road, Bedford, NH 03110  603-471-7128
>

Re: ANOVA and normality

[Mike Wogan]

Greg,

  For your EEG problem, there are "30 measures" taken across a five minute
interval, but you don't say how many leads per subject.  Are you using a
standard 19-lead EEG configuration?  How many active leads per subject?

  You say you can't equate the order in which the measures are taken for
one subject with the order in which they are taken for another.  Have I
got that right?  If so, then you can't compare across subjects, can you?

  You say there is a temporal window of 2 seconds, within which analysis
occurs.  I take that to mean you sample 2 sec. of EEG from each lead
(simultaneously?  in succession?).  So within a five minute period, for
each lead there are 30 samples, each one about 2 sec. long.  Correct?

  Since you don't say otherwise, I assume that during the five minutes of
EEG collection your subjects are just sitting there.  I.e., during the
five minutes, there's no reason to think they switch from one type of
mental processing to another, is there?  (or any such switching is random,
since the Ss are just asked to sit there, or whatever...).  There are
task-dependent shifts in EEG frequency, both between L/R hemispheres and
posterior-frontal, which is why I ask.

  If all this is reasonably accurate, then it seems to me that each *lead*
is the unit of measurement.  You want to know that the error of
measurement per lead is relatively stable, before you proceed to do
cross-lead (but within one subject) comparisons.  The cross-lead
comparisons are what will eventually yeild up the information as to
whether or not there is one (or a few) brain locus from which the alpha
frequency is generated, or at least pulsed, timed, or turned on/off.

  Brains, like faces show individual differences.  So whether or not a
"central locus" for individual one is in the exact same spot as the locus
for individual two is irrelevant.  What I mean is, the *group* average
locus is less interesting than the fact that you can (eventually) pinpoint
a locus for an individual person with reasonable accuracy.

  This isn't "the answer" yet, and I'm sure others on this list will have
more sophisticated suggestions than I, but I thought it would help to
clear away some of the underbrush & facilitate the discussion.

Mike

**
* Michael Wogan, Ph.D., J.D.Department of Psychology *
* e-mail: [EMAIL PROTECTED] Rutgers University *
* phone: (856) 225-6520 311 N. Fifth St. *
*(856) 225-6089  Camden, N.J. 08102-1461 *
* fax:   (856) 225-6602 Office: Armitage Rm. 306 *
*   (please note new area code, required after Nov., 1999)   *

  note: Mike Wogan is Y2K compliant.

**

repeated measures ANOVA + SPSS

[Ole Breithardt]

Hi to all the experts,
I measured a few Variable in let´s say 20 Patients under 10 different
conditions, f.e.heart rate at 10 different exercise levels.
1.) To compare the results I understood that I have to use a repeated
measures ANOVA, am I correct?
2.) If I want to use SPSS, where do I find that test? If I understood
the Online-Help correctly then I should use "GLM-Messwiederholungen"
(sorry for the German version, in English that would probably be
something like "GLM-repeated Measures"??)
3.) Great! ? Here I have to define several things, that I do not really
understand - o.k. let´s try: I give the "Innersubjectfactor" (that´s how
it sounds in German") a name and tell SPSS how many repeated measures I
performed.is that correct ?? 
4.) If I go on, on the next screen I have to define the different
measurment/variables - however if I leave the two boxes below ("between
subject factors" and "covariates") open, then SPSS won´t let me define
any post-hoc-test , why not??? I understood that "between subject
factors" has something to do with f.e. male and female ?? So, do I
really have to define that or can I leave it open??

Any comments or help is very appreciated!!!
Thank you for your patience
;-)) Ole

--

Dr. Ole-A. Breithardt
Medizinische Klinik I - Kardiologie
Klinikum der RWTH Aachen
Pauwelsstr. 30
D-52057 Aachen

Tel.: +49-241-8089659 (Med. Klinik I, Echo)
 +49-241-73211 (priv)
 +49-170-4089962 (mobil)
Fax.: +49-241-414 (Med. Klinik I)
 +49-241-9890988 (priv)

mailto:[EMAIL PROTECTED]

Re: ANOVA causal direction

[dennis roberts]

At 12:40 PM 2/10/00 +, sofyan2000 wrote:
>Is there a statistical test in ANOVA / MANOVA that can show the causal
>direction between 2 variables (Independent and Dependent).

i don't think so ... this is determined (if it can be at all) by the DESIGN
of the investigation ... and what you did when you called a variable
INDependent and DEpendent ... 

for example ... say i experimentally vary the amount of time i allow
students to study for a test AND, on followup ... i find that the means on
the test vary positively with the amount of time i maniupated ... it seems
to me that the DESIGN says (if it can say anything) that time produces test
performance . surely the other way around would make no sense

what kind of data are you thinking about when you pose this question? 
==
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/droberts.htm


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Re: ANOVA causal direction

[Alex Yu]

A statistical procedure alone cannot determine casual relationships. 
Rather it involves the design and measurement issues. The following is 
extracted from my handout:

One of the objectives of conducting experiments is to make causal 
inferences. At least three criteria need to be fulfilled to validate a 
causal inference (Hoyle, 1995):

Directionality: The independent variable affects the dependent variable. 

Isolation: Extraneous noise and measurement errors must be isolated from 
the study so that the observed relationship cannot be explained by 
something other than the proposed theory.
 
Association: The independent variable and the dependent variable are 
mathematically correlated. 

To establish the direction of variables, the researcher can apply logic 
(e.g. physical height cannot cause test performance), theory (e.g. 
collaboration affects group performance), and most powerfully, research 
design (e.g. other competing explanations are ruled out from the 
experiment).
 
To meet the criterion of isolation, careful measurement should be 
implemented to establish validity and reliability, and to reduce 
measurement errors. In addition, extraneous variance, also known as 
threats against validity of experiment, must be controlled in the design 
of experiment. 

Last, statistical methods are used to calculate the mathematical 
association among variables. However, in spite of a strong mathematical 
association, the causal inference may not make sense at all if 
directionality and isolation are not established. 

In summary, statistics analysis is only a small part of the entire 
research process. Hoyle (1995) explicitly warned that researchers should 
not regard statistical procedures as the only way to establish a causal 
and effect interpretation. 

Hoyle, R. H.. (1995). The structural equation modeling approach: Basic 
concepts and fundamental issues. In R. H. Hoyle (Eds.), Structural 
equation modeling: Concepts, issues, and applications (pp. 1-15). 
Thousand Oaks: Sage Publications.


Chong-ho (Alex) Yu, Ph.D., CNE, MCSE
Instruction and Research Support
Information Technology
Arizona State University
Tempe AZ 85287-0101
Voice: (602)965-7402
Fax: (602)965-6317
Email: [EMAIL PROTECTED]
URL:http://seamonkey.ed.asu.edu/~alex/
   
  



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Re: ANOVA causal direction

[Richard M. Barton]

--- Alex Yu wrote:

A statistical procedure alone cannot determine casual relationships. 
---


Correct.  A lot depends on eye contact.

rb


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Re: ANOVA causal direction

[Travis Gee]

sofyan2000 wrote:
> 
> Is there a statistical test in ANOVA / MANOVA that can show the causal
> direction between 2 variables (Independent and Dependent).

In short, no. 

In more detail, causal inference is dependent on the design you used,
not
the statistical technique applied to the data. If you randomly assigned
cases to
groups, there is evidence for a causal effect of your treatment. If you
selected
(randomly or otherwise) from pre-existing groups, then a straightforward
causal 
interpretation is not supported.

Suppose it's Males vs. Females on a math test, and a significant
difference is
found.  Is a biological gender difference causing it (and if so, which
one?), or are factors associated with gender at work (e.g., in school
boys are encouraged to lean towards maths while
girls are not)?

Hope this helps,

Travis.


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Re: ANOVA causal direction

[Bruce Weaver]

On 10 Feb 2000, Richard M. Barton wrote:

> --- Alex Yu wrote:
> 
> A statistical procedure alone cannot determine casual relationships. 
> ---
> 
> 
> Correct.  A lot depends on eye contact.
> 
> rb


And also, at least 2 statistical procedures are required...



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Re: ANOVA causal direction

[William Chambers]

Bill said earlier:

>> Yes, we do this so that we will have examples of all combinations of x1
and
>> x2,as we would do when using a factorial anova design.  But such uniform
>> sampling does not make the variables into causes,  Adding x1 to x2 causes
y,
>
Gus responded:

>Here you are using a very different notion of causality than I am
>willing to accept. If you are serious about this notion, then I concede the
>argument. In your sense, of course y is caused by x1 and x2. For me, that
is then
>simply a "so what?".


Bill responded,

In so far as we use numbers to model causes, the causes should also
demonstrate the properties of those numbers, If not we are being deceptive
to use numbers at all, This is point that Michell makes, as referenced in my
most recent paper, We learn more about the phenomenon by what we know about
numbers,  This is the whole point of statistics,   What do you use numbers
for in causal modeling?

You concede the argument in a manner that suggests I am trying to get away
with something unusual, I most definitely am not. The use of operations to
model causes is implicit through the literature, For example, why do you
think the word "nonadditive" is used to describe interactions in ANOVA?


Bill said:
>> We do not infer that x1 and x2 are the causes because they are uniformly
>> sampled.  We infer they are the causes because their correlations
polarize
>> across the ranges of the dependent variable y,


>Gus responded:

>I have to agree with Gottfried Helms and Jerry Dallal and others that
>this is exactly the same thing. Uniform sampling of x1 and x2 _causes_ (in
my
>sense of the term) y to have a triangular distribution. If y has a
>triangular distribution, then the correlations polarize, by definition.


Bill responded:

First of all, none of you have given an explanation for your beliefs, It
would not matter if every famous statistician in the world made the same
claim, Without an explanation that stands up to the tests of logic, your
claims are not scholarly,

By your definition, if we sample all the variables uniformly, then CR will
not know what to make of the data, In fact, CR will work just as well, I
gave the example of the ranked data below, to which you responded:


Gus said:
>Of course! Ranks are uniformly distributed. In fact, if you apply
>ranking,
>then you don't have to use uniform data from the beginning.
>
Bill responds:

I am ranking them AFTER the causes are first generated using interval or
ratio data,  Of course we could use the ranks of the independent variables
in the actual causal generation but their sums would still be triangular,  I
do not deny this, only I say it is not enough to warrant causal inference
because other things could cause the triangularity of some variable.  I am
saying that if AFTER we get the triangular sums (Y) of the uniform interval,
ratio or ordinal causes, we rank Y, then CR still works..even though the
math is being done on THREE uniform variables, x1, x2 and Y.

You are insisting that the presto is in the distributions, Please explain
why.  How does having different distributions allow us to infer causation?
It does not,  We could have two uniform variables and a third triangular
variable that is NOT the effect of the two uniform variables,

>
>> >Of course the Y you generate by adding them will then be triangular. Of
>> >course
>> >the correlations will come out the way you want them to. But does that
>> >prove
>> >causality? Of course not. Look at your model in the opposite direction:
>> >Y is caused by x1 and x2, but I want to prove it isn't, that the
>> >causality
>> >effect is y, x2 => x1. What do I do? I follow your recommendations and
>> >select
>> >the y uniformly and presto: causality goes the other way.
>> >
>> No it does not,  You do not infer that the uniformly sampled variable is
the
>> cause,  You sample the variables you think may be the causes uniformly
and
>> then see if you get the polarization effect across the ranges of any
other
>> variables, whether they are uniform or triangular,
>
>In other words, you do have reasons other than purely statistical ones
>for suspecting a causation.

Bill responded:

No. We could simply sample all possible models using uniform distributions
on the current hypothesized causes and the method would still work, The
inference is based completely on the data.  Try generating a very large data
set and taking a subsample in which the effect is uniform,  See what
happens.

Gus said:
>You then change the data (by insisting on a
>uniform sample) to give you the polarization of the correlations that
>you want. That still looks like circular reasoning to me.


Bill responded:

Not if you are free to sample every variable under consid

Re: ANOVA causal direction

[William Chambers]

Gus,

You are making a defense of studying distributions as they are thrown at us
by nature/circumstances,  This seem the way to go to social scientists
because we tend to believe that our causes are embedded in all sorts of
complex interactions and can not be isolated from their context,  If we look
however to the physical sciences,  we see a very different strategy, The
chemist tends not to go out and perform experiments on naturally occuring
clusters of chemicals, Instead, she isolates each chemical and then studies
their interactions in pure states, so that the fundamental mechanisms of
causation are revealed,  The experimental psychologist does the same thing
in his lab,  Both tend to use manipulation and anova designs, in which equal
cell sizes are sought across the levels of the factors,  By doing so they
experimentalist progresses systematically by carefully controling his
research,

I am simply saying that those who wish to pursue causal models without
manipulation should learn something about the control afforded by isolation
of variables,  Do you think it is wooly minded for a user of an anova design
to seek out equal cell sizes across the levels of the putative factor?

Bill Chambers







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Re: ANOVA causal direction

[William Chambers]

Gottfried said:
>
>Here you focus the crux of the normal-distributed variables.
>If there is a reality with n1 and n2 as normal distributed causes and
>y as effect like y<-n1+n2, you have measured standardized z1 and z2 (not
knowing
>which represents y and which represents n1 of the model)
>then you will find about 5% cases with values >2 - in both items.
>Now how will you resample: for uniformity of x1 or uniformity of x2?



Bill responds:

First, when we use least square methods the estimates are driven by the
frequency of certain patterns in the data.   Part of the pattern we seek in
corresponding regressions concerns the values of x1 and x2 are the extremes
of y, We look for correlation(and the polarization effect), since two
extremes of x1 and x2 lead to higher extremes of y,  But these two extremes
are very rare because our design fails to sample at the extremes, then we
are simply loading the research against the detection of polarization, This
is an artifact,

If I am interested in discovering causes I will do as the experimentalists
do when they seek to isolate and control their measurements,  Because I was
trainned as an experimental personality psychologist, this seems a natural
thing to do,  It would also be the best strategy to a chemist or physicist,
Experimental scientists seek to understand causal connections in their
simplicity and then build up the complex model,  Applied social scientists
tend to mistrust such systematic research and prefer to constrain their
modeling to the joint causes expressed in a particular sample of numerous
variables,  But because the circumstances present myriad dimensional
possible interactions, we end up with the ambiguity that SEM researchers
face, The same data will support many models,

I would hypothesize that variables A and B are causes of C and then collect
a uniformly distributed array of both A and B, or better yet, do a factorial
sampling in which all levels of A and B are crossed with equal frequency per
cell,  This is what I call a manifold in my papers, I would then see if A
and B cause C, using corresponding regressions or correlations,  Thus I am
interested in the simple statement do A and B cause C. I am not
hypothesizing the complex nonlinear functions that are entailed by the
assumption that A and B are normally distributed,

>As the direction-coefficient depends much on the (rare) extremes, I expect
>the coefficient will show that variable z1 or z2 as independent, which
>you sample uniformly. In which of z1 or z2 you assume you were missing
>some values, if you have a normal distributed sample in z1 and z2?
>I have not tested this procedure, but I may modify a graph, that I
>have shown last year (with uniform causes), for normal variables.


Bill responded:

I am not sure what you are saying, But if you are suggesting that CR will
say the cause is which ever variable is sampled uniformly then you are
wrong,  It is not the shape of the distribution that defines the cause,  A
uniform distribution is a prerequisite for uniform cause, But uniformity
does not imply causation,  Polarization of the correlations between x1 and
x2 across the ranges of the dependent variable (y) implies causation,

>
>Let z1 and z2 be instances for n1 and y in our sample, not knowing
>which z represents y. We will get a bivariate distribution like the
>following, where rare combinations are indicated with the period,
>medium frequent combinations with the star and most frequent
>combinations with a double-cross:
>
>.!.
>*!* * .
>  * #!# * * .
>   ---.-*-#-#!# # *- z1
>* * #!# *
>  * *!* .
>.! z2
>
>You can produce a direction coefficient showing any variable as dependent
>just by resampling and weighting some cases.


>
>a)
>For instance to have uniformity in z2 and triangularity in z1 weight all
>cases to the frequency of the edges in 30 deg and 210 deg (extreme values
>of z1)
>
> !
>*!* * * * *
>  * *!* * * *
>   -*-*-*!* * *- z1
>  * * * *!* *
>* * * * *!*
> ! z2



>
>This shows z1 dependent (more complex distribution: triangular) and assumes
>a third (latent) cause z0, which can be retrieved as residual of a
>regression.


Bill responds,  NO. No. No. It is not the triangularity as such that implies
the complexity of a dependent variable, It is the polarization of the causes
across the ranges of the dependent variable that implies greater complexity
in y, This is because y contains x1 and x2, not because y is triangular,
True y is triangular, but this another issue,  This is why CR works even if
we feed it the uniform ranks of all the data AFTER the model is first
generated using uniform causes.

Gottfried continues:
>
>b)
>For instance to have uniformity in z1 and triangularity in z2 weight all
>cases to the frequency of 

Re: ANOVA causal direction

[Gus Gassmann]

William Chambers wrote:
> 
> Gus,
> 
> You are making a defense of studying distributions as they are thrown at us
> by nature/circumstances,  This seem the way to go to social scientists
> because we tend to believe that our causes are embedded in all sorts of
> complex interactions and can not be isolated from their context,  If we look
> however to the physical sciences,  we see a very different strategy, The
> chemist tends not to go out and perform experiments on naturally occuring
> clusters of chemicals, Instead, she isolates each chemical and then studies
> their interactions in pure states, so that the fundamental mechanisms of
> causation are revealed,  The experimental psychologist does the same thing
> in his lab,  Both tend to use manipulation and anova designs, in which equal
> cell sizes are sought across the levels of the factors,  By doing so they
> experimentalist progresses systematically by carefully controling his
> research,
> 
> I am simply saying that those who wish to pursue causal models without
> manipulation should learn something about the control afforded by isolation
> of variables,  Do you think it is wooly minded for a user of an anova design
> to seek out equal cell sizes across the levels of the putative factor?

There is nothing wrong with that, but that hardly qualifies as the
uniform
distribution of the putative independent variables x1 and x2 that you
were
talking about earlier. And the paper of yours that I downloaded
(bug-free)
from the web site you mentioned does not talk about restricting your
attention
to just ANOVA, either. Here is how I interpret what you've said to date:
1. If you take two uniformly distributed random variables x1 and x2 and
form 
   the sum y = x1 + x2, then y has a distribution that is not uniform.
2. If you have two variables x and y and want to determine whether x
depends
   on y or y depends on x, first select the x variable uniformly, then
run 
   two regressions, one with each of the two variables as the IV. The y
   variable is not going to be uniform, of course, but according to you 
   this proves causality. 

What have I got wrong?


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Re: ANOVA causal direction

[William Chambers]

Gus said:

>Here is how I interpret what you've said to date:

>1. If you take two uniformly distributed random variables x1 and x2 and
>form
>   the sum y = x1 + x2, then y has a distribution that is not uniform.
>2. If you have two variables x and y and want to determine whether x
>depends
>   on y or y depends on x, first select the x variable uniformly, then
>run
>   two regressions, one with each of the two variables as the IV. The y
>   variable is not going to be uniform, of course, but according to you
>   this proves causality.
>
>What have I got wrong?

Bill responded:

Well you left out a whole lot of stuff. I have another paper (virus free
that may help) I will send to you on request that explains things more
simply, But the essence was expressed in my recent post in which I explained
the polarization effect,  Simply running regressions is not the point, Its
what kind of regressions (or correlatins),  The simplest expression of the
effect is that the correlations between the two independent variables X1 and
x2 will be opposite in the extremes versus midranges of y (the dependent
variable),  The correlations between x1 and x2 will not be opposite across
the ranges of either x variable,

Does this make sense?

Bill




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Re: ANOVA causal direction

[Gus Gassmann]

William Chambers wrote:
> 
> Gus said:
> 
> >Here is how I interpret what you've said to date:
> 
> >1. If you take two uniformly distributed random variables x1 and x2 and
> >form
> >   the sum y = x1 + x2, then y has a distribution that is not uniform.
> >2. If you have two variables x and y and want to determine whether x
> >depends
> >   on y or y depends on x, first select the x variable uniformly, then
> >run
> >   two regressions, one with each of the two variables as the IV. The y
> >   variable is not going to be uniform, of course, but according to you
> >   this proves causality.
> >
> >What have I got wrong?
> 
> Bill responded:
> 
> Well you left out a whole lot of stuff. I have another paper (virus free
> that may help) I will send to you on request that explains things more
> simply, But the essence was expressed in my recent post in which I explained
> the polarization effect,  Simply running regressions is not the point, Its
> what kind of regressions (or correlatins),  The simplest expression of the
> effect is that the correlations between the two independent variables X1 and
> x2 will be opposite in the extremes versus midranges of y (the dependent
> variable),  The correlations between x1 and x2 will not be opposite across
> the ranges of either x variable,
> 
> Does this make sense?

No. You said yourself that you are _selecting_ the x1 and x2 to be
uniform.
Of course the Y you generate by adding them will then be triangular. Of
course
the correlations will come out the way you want them to. But does that
prove
causality? Of course not. Look at your model in the opposite direction:
Y is caused by x1 and x2, but I want to prove it isn't, that the
causality
effect is y, x2 => x1. What do I do? I follow your recommendations and
select
the y uniformly and presto: causality goes the other way.

Again I ask: What did I miss?


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Re: ANOVA causal direction

[William Chambers]

Guss said:
>
>No. You said yourself that you are _selecting_ the x1 and x2 to be
>uniform.

Yes, we do this so that we will have examples of all combinations of x1 and
x2,as we would do when using a factorial anova design.  But such uniform
sampling does not make the variables into causes,  Adding x1 to x2 causes y,
We do not infer that x1 and x2 are the causes because they are uniformly
sampled.  We infer they are the causes because their correlations polarize
across the ranges of the dependent variable y,

>Of course the Y you generate by adding them will then be triangular. Of
>course
>the correlations will come out the way you want them to. But does that
>prove
>causality? Of course not. Look at your model in the opposite direction:
>Y is caused by x1 and x2, but I want to prove it isn't, that the
>causality
>effect is y, x2 => x1. What do I do? I follow your recommendations and
>select
>the y uniformly and presto: causality goes the other way.
>
No it does not,  You do not infer that the uniformly sampled variable is the
cause,  You sample the variables you think may be the causes uniformly and
then see if you get the polarization effect across the ranges of any other
variables, whether they are uniform or triangular,  You are being misled I
think by Gottfried's speculations about distributions, But Gottfried and I
have long had a friendly disagreement about this,  He sees the presto in the
distributions, I do not, My point is supported by the fact that you could
have two variables that are uniformly distributed and a third that is
triangular and (according to both reality and corresponding
correlations/regressions) there be no causal relationship between the
variables. Furthermore, if you convert the data to ranks after generating
the y=x1+x2 model based on interval data, then CR still reveals the causal
pattern.  CR does not "know" the data you pass to it are not all uniform,
It simply looks for the polarization, not for the distribution,

Let's focus this conversation, What do you think about the polarization
effect, assuming for the moment that it is wise to sample factors uniformly,
in the way experimenters do in ANOVA designs?

Bill



>Again I ask: What did I miss?




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Re: ANOVA causal direction

[Gus Gassmann]

William Chambers wrote:
> 
> Guss said:
> >
> >No. You said yourself that you are _selecting_ the x1 and x2 to be
> >uniform.
> 
> Yes, we do this so that we will have examples of all combinations of x1 and
> x2,as we would do when using a factorial anova design.  But such uniform
> sampling does not make the variables into causes,  Adding x1 to x2 causes y,

Here you are using a very different notion of causality than I am
willing to
accept. If you are serious about this notion, then I concede the
argument.
In your sense, of course y is caused by x1 and x2. For me, that is then
simply a "so what?".

> We do not infer that x1 and x2 are the causes because they are uniformly
> sampled.  We infer they are the causes because their correlations polarize
> across the ranges of the dependent variable y,

I have to agree with Gottfried Helms and Jerry Dallal and others that
this
is exactly the same thing. Uniform sampling of x1 and x2 _causes_ (in my
sense of the term) y to have a triangular distribution. If y has a
triangular
distribution, then the correlations polarize, by definition. 
 
> >Of course the Y you generate by adding them will then be triangular. Of
> >course
> >the correlations will come out the way you want them to. But does that
> >prove
> >causality? Of course not. Look at your model in the opposite direction:
> >Y is caused by x1 and x2, but I want to prove it isn't, that the
> >causality
> >effect is y, x2 => x1. What do I do? I follow your recommendations and
> >select
> >the y uniformly and presto: causality goes the other way.
> >
> No it does not,  You do not infer that the uniformly sampled variable is the
> cause,  You sample the variables you think may be the causes uniformly and
> then see if you get the polarization effect across the ranges of any other
> variables, whether they are uniform or triangular,  

In other words, you do have reasons other than purely statistical ones
for
suspecting a causation. You then change the data (by insisting on a
uniform sample) to give you the polarization of the correlations that
you
want. That still looks like circular reasoning to me.

> You are being misled I
> think by Gottfried's speculations about distributions, But Gottfried and I
> have long had a friendly disagreement about this,  He sees the presto in the
> distributions, I do not, My point is supported by the fact that you could
> have two variables that are uniformly distributed and a third that is
> triangular and (according to both reality and corresponding
> correlations/regressions) there be no causal relationship between the
> variables. 

Exactly. I agree with Gottfried's presto. If you add two uniformly
distributed
variables, the result will be triangular, and the correlations will
polarize.
End of story. What would you say to a model in which
x1 = Annual observations on the number of storks
y  = Annual observations on the number of births (of human babies)

If you throw out a few data points so that x1 is nearly uniform, then
you
will see the polarization of correlations. Does that translate into
causation 
in your book?

> Furthermore, if you convert the data to ranks after generating
> the y=x1+x2 model based on interval data, then CR still reveals the causal
> pattern.  

Of course! Ranks are uniformly distributed. In fact, if you apply
ranking,
then you don't have to use uniform data from the beginning.

> CR does not "know" the data you pass to it are not all uniform,
> It simply looks for the polarization, not for the distribution,
> 
> Let's focus this conversation, What do you think about the polarization
> effect, assuming for the moment that it is wise to sample factors uniformly,
> in the way experimenters do in ANOVA designs?

So far I am not impressed, I'm sorry to say.


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Re: ANOVA causal direction

[David B. Hedrick]

William and Gus:

Please excuse a lurker for stepping in here, I've been following this
thread for several days and would like to add something.  Perhaps
something that has been said already.  
Proving causality from a correlation algorithm would be wonderful, but
I don't think it is there.  The reason I think this is that all that
statistics can have is the numbers, and the numbers are not the system. 
Finding the correlations and the significant differences can lead to
understanding the system (often assuming for the nonce that some
correlation is a causal relationship), and that understanding hopefully
leads to further experiments.  A properly designed experiment can prove
causality.  
As a scientist, I often feel that each of us is too specialized, by
necessity.  There is so much material (data, papers, texts) to absorb. 
I find myself wanting the understanding that a multivariate statistician
has, without the time to get it.  I feel the same about certain
specialties in biology and chemistry.  The danger of this is that we may
try to push foreward when we don't have the leverage.  I just read a
paper by a fellow, knowledgable in complexity theory and computers, who
applied his knowledge to evolution and thought he had found an error, as
well as a theory to correct the error.  It was all smoke and mirrors
because he didn't know how DNA works.  He treated the genetic code like
the perfect one's and zero's that a computer deals with.  The A,T,G, and
C of DNA operate in the real world, and the real world has few
integers.  
I suppose that what I'm trying to get to is that interaction with the
scientist dealing with the system is more likely to find a proof of
causality, than chewing on the data more.  
William/Bill, if you are still bothering to read this, I would like a
copy of the paper you offered to Gus.  As I say, I'm not convinced, but
I am willing to be.  Address and eddress given below.  
 
> Bill said earlier:
> 
> >> Yes, we do this so that we will have examples of all combinations of x1
> and
> >> x2,as we would do when using a factorial anova design.  But such uniform
> >> sampling does not make the variables into causes,  Adding x1 to x2 causes
> y,
> >
> Gus responded:
> 
> >Here you are using a very different notion of causality than I am
> >willing to accept. If you are serious about this notion, then I concede the
> >argument. In your sense, of course y is caused by x1 and x2. For me, that
> is then
> >simply a "so what?".
> 
> Bill responded,
> 
> In so far as we use numbers to model causes, the causes should also
> demonstrate the properties of those numbers, If not we are being deceptive
> to use numbers at all, This is point that Michell makes, as referenced in my
> most recent paper, We learn more about the phenomenon by what we know about
> numbers,  This is the whole point of statistics,   What do you use numbers
> for in causal modeling?
> 
> You concede the argument in a manner that suggests I am trying to get away
> with something unusual, I most definitely am not. The use of operations to
> model causes is implicit through the literature, For example, why do you
> think the word "nonadditive" is used to describe interactions in ANOVA?
> 
> Bill said:
> >> We do not infer that x1 and x2 are the causes because they are uniformly
> >> sampled.  We infer they are the causes because their correlations
> polarize
> >> across the ranges of the dependent variable y,
> 
> >Gus responded:
> 
> >I have to agree with Gottfried Helms and Jerry Dallal and others that
> >this is exactly the same thing. Uniform sampling of x1 and x2 _causes_ (in
> my
> >sense of the term) y to have a triangular distribution. If y has a
> >triangular distribution, then the correlations polarize, by definition.
> 
> Bill responded:
> 
> First of all, none of you have given an explanation for your beliefs, It
> would not matter if every famous statistician in the world made the same
> claim, Without an explanation that stands up to the tests of logic, your
> claims are not scholarly,
> 
> By your definition, if we sample all the variables uniformly, then CR will
> not know what to make of the data, In fact, CR will work just as well, I
> gave the example of the ranked data below, to which you responded:
> 
> Gus said:
> >Of course! Ranks are uniformly distributed. In fact, if you apply
> >ranking,
> >then you don't have to use uniform data from the beginning.
> >
> Bill responds:
> 
> I am ranking them AFTER the causes are first generated using interval or
> ratio data,  Of course we could use the ranks of the independent variables
> in th

Re: ANOVA: planned comparisons

[Donald F. Burrill]

It rather sounds as though data are already in hand, rather than yet to 
be collected.  That being the case, as I shall assume, your 2nd model has 
half the data that your 1st model has, and it is not clear whether this 
reflects the discarding of half the available data, or the averaging 
together of pairs of observations from the first model to fit the second. 
My preference would therefore be to start with the 1st model, 
since everything you want to know from the 2nd can be deduced from the 
1st, unless I have badly misconstrued your descriptions.

You write, 
> In each of the above months I have 3 sampling dates (which are actually 
> 3 different years) and in each date I have 10 estimates of A density. 

This appears to entail an assumption that the measured density is 
constant across years.  Is this assumption realistic?  
(If not, it would presumably be desirable to seek evidence on the point, 
which would call for a more complex model or for certain specific sets 
of contrasts not so far described.)

> The hypothesis states that there should be a decrease in
> density in winter, an increase in spring (growing season)
> and a possible decrease in summer (summer disturbance is 
> not supposed to be as effective as the winter one).

The corresponding null hypothesis in ANOVA is that there are no changes 
in density at all.  But you want also to be able to detect patterns of 
differences, should they exist, other than the patterns your research 
hypothesis lead you to expect.  Hence, in the first instance at least, 
do not omit sources of variation unaccounted for in your hypothesis.

The model you describe leads to the summary table below, where the 1-df 
subdivisions of "Periods" are orthogonal contrasts.  You claim to be 
interested only in the first 3 of these, which is fair from a theoretical 
perspective;  but from an empirical perspective it is possible your 
hypothesis is, if not wrong, incomplete, and you surely would wish to 
detect this shokuld it be the case.  Treat the last two d.f. as a single 
source orthogonal to the other 3 d.f., and see whether the associated SS 
is large enough to make this source empirically interesting.  If it is, 
you can use standard post hoc comparisons (Scheffe' contrasts, e.g.) to 
pursue whatever patterns there may be.  No need to decide beforehand, in 
the absence of evidence.

> Source of Variation DF Test against
> --
> Periods   5  P*L
>Between winter months   1  P*L  
>Between spring months   1  P*L 
>Between summer months   1  P*L   
>Winter vs Others1  P*L  > Combine these, with
>Summer vs Spring1  P*L  > 2 d.f.
> Locations 3  D(P*L)
> Periods*Locations15  D(P*L)
> Dates(Periods*Locations) 48  Residual
> Residual648 
> ---
> TOTAL   719 

You do not mention the possibilities of interesting interactions, which 
would lead to the pursuit of other details.  Presumably these would be 
pursued via post hoc contrasts, depending on the apparent pattern(s), 
among the 24 P*L means.

On Wed, 17 May 2000, A. Murias Santos wrote, inter alia:

> I've got two possible models of ANOVA to test for differences 
> in space occupancy between periods. 
> 
> Lets assume population A as a dominant space occupier. It
> outcompete other species, growing over them, but never 
> monopolizes space (Density < 100%, and is usually below 60%). 
> The hypothesis is that external disturbance events prevent 
> it from reaching 100% of space occupancy. 
> 
> Disturbance events are seasonal. Lets assume W as a winter
> disturbance, beginning in November--December and ending
> in March--April; S is a summer disturbance, beginning in
> June--July and ending in November--December; P stands for
> spring season, begins in April--March and ends in June--July,
> and no disturbance occurs between these periods.
> 
> In each of the above months I have 3 sampling dates (which 
> are actually 3 different years) and in each date I have
> 10 estimates of A density.
> 
> The hypothesis states that there should be a decrease in
> density in winter, an increase in spring (growing season)
> and a possible decrease in summer (summer disturbance is 
> not supposed to be as effective as the winter one).
> 
> First model:
>  
> Factors are locations (4, random), periods (6, fixed) 
> and sampling dates (3, nested, random) with 10 replicates 
> per combination. Periods are:
> 
> March (end of winter), 
> April (beginning of spring), 
> June(

Re: Repeated Measures ANOVA

[Donald Burrill]

Sounds to me as though you have in fact 5 within-subject variables:
the four you list plus
  5) Replications (with 10 levels)
Of course, this is a random factor, whereas the other four are presumably 
fixed factors, but presumably there's a way of telling GLM that.  And 
there is presumably no connection between Replication 1 in Colour and 
Replication 1 in Shape (e.g.), (unless replications are numbered in 
temporal order, in which case the factor can be interpreted as a practice 
and/or fatigue factor) so interactions between Replications and the 
other four factors are meaningless or uninterpretable, save as sources of 
error variation for particular F-tests of the four binary factors and 
their interactions.
Since you have required each subject to perform 160 times, there 
might be some point to using the sequence number (1,...,160) as a 
covariate, to control for an _overall_ fatigue or practice (or boredom!) 
effect.  Whatever merit this notion has may depend on whether the 10 
replications for each combination of Colour/Shape/Pattern/Movement were 
all massed (so to speak) at one time, or dispersed among the replications 
for the other 15 cells;  and on whether the sequence of replications by 
combinations was the same for each of the 10 subjects, or differed from 
subject to subject.

On Tue, 13 Jun 2000 [EMAIL PROTECTED] wrote:

> I have conducted an experiment with 4 within subject variables.
> 1) Colour
> 2) Shape
> 3) Pattern
> 4) Movement
> 
> Each of these 4 factors have 2 levels so each subject would be exposed
> to 16 conditions in total. However, I have made each subject do 10
> replications per condition and I have 10 subjects so I have a total of
> 1600 data points.
> 
> I have tried using SPSS repeated measures in GLM to analyse my data but
> I don't know how to include my replications. SPSS requires that I
> select 16 columns of dependant variables each representing a
> combination of my factors. However, I am only allowed one row per
> subject, so how do I input the 10 replications that each subject
> performed for each combination?
> 
> Thanks !
> 
> Alfred
> 
> 
> 
> 
> 
> Sent via Deja.com http://www.deja.com/
> Before you buy.
> 
> 
> ===
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> 

 
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Re: Repeated Measures ANOVA

[Thom Baguley]

[EMAIL PROTECTED] wrote:
> 
> Hi.
> 
> I have conducted an experiment with 4 within subject variables.
> 1) Colour
> 2) Shape
> 3) Pattern
> 4) Movement
> 
> Each of these 4 factors have 2 levels so each subject would be exposed
> to 16 conditions in total. However, I have made each subject do 10
> replications per condition and I have 10 subjects so I have a total of
> 1600 data points.
> 
> I have tried using SPSS repeated measures in GLM to analyse my data but
> I don't know how to include my replications. SPSS requires that I
> select 16 columns of dependant variables each representing a
> combination of my factors. However, I am only allowed one row per
> subject, so how do I input the 10 replications that each subject
> performed for each combination?

You have 5 within subject variables. Include a 10 level factor "replication"
or use the mean for the 10 replications as the DV (though there are problems
with this).

Thom


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Re: Repeated Measures ANOVA

[Bruce Weaver]

On Tue, 13 Jun 2000 [EMAIL PROTECTED] wrote:

> Hi.
> 
> I have conducted an experiment with 4 within subject variables.
> 1) Colour
> 2) Shape
> 3) Pattern
> 4) Movement
> 
> Each of these 4 factors have 2 levels so each subject would be exposed
> to 16 conditions in total. However, I have made each subject do 10
> replications per condition and I have 10 subjects so I have a total of
> 1600 data points.
> 
> I have tried using SPSS repeated measures in GLM to analyse my data but
> I don't know how to include my replications. SPSS requires that I
> select 16 columns of dependant variables each representing a
> combination of my factors. However, I am only allowed one row per
> subject, so how do I input the 10 replications that each subject
> performed for each combination?
> 
> Thanks !
> 
> Alfred
> 

Hi Alfred,
You might be better off using UNIANOVA for this analysis instead 
of GLM.  For example, here's the GLM syntax for a mixed-design (A and B as 
between subjects variables; C and D within-subjects):

GLM
  c1d1 c1d2 c2d1 c2d2 c3d1 c3d2 BY a b
  /WSFACTOR = c 3 Polynomial d 2 Polynomial
  /METHOD = SSTYPE(3)
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = c d c*d
  /DESIGN = a b a*b .

This analysis required the 6 repeated meaures (3*2) to be strung out
across one row for each subject.  But I was able to produce exactly the
same results using 6 rows per subject (one for each of the c*d
combinations) and the following syntax: 

UNIANOVA
  y  BY subj a b c d
  /RANDOM = subj
  /METHOD = SSTYPE(3)
  /INTERCEPT = INCLUDE
  /EMMEANS = TABLES(OVERALL)
  /EMMEANS = TABLES(a)
  /EMMEANS = TABLES(b)
  /EMMEANS = TABLES(c)
  /EMMEANS = TABLES(d)
  /CRITERIA = ALPHA(.05)
  /DESIGN = a b a*b subj(a*b) 
c c*a c*b c*a*b  c*subj(a*b)
d d*a d*b d*a*b  d*subj(a*b)
c*d c*d*a c*d*b c*d*a*b  c*d*subj(a*b).

Note that SUBJ is now listed explicitly as one of the variables.  And you 
must explicitly list each of the error terms for within-subjects 
effects.  If you do not list these error terms, a pooled error term is 
used for tests of the within-subjects effects.  Finally, note as well 
that SUBJ appears on the /Random line; and the nesting of subjects within 
a*b cells is indicated as subj(a*b).

I haven't tried this with a completely within-subjects design.  But if you
let y=DV a=colour b=shape c=pattern d=movement e = repetition (as
suggested by Donald Burril), your syntax should look something like this,
I think: 

UNIANOVA
  y  BY subj a b c d e
  /RANDOM = subj e
  /METHOD = SSTYPE(3)
  /INTERCEPT = INCLUDE
  /EMMEANS = TABLES(a)
  /EMMEANS = TABLES(b)
  /EMMEANS = TABLES(c)
  /EMMEANS = TABLES(d)
  /EMMEANS = TABLES(d)
  /CRITERIA = ALPHA(.05)
  /DESIGN = a a*subj
b b*subj
c c*subj
d d*subj
e e*subj
a*b a*b*subj
a*c a*c*subj
etc...
a*b*c*d*e a*b*c*d*e*subj .

Your data file would have 2*2*2*2*10 = 160 rows per subject with variables
that code for a-e and another for the DV. 

Hope this helps.
Cheers,
Bruce
-- 
Bruce Weaver
[EMAIL PROTECTED]
http://www.angelfire.com/wv/bwhomedir/




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Re: Repeated Measures ANOVA

[Gene Gallagher]

In article <[EMAIL PROTECTED]>,
  [EMAIL PROTECTED] (Donald Burrill) wrote:
> Sounds to me as though you have in fact 5 within-subject variables:
> the four you list plus
>   5) Replications (with 10 levels)
> Of course, this is a random factor, whereas the other four are
presumably
> fixed factors, but presumably there's a way of telling GLM that.



I believe you (another post comes up with the same solution).  Do
you have a citation for a book chapter or article that discusses
the general issue of replication in repeated measures designs?  I'm
intrigued about the value of having subjects doing lots of
replicate trials.
--
Eugene D. Gallagher
ECOS, UMASS/Boston

--
Eugene D. Gallagher
ECOS, UMASS/Boston


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Re: Repeated Measures ANOVA

[alfseet]

Thanks everyone for replying! You have all been very helpful and I
appreciate it greatly. I'll try out your suggestions immediately!


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Replicated within subjects ANOVA

[alfseet]

Hello,

I'm new to SPSS and I need help. I conducted an experiment with 4
within subject factors (A,B,C,D) , 10 subjects (S), and 10 replications
per subject at each condition. Thus, I have 10 observations per cell.
How do I tell SPSS to use my within cell variation as the error term
for the ANOVA instead of the usual Subject X Factor interaction?


Thanks!

Alfred


Sent via Deja.com http://www.deja.com/
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ANOVA, Robustness, and Power

[Alex Yu]

ANOVA is said to robust against assumption violations when the sample 
size is large. However, when the sample size is huge, it tends to 
overpower the test and thus the null may be falsly rejected. Which is a 
lesser evil? Your input will be greatly appreciated.


Chong-ho (Alex) Yu, Ph.D., CNE, MCSE
Instruction and Research Support
Information Technology
Arizona State University
Tempe AZ 85287-0101
Voice: (602)965-7402
Fax: (602)965-6317
Email: [EMAIL PROTECTED]
URL:http://seamonkey.ed.asu.edu/~alex/
   
  



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Three Factor ANOVA Help

[Luís Silva]

For a certain variable I applied a Three Factor ANOVA and found a
significant interaction between two factors. I have two levels for each
factor. Then, I applied the HSD Tukey test for multiple unplanned
comparisons, in order to detect what are the significantly different
treatments. Since I detected an interaction between two factors, is it
correct to apply Tukey test? If not, are there other type of unplanned
comparisons that might be used?

Thank you for your suggestions

Best Regards




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Re: Regression vs ANOVA

[Bob Wheeler]

It is a matter of emphasis. Both regression and
ANOVA are techniques for dealing with linear
models. ANOVA focuses on experiments where the
variables may be random and where there may be
several error terms. Regression on models which
tend to have fixed, continuous, independent fixed
variables and a single error term. To say that
ANOVA is a special case of regression, in effect
redefines regression as "linear model analysis,"
which can be done, but is a stretch. As definitive
a statement as is likely to be find is given by
Scheffé in The analysis of variance (1959), and a
good discussion of using multiple regression to
perform some ANOVA calculations for fixed effect
models is given in Draper and Smith's  Applied
regression analysis (1966). 

I speculate that this now seems confusing because
texts in applied areas have perhaps dwelt too
heavily on the mechanics of ANOVA calculations and
mentioned the linear model part only briefly. The
upshot is that students in those areas are
surprised when the linear model part is called to
their attention, and apparently Jacob Cohen (1968)
felt strongly enough about it to write a paper
explaining the connection. Standard statistical
texts have always insisted on the mathematics, and
Kempthorne for example in Design and analysis of
experiments (1952) takes great pains to structure
ANOVA in terms of linear models -- he even derives
the normal equations.  


Alexander Tsyplakov wrote:
> 
> An interesting problem have arised during discussion of the
> origins of "eigenvalue".
> 
> My own point of view is that ANOVA is just a particular case
> of regression analysis with dummy (1/0) regressors and
> either fixed or random effects. Block orthogonality of
> regression matrix in the special case of ANOVA makes it
> possible to decompose the sum of squared residuals (and
> variance) into several components.
> 
> If people misuse the term ANOVA then what is it's correct
> meaning? Is it a statistical model which is different from
> regression model y=Xb+e? Then there must be some clear
> formal discription.
> 
> -
> Alexander Tsyplakov
> Novosibirsk State University
> http://www.nsu.ru/ef/tsy/
> 
> Elliot Cramer wrote...
> > Werner Wittmann <[EMAIL PROTECTED]>
> wrote:
> > : inverting the
> > : correlation matrix to get the effects was too
> complicated to compute by
> > : hand, so Sir Ronald developed the ANOVA shortcut.
> >
> > hardly.  They do have some mathematics in common (through
> use of dummy
> > variables which some of us think is for dummies).  they
> are comceptually
> > completely different/  Unfortunately many people misuse
> ANOVA because they
> > think of it as regression analysis.
> 
> > : I'm always teasing my colleagues and students, if you
> spent one year
> > : learning ANOVA and one year multiple regression you've
> wasted almost one
> > : year of your life.
> 
> > you can learn the mathematics of regression analysis in 10
> minutes but
> > you're still a long way from understanding either it or
> ANOVA

-- 
Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
ECHIP, Inc.


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Re: Regression vs ANOVA

[George W. Cobb]

I, too, think of ANOVA and regression as variations on a common
theme.  Here's an additional way in which they differ:  For balanced
ANOVA, the decomposition of the data into sums of squares and degrees of
freedom is determined by a group of symmetries.  For example, consider a
one-way randomized complete block design with R rows as blocks and
C columns as treatments.  The analysis is invariant under all row
permutations, and all column permutations, i.e., interchanging any two
rows of the data, or any two columns of the data, won't change the
analysis.  If you now think of the data as a vector in RxC-dimensional
space, the symmetries (row permutations, column permutations) determine
invariant subspaces; these are precisely the subspaces you project the
data vector onto to get the SSs and dfs.  In regression, the subspaces
you project onto are determined directly by a spanning set of carrier
variables; in balanced ANOVA, the subspaces are uniquely determined by the
symmetries, and the spanning sets are somewhat arbitrary.  (I claim 
no credit for this lovely way of looking at things; I learned it from
Peter Fortini  and Persi Diaconis.  It's written up in Fortini's
dissertation from the 1970s, and Diaconis's IMS lecture notes on group
theory and statistics.)

Of course you only have such clean sets of symmetries for balanced
designs, and the approach via symmetries doesn't address such things as
the difference between fixed and random effects, which Bob 
Wheeler raises.  Nevertheless, to the extent that I think of ANOVA
as distinct from regression, I find the role of symmetries worth
keeping in mind.

  George

George W. Cobb
Mount Holyoke College
South Hadley, MA  01075
413-538-2401




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Re: Regression vs ANOVA

[Alexander Tsyplakov]

Bob Wheeler wrote...
> It is a matter of emphasis. Both regression and
> ANOVA are techniques for dealing with linear
> models.

> ANOVA focuses on experiments where the
> variables may be random and where there may be
> several error terms. Regression on models which
> tend to have fixed, continuous, independent fixed
> variables and a single error term.

No, regression models can have stochastic and/or discrete
regressors. I can only agree that regression models have
single error term as compared to ANOVA with random effects.
But a more clear way to look at ANOVA with random effects is
as follows.

ANOVA with random effects is a modification of ANOVA with
fixed effects (which is just a plain linear regression) in
which coefficients are random. Hence, coefficients in the
former case are not the parameters to be estimated. Only
parameters of the distribution of the coefficients are
estimated. This gives efficiency gain relative to ANOVA with
fixed effects. But, of course, additional assumptions about
the distribution of coefficients are needed. This is
sometimes called "random coefficients model". Note, that
random coefficients model has a matrix of regressors (matrix
of plan) which is deterministic, fixed.

> To say that
> ANOVA is a special case of regression, in effect
> redefines regression as "linear model analysis,"
> which can be done, but is a stretch.

OK, let it be "linear model analysis".

> As definitive
> a statement as is likely to be find is given by
> Scheffé in The analysis of variance (1959),

Regretfully, I've lost my Scheffé. But, as far as I
remember, Scheffé also uses regression analysis approach
to ANOVA. Am I wrong?

> and a
> good discussion of using multiple regression to
> perform some ANOVA calculations for fixed effect
> models is given in Draper and Smith's  Applied
> regression analysis (1966).

Yes, this book greately reduced the confusion which I
previousely had with ANOVA.

> I speculate that this now seems confusing because
> texts in applied areas have perhaps dwelt too
> heavily on the mechanics of ANOVA calculations and
> mentioned the linear model part only briefly.

Exactly.

> The
> upshot is that students in those areas are
> surprised when the linear model part is called to
> their attention, and apparently Jacob Cohen (1968)
> felt strongly enough about it to write a paper
> explaining the connection. Standard statistical
> texts have always insisted on the mathematics, and
> Kempthorne for example in Design and analysis of
> experiments (1952) takes great pains to structure
> ANOVA in terms of linear models -- he even derives
> the normal equations.

I opened this discussion because Elliot Cramer wrote
"Unfortunately many people misuse ANOVA because they
think of it as regression analysis". Do you agree with him?
I think, to the contrary, that ANOVA _must_ be analysed
in the context of regression analysis to avoid confusion.
It might be better not to use term "ANOVA" at all.
Traditional ANOVA approach is vague and even misleading.
ANOVA tables in most cases are not informative. I was
once greatly pusseled by Statgraphics multiple regression
output with ANOVA table. Does anybody use those sums
of squares?

> Alexander Tsyplakov wrote:
> >
> > An interesting problem have arised during discussion of
the
> > origins of "eigenvalue".
> >
> > My own point of view is that ANOVA is just a particular
case
> > of regression analysis with dummy (1/0) regressors and
> > either fixed or random effects. Block orthogonality of
> > regression matrix in the special case of ANOVA makes it
> > possible to decompose the sum of squared residuals (and
> > variance) into several components.
> >
> > If people misuse the term ANOVA then what is it's
correct
> > meaning? Is it a statistical model which is different
from
> > regression model y=Xb+e? Then there must be some clear
> > formal discription.
> >
> > -
> > Alexander Tsyplakov
> >     Novosibirsk State University
> > http://www.nsu.ru/ef/tsy/
> >
> > Elliot Cramer wrote...
> > > Werner Wittmann
<[EMAIL PROTECTED]>
> > wrote:
> > > : inverting the
> > > : correlation matrix to get the effects was too
> > complicated to compute by
> > > : hand, so Sir Ronald developed the ANOVA shortcut.
> > >
> > > hardly.  They do have some mathematics in common
(through
> > use of dummy
> > > variables which some of us think is for dummies).
they
> > are comceptually
> > > completely different/  Unfortunately many people
misuse
> > ANOVA because they
> > > think of i

Re: Regression vs ANOVA

[Bob Wheeler]

Good points, well worth our attention. I haven't
seen your references, but Bill Kruskal's coordiate
free approach treats the same ideas. He was
teaching it in the late 50's and early 60's at
Chicago and wrote it up in the fourth Berkeley.
The first part of Scheffé treats projections into
the various subspaces for those who might be
interested.

"George W. Cobb" wrote:
> 
> I, too, think of ANOVA and regression as variations on a common
> theme.  Here's an additional way in which they differ:  For balanced
> ANOVA, the decomposition of the data into sums of squares and degrees of
> freedom is determined by a group of symmetries.  For example, consider a
> one-way randomized complete block design with R rows as blocks and
> C columns as treatments.  The analysis is invariant under all row
> permutations, and all column permutations, i.e., interchanging any two
> rows of the data, or any two columns of the data, won't change the
> analysis.  If you now think of the data as a vector in RxC-dimensional
> space, the symmetries (row permutations, column permutations) determine
> invariant subspaces; these are precisely the subspaces you project the
> data vector onto to get the SSs and dfs.  In regression, the subspaces
> you project onto are determined directly by a spanning set of carrier
> variables; in balanced ANOVA, the subspaces are uniquely determined by the
> symmetries, and the spanning sets are somewhat arbitrary.  (I claim
> no credit for this lovely way of looking at things; I learned it from
> Peter Fortini  and Persi Diaconis.  It's written up in Fortini's
> dissertation from the 1970s, and Diaconis's IMS lecture notes on group
> theory and statistics.)
> 
> Of course you only have such clean sets of symmetries for balanced
> designs, and the approach via symmetries doesn't address such things as
> the difference between fixed and random effects, which Bob
> Wheeler raises.  Nevertheless, to the extent that I think of ANOVA
> as distinct from regression, I find the role of symmetries worth
> keeping in mind.
> 
>   George
> 
> George W. Cobb
> Mount Holyoke College
> South Hadley, MA  01075
> 413-538-2401
> 
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> the problem of INAPPROPRIATE MESSAGES are available at
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-- 
Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
ECHIP, Inc.


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Re: Regression vs ANOVA

[Ken K.]

Regression is the act of obtaining least squares (best fit) estimates for B
in a linear model, where y = XB + E, where y is a vector of observed
dependent values, X is a matrix of independent values, and E is a random
variable (usually normal with mean=0 & variance = sigma^2).

For simple linear regression X is comprised of a column of 1's associated
with the intercept and the typical x values.

For multiple regression we simply add more column of x values.

For k-way fixed, mixed, and random effects ANOVA's X is comprised of sets of
dummy variables (0's & 1's) that correspond to the respective groups or
factor levels.

ANOVA is a methodology for splitting up the variation associated with a
linear model - some limit it to fixed, mixed, and random effects models, but
the more classic regression models most certainly can utilize ANOVA's.
Another thing to consider is that the classic ANOVA models (fixed, mixed, &
random effects) are typically over-parameterized. That is, you have to play
around with the X-matrix to make sure it is orthogonal. Minitab and (I
think) SAS make the last coefficient equal to the negative sum of the rest
of the coefficients. You could also just make the last coefficient equal to
zero.

They both involve linear models.


"George W. Cobb" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
>
> I, too, think of ANOVA and regression as variations on a common
> theme.  Here's an additional way in which they differ:  For balanced
> ANOVA, the decomposition of the data into sums of squares and degrees of
> freedom is determined by a group of symmetries.  For example, consider a
> one-way randomized complete block design with R rows as blocks and
> C columns as treatments.  The analysis is invariant under all row
> permutations, and all column permutations, i.e., interchanging any two
> rows of the data, or any two columns of the data, won't change the
> analysis.  If you now think of the data as a vector in RxC-dimensional
> space, the symmetries (row permutations, column permutations) determine
> invariant subspaces; these are precisely the subspaces you project the
> data vector onto to get the SSs and dfs.  In regression, the subspaces
> you project onto are determined directly by a spanning set of carrier
> variables; in balanced ANOVA, the subspaces are uniquely determined by the
> symmetries, and the spanning sets are somewhat arbitrary.  (I claim
> no credit for this lovely way of looking at things; I learned it from
> Peter Fortini  and Persi Diaconis.  It's written up in Fortini's
> dissertation from the 1970s, and Diaconis's IMS lecture notes on group
> theory and statistics.)
>
> Of course you only have such clean sets of symmetries for balanced
> designs, and the approach via symmetries doesn't address such things as
> the difference between fixed and random effects, which Bob
> Wheeler raises.  Nevertheless, to the extent that I think of ANOVA
> as distinct from regression, I find the role of symmetries worth
> keeping in mind.
>
>   George
>
> George W. Cobb
> Mount Holyoke College
> South Hadley, MA  01075
> 413-538-2401
>
>
>
>
> =
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Re: Regression vs ANOVA

[Elliot Cramer]

Alexander Tsyplakov <[EMAIL PROTECTED]> wrote:

: No, regression models can have stochastic and/or discrete
: regressors. I can only agree that regression models have

There are no constraints whatsoever on the x variables for the
significance tests and estimates to be valid.  Power is another matter.
Wheeler is right; both are special cases of the general linear model.



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Re: ANOVA : Repeated Measures?

[Paul R Swank]

Whether or not to use random effects should depend on whether you wish to generalize the results to some populations that the sample is (hopefully) representative of. Usually we wish to generalize to some population of subjects. Typically (but not neccesarily) we are not interested in generalizing to a population of treatments that our current treatments represent. The measure issue is also more commonly seen as fixed rather than random. I am assuming you have some interest in comparing measures to each other (assuming they are comparable) rather than  considering this design a multivariate one. The latter case would give rise to a fourth possibility of a two way multivariate anova rather than a three way univariate anova. In either case, I suspect you want subjects random and treatments fixed.


At 04:17 PM 2/9/01 GMT, you wrote:
>
>We have data from an experiment in psychology of hearing. There are 3
>experimental conditions (factor C). We have collected data from 5
>subjects (factor S). For each subject we get 4 measures of performance
>(M for Measure factor) in each condition. What is the best way to
>analyse these data?
>
>We've seen these possibilities :
>
>a)  ANOVA with repeated measures with 2 fixed factors : subjects &
>conditions  and the different measures as the repeated measure factor
>(random factor).
>
>b) ANOVA with two fixed factor (condition & measure) and a random
>factor (repeated measure-> subject factor).
>
>c) ANOVA with one fixed factor (condition) and the other two as
>random.
>
>We think that the a) design is correct (assuming and verifying that
>there is no special effect of the measure factor such as training
>effects).
>
>Other psychologist advised us to use the b) design because
>psychologists use to consider the subject effect as random. (in
>general experiments in psychology are ran with at least 20 to 30
>subjects).
>
>The last design (c)) is a possibility if we declare that we have no
>hypothesis on the effects of subject & repetition factors.
>
>
>I have only little theoretical background in stats and I like to know
>what exactly imply these possible designs.
>
>Thanks in advance for your help
>
>Sylvain Clement
>"Auditory function team"
>Bordeaux, France
>
>
>
>
>=
>Instructions for joining and leaving this list and remarks about
>the problem of INAPPROPRIATE MESSAGES are available at
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>

Paul R. Swank, PhD.
Professor & Advanced Quantitative Methodologist
UT-Houston School of Nursing
Center for Nursing Research
Phone (713)500-2031
Fax (713) 500-2033

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Re: ANOVA by items

[jim clark]

Hi

On Thu, 18 Oct 2001, Wouter Duyck wrote:
> Suppose i have a factorial design with two between-subject factors (one
> factor A of 3 levels and one factor B of 2 levels) en two within-subject
> factors (one factor C of 2 levels and one factor D of 5 levels). Of course,
> to perform an ANOVA on this data, my matrix should like :
> 
> Subj. ABC1D1C1D2 ...C1D5...C2D1...
> C2D5
> 111
> 222
> 331
> 
> Every cell is the number of correct responses (0 through 8) to a given task
> under certain conditions (factors C en D)
> 
> But if I want to do an ANOVA with items instead of subjects as a random
> factor, how should my data matrix look like? I am pretty sure i did it
> correct, but i would very much like to see that confirmed by anybody...

I assume by items you mean the 8 items that produced the scores
from 0 to 8.  The layout will depend on whether the same 8 items
were used in all of the conditions, or if some of your conditions
are between-item effects (e.g., concreteness, frequency).  If the
same 8 in all conditions, then you would have 8 cases with
3x2x2x5 = 60 scores for each.  Probably not a very powerful
analysis, which could be problematic if you were planning to
combine the subject and item analyses (e.g., Min F').  If not the
same 8 in all conditions, then you need to provide more
information about the design of the study.

Best wishes
Jim


James M. Clark  (204) 786-9757
Department of Psychology(204) 774-4134 Fax
University of Winnipeg  4L05D
Winnipeg, Manitoba  R3B 2E9 [EMAIL PROTECTED]
CANADA  http://www.uwinnipeg.ca/~clark




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Re: ANOVA by items

[Thom Baguley]

jim clark wrote:
> I assume by items you mean the 8 items that produced the scores
> from 0 to 8.  The layout will depend on whether the same 8 items
> were used in all of the conditions, or if some of your conditions
> are between-item effects (e.g., concreteness, frequency).  If the
> same 8 in all conditions, then you would have 8 cases with
> 3x2x2x5 = 60 scores for each.  Probably not a very powerful
> analysis, which could be problematic if you were planning to
> combine the subject and item analyses (e.g., Min F').  If not the
> same 8 in all conditions, then you need to provide more
> information about the design of the study.
> 
> Best wishes
> Jim

Depending on the design, minF' may not be necessary (or
appropriate). Take a look at

Raaijmakers, J. G. W., Schrijnemakers, J. M. C., & Gremmen, F.
(1999). How to deal with "The language-as fixed-effect fallacy":
Common misconceptions and solutions. Journal of Memory and Language,
41, 416-426.

Thom


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one-way ANOVA question

[Thomas Souers]

Hello, I have two questions regarding multiple comparison tests for a one-way ANOVA 
(fixed effects model).

1) Consider the "Protected LSD test," where we first use the F statistic to test the 
hypothesis of equality of factor level means. Here we have a type I error rate of 
alpha. If the global F test is significant, we then perform a series of t-tests 
(pairwise comparisons of factor level means), each at a type I error rate of alpha. 
This may seem like a stupid question, but how does this test preserve a type I error 
for the entire experiment? I understand that with a Bonferroni-type procedure, we can 
test each pairwise comparison at a certain rate, so that the overall type I error rate 
of the experiment will be at most a certain level. But with the Protected LSD test, I 
don't quite see how the comparisons are being protected. Could someone please explain 
to me the logic behind the LSD test?

2) Secondly, are contrasts used primarily as planned comparisons? If so, why? 

I would very much appreciate it if someone could take the time to explain this to me. 
Many thanks. 


Go Get It!
Send FREE Valentine eCards with Lycos Greetings
http://greetings.lycos.com


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Re: repeated measures ANOVA + SPSS

[Mike Wogan]

Ole,

  It sounds to me like Male/Female is your between-subjects factors.

  In the Unix version of SPSS, this runs under MANOVA.  But it sounds like
you've got the same thing running in Windows.

  I think you're right about the repeated measures (within subjects)
factor.

Mike

Re: repeated measures ANOVA + SPSS

[Leif Saager]

Hi, aber ich glaub ich antworte mal auf deutsch.

Mein Vorschlag zur Lösung deines Problems, so ich es richtig verstanden habe
würde so aussehen:

20 Patienten
1 Variable (Herzfrequenz, hf)
10 Meßzeitpunkte (m1-m10)

unter GLM mit Meßwiederholung als Innersubjektfaktor (is doch echt ein
klasse Name:) ) einen Namen
wie zB hf und als Anzahl der Stufen 10 angeben und "Hinzufügen".
In der folgenden Dialogbox als Innersubjektvariablen die m1 bis m10 für die
hf hinzufügen.

So könnte man einen weiteren Wert (RR sys ) und dessen Meßwiederholung auch
noch definieren.

Zwischensubjektfaktoren wären z.B. Alter oder Geschlecht, sofern für die
Fragestellung relevant.

Kovariaten wären bei Ausgangslagenunterschieden anzugeben.

soweit also alles wie Du vorgesehen hast, nun aber die schlechte Nachricht,
post-hoc Tests sind in SPSS nur für
Designs ohne Meßwiederholung implementiert. Bei Signifikanzen in dieser
Analyse bleibt nur der paired t-test.

Ich hoffe für die schnelle ist Dir geholfen.

Viele Grüße aus Lübeck
Leif


Ole Breithardt schrieb:

> Hi to all the experts,
> I measured a few Variable in let´s say 20 Patients under 10 different
> conditions, f.e.heart rate at 10 different exercise levels.
> 1.) To compare the results I understood that I have to use a repeated
> measures ANOVA, am I correct?
> 2.) If I want to use SPSS, where do I find that test? If I understood
> the Online-Help correctly then I should use "GLM-Messwiederholungen"
> (sorry for the German version, in English that would probably be
> something like "GLM-repeated Measures"??)
> 3.) Great! ? Here I have to define several things, that I do not really
> understand - o.k. let´s try: I give the "Innersubjectfactor" (that´s how
> it sounds in German") a name and tell SPSS how many repeated measures I
> performed.is that correct ?? 
> 4.) If I go on, on the next screen I have to define the different
> measurment/variables - however if I leave the two boxes below ("between
> subject factors" and "covariates") open, then SPSS won´t let me define
> any post-hoc-test , why not??? I understood that "between subject
> factors" has something to do with f.e. male and female ?? So, do I
> really have to define that or can I leave it open??
>
> Any comments or help is very appreciated!!!
> Thank you for your patience
> ;-)) Ole
>
> --
> 
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> Medizinische Klinik I - Kardiologie
> Klinikum der RWTH Aachen
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>
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> Fax.: +49-241-414 (Med. Klinik I)
>  +49-241-9890988 (priv)
>
> mailto:[EMAIL PROTECTED]

Re: Advice ANOVA t-test

[Donald F. Burrill]

On Mon, 24 Apr 2000, Timothy Graves wrote:

>  I could really use a little advice.
> I am preparing a research paper proposal for my  M. Ed. I am not 
> sure on a few issues:
> Is  ANOVA is a suitable form of t-test to determine if there is any
> significant differences between the means of three different subject
> groups on a Likert scale instrument?
> Am I off base here?  Any suggestions?

'Twould be nearer the mark to say that the t-test is the special case of 
ANOVA when there are only two groups.  Is ANOVA suitable for your 
situation?  Probably.  Some would dispute that, if by "a Likert scale 
instrument" you mean a single bipolar scale with Likert-like responses.  
If you mean an instrument comprising a bunch of items, each item being 
Likert scaled, and you are summing (or, equivalently, averaging) a 
subject's responses to all those items, hardly anyone would argue against 
using ANOVA.  The usual alternatives are less desirable for a variety of 
reasons, som eof which have recently been posted on the edstat list. 

>   I am also trying to decide upon what internal-consistency method is 
> suitable to use in determining the Reliability of a Likert scale
> instrument?  Kuder-Richardson approaches?  Alpha Coefficient?

Well, as some of my colleagues will cheerfully point out at the drop of a 
hat, "reliability" is not a characteristic of an instrument.  However you 
choose to measure it, it reflects the behavior of a particular group of 
persons who have responded to the instrument, and thus depends on (inter 
alia) the homogeneity of the responding population(s), the homogeneity of 
the items in the instrument, etc.  Do you have a compelling reason to 
obtain a reliability coefficient at all, or to settle on any particular 
one in your proposal?  (I suppose a compelling reason is that one or more 
of your committee members demands such a thing;  but I meant substantive 
or logical reasons.)  What do you think you'd do with such a thing, once 
you'd got it?
My general advice regarding proposals is not to promise more than 
you're sure you can deliver, not to commit yourself to any details that 
you can avoid, and not to belabor the obvious.  If your proposal entails 
some comparison among several groups, ANOVA or an ANOVA-like procedure is 
obviously going to be required;  you need not say so (unless you need 
more boiler plate than I would accept in a proposal!) in writing, and in 
oral questioning you need only indicate, rather off-handedly, that of 
course ANOVA is one obvious way to address such comparisons.  But it is 
entirely imaginable that you will have other variables lurking around, 
perhaps even explicitly measured, and that some more general linear model 
than ANOVA would be useful to apply -- a variant of multiple linear 
regression, for example, of which ANOVA is a particular family of 
subsets. 
Is that Likert scale instrument something of your own devising, 
or is it an extant device of some sort?  If it's original with you, your 
committee may well feel that some sort of instrument development phase 
might be desirable, or even necessary;  though I wouldn't usually expect 
that at the M.Ed. level.  If they do require you to do some of that, 
you'll need to know something about measurement in general, and should 
read up in some of the elementary texts in the area.  (And if they do 
require anything of the sort, ask them whether the instrument-development 
phase would suffice for your magistral research.  I've known that to be 
accepted in a Ph.D. proposal at OISE, when the area of proposed research 
really had no instruments to speak of, and the candidate was going to be 
spending a lot of time, energy, and theory on developing an instrument to 
measure what she needed to measure if she were ever going to carry out 
the research she had in mind in the first place.

> This is my first crack at this type of research, and any help in this
> regard would be greatly appreciated.

Hope this has helped some.
-- DFB.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  
 (Professor Emeritus, Department of MECA, OISE)


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Re: ANOVA, Robustness, and Power

[Donald Burrill]

On Thu, 22 Jun 2000, Alex Yu wrote (slightly edited):

> ANOVA is said to be robust against assumption violations when the 
> sample size is large.  However, when the sample size is huge, it tends 
> to overpower the test and thus the null may be falsely rejected.  
> Which is a lesser evil?  Your input will be greatly appreciated.

Hm.  Well, those who argue that the null hypothesis is always false 
anyway would doubtless consider that a proper outcome.  ;-)

Are you saying, in effect, that (under some conditions) the precision of 
the data exceeds the precision with which the null hypothesis is stated 
(or intended to be stated)?  Then at the outset you should devote some 
attention to the precision you want to associate with the null, and 
acknowledge that the current data have excessive power against the MUD 
(minimum useful departure from the null);  it follows that you are only 
going to be interested in rejections of the null hypothesis for which 
the effect size exceeds the MUD, and possibly even significantly exceeds 
it.  (You may want to direct a comment or two in the direction of 
readers whose notion of MUD is smaller than yours.)
-- DFB.
 
 Donald F. Burrill [EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 603-535-2597
 184 Nashua Road, Bedford, NH 03110  603-471-7128  



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ANOVA question on transformed variable

[Beng Hai Chea]

Hi all,

I have a very basic ANOVA question regarding transformed variable.

Example: I have 6 different types of habitats and I have obtained 25 
readings from each of the different type of habitats. After doing the ANOVA 
procedure, I discovered that non-constant error variance is present.

Thus, I would need to transform the readings with natural log to be able to 
use the ANOVA procedure.

Question: After transformation, does any of the hypothesis regarding the 
original variable still holds, using the latest ANOVA procedure?

If it still holds, may I know what is the rationale?

If it does not hold, why then bother on transforming the readings variable 
in the first place?

I hope some "enlighten" ones who are on this mailing list can shed some 
light on this issue.

Thanks in advance!
Beng Hai
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Re: Three Factor ANOVA Help

[Donald Burrill]

On Fri, 29 Sep 2000, Luís Silva wrote:

> For a certain variable I applied a Three Factor ANOVA and found a
> significant interaction between two factors. 

Was this the only significant effect, or were there others? 
Actually, it would be easier to address your question usefully if 
you'd supply the eight means (and the ANOVA summary table).

> I have two levels for each factor.  Then, I applied the HSD Tukey test 
> for multiple unplanned comparisons, in order to detect what are the 
> significantly different treatments.

OK so far, although "I applied the HSD Tukey test" is not very 
informative.  (One cannot tell whether you applied it correctly, for 
example, let alone completely.)

> Since I detected an interaction between two factors, is it correct to 
> apply Tukey test? 

Sure.  Why wouldn't it be?  If the three factors are all fixed, there 
isn't even any quibble to be made about what the proper error mean square 
is for the test.

> If not, are there other type of unplanned comparisons that might be 
> used? 

The Scheffe' method comes to mind.  For pairwise comparisons, Tukey's 
method is said to yield narrower confidence intervals;  for more complex 
contrasts, Scheffe' intervals are narrower.  (All other post hoc 
comparison methods that I know of either are designed explicitly for 
pairwise comparisons, or are customarily applied only to pairwise 
comparisons (as is the case with Tukey's method).  Pairwise comparisons, 
in my experience, are often too simple-minded to convey a decently clear 
picture of what's going on in the data.) 
 When you're dealing with an interaction, particularly in a 2**k 
design, it may well be parsimonious to analyze the pattern of means in a 
series of complex, preferably orthogonal, contrasts, rather than in terms 
of the stereotypical main effects and interactions.  Can't tell without 
seeing the results. 
-- DFB.
 --
 Donald F. Burrill[EMAIL PROTECTED]
 348 Hyde Hall, Plymouth State College,  [EMAIL PROTECTED]
 MSC #29, Plymouth, NH 03264 (603) 535-2597
 Department of Mathematics, Boston University[EMAIL PROTECTED]
 111 Cummington Street, room 261, Boston, MA 02215   (617) 353-5288
 184 Nashua Road, Bedford, NH 03110  (603) 471-7128



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Re: Three Factor ANOVA Help

[jim clark]

Hi

> On Fri, 29 Sep 2000, Lu=EDs Silva wrote:
> > For a certain variable I applied a Three Factor ANOVA and found a
> > significant interaction between two factors.=20
> > I have two levels for each factor.  Then, I applied the HSD Tukey test=
=20
> > for multiple unplanned comparisons, in order to detect what are the=20
> > significantly different treatments.

Given an interaction, the comparisons that generally are of most
interest are the simple effects; that is, the effects of one
factor at each level of the other.  With four conditions defined
by two levels each of A and B, one would have A1B1, A1B2, A2B1,
and A2B2.  The possible simple effects are A1B1 vs A1B2 and A2B1
vs A2B2  OR  A1B1 vs A2B1 and A1B2 vs A2B2.  Normally you would
choose one of these two sets (i.e., simple effects of B within A1
and A2 or simple effects of A within B1 and B2).

You probably have some flexibility as to whether you use some
correction (e.g., Tukey's), depending on whether the pattern was
expected, how strong the different simple effects are, and so on. =20
One "ideal" outcome is for one simple effect (e.g., A1 vs A2 at
B1) to be not at all significant (no matter how liberal the
test), and the other to be clearly significant (e.g., A1 vs A2 at
B2) (no matter how conservative the test).

Best wishes
Jim

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D
James M. Clark=09=09=09=09(204) 786-9757
Department of Psychology=09=09(204) 774-4134 Fax
University of Winnipeg=09=09=094L05D
Winnipeg, Manitoba  R3B [EMAIL PROTECTED]
CANADA=09=09=09=09=09http://www.uwinnipeg.ca/~clark
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D



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ANOVA with dichotomous dependent variable

[Gerhard Luecke]

Can anyone name some references where the problem of using a DICHOTOMOUS
variable as a DEPENDENT variable in an ANOVA is discussed?

Many thanks in advance,
Gerhard Luecke


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ANOVA with dichotomous dependent variable

[Gerhard Luecke]

Can anyone name some references where the problem of using a DICHOTOMOUS
variable as a DEPENDENT variable in an ANOVA is discussed?

Many thanks in advance,
Gerhard Luecke


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Re: one-way ANOVA question

[David C. Howell]

You have to keep in mind that the LSD is concerned with familywise error
rate, which is the probability that you will make at least one
type I error in your set of conclusions. For the familywise error rate, 3
errors are no worse than 1.
Suppose that you have three groups. If the omnibus null is true, the
probability of erroneously rejecting the null with the overall Anova is
equal to alpha, which I'll assume you set at .05. IF you reject the null,
you have already made one type I error, so the chances of making more do
not matter to the familywise error rate. Your Type I error rate is
.05.
Now suppose that the null is false-- mu(1) = mu(2) /= mu(3). Then it is
not possible to make a Type I error in the overall F, because the omnibus
null is false. There is one chance of making a Type I error in testing
individual means, because you could erroneously declare mu(1) /= mu(2).
But since the other nulls are false, you can't make an error there. So
again, your familywise probability of a Type I error is .05.
Now assume 4 means. Here you have a problem. It is possible that mu(1) =
mu(2) /= mu(3) = mu(4). You can't make a Type I error on the omnibus
test, because that null is false. But you will be allowed to test mu(1) =
mu(2), and to test mu(3) = mu(4), and each of those is true. So you have
2 opportunities to make a Type I error, giving you a familywise rate of
2*.05 = .10.
So with 2 or 3 means, the max. familywise error rate is .05. With 4 or 5
means it is .10, with 6 or 7 means it is .15, etc.
But keep in mind that, at least in psychology, the vast majority of
experiments have no more than 5 means, and many have only 3. In that
case, the effective max error rate for the LSD is .10 or .05, depending
on the number of means. Other the other hand, if you have many means, the
situation truly gets out of hand.
Dave Howell
At 10:37 AM 2/8/2002 -0800, you wrote:
Hello, I have two questions
regarding multiple comparison tests for a one-way ANOVA (fixed effects
model).
1) Consider the "Protected LSD test," where we first use the F
statistic to test the hypothesis of equality of factor level means. Here
we have a type I error rate of alpha. If the global F test is
significant, we then perform a series of t-tests (pairwise comparisons of
factor level means), each at a type I error rate of alpha. This may seem
like a stupid question, but how does this test preserve a type I error
for the entire experiment? I understand that with a Bonferroni-type
procedure, we can test each pairwise comparison at a certain rate, so
that the overall type I error rate of the experiment will be at most a
certain level. But with the Protected LSD test, I don't quite see how the
comparisons are being protected. Could someone please explain to me the
logic behind the LSD test?
2) Secondly, are contrasts used primarily as planned comparisons? If so,
why? 
I would very much appreciate it if someone could take the time to explain
this to me. Many thanks. 

Go Get It!
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**
David C. Howell
Phone:
(802) 656-2670
Dept of Psychology  
   Fax:  
(802) 656-8783
University of Vermont
  email:
[EMAIL PROTECTED]
Burlington, VT 05405 

http://www.uvm.edu/~dhowell/StatPages/StatHomePage.html
http://www.uvm.edu/~dhowell/gradstat/index.html

Re: one-way ANOVA question

[Dennis Roberts]

At 10:37 AM 2/8/02 -0800, Thomas Souers wrote:

>2) Secondly, are contrasts used primarily as planned comparisons? If so, why?

well, in the typical rather complex study ... all pairs of possible mean 
differences (as one example) are NOT equally important to the testing of 
your theory or notions

so, why not set up ahead of time ... THOSE that are (not necessarily 
restricted to pairs) you then follow ... let the other ones alone

no law says that if you had a 3 by 4 by 3 design, that the 3 * 4 * 3 = 36 
means all need pairs testing ... in fact, come combinations may not even 
make a whole lot of sense EVEN if it is easier to work them into your design


>I would very much appreciate it if someone could take the time to explain 
>this to me. Many thanks.
>
>
>Go Get It!
>Send FREE Valentine eCards with Lycos Greetings
>http://greetings.lycos.com
>
>
>=
>Instructions for joining and leaving this list, remarks about the
>problem of INAPPROPRIATE MESSAGES, and archives are available at
>   http://jse.stat.ncsu.edu/
>=

Dennis Roberts, 208 Cedar Bldg., University Park PA 16802

WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm
AC 8148632401



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Re: one-way ANOVA question

[jim clark]

Hi

On 8 Feb 2002, Thomas Souers wrote:

> 2) Secondly, are contrasts used primarily as planned
> comparisons? If so, why?

There are a great many possible contrasts even with a relatively
small number of means.  If you examine the data and then decide
what contrasts to do, then you have in some informal sense
performed a much larger set of contrasts than you actually
formally test.  Specifying the contrasts in advance means that
you have only performed the number of statistical tests actually
calculated.

Another (related) way to think of it is that planned contrasts
take advantage of pre-existing theory and data to perform tests
that favor certain outcomes.  To do this, however, contrasts must
be specified independently of the data (i.e., planned).  Perhaps
could be thought of as some kind of quasi-bayesian thinking?  
That is, given a priori factors favoring certain outcomes, the
actual data does not need to be as strong to tilt the results in
that direction.

Best wishes
Jim


James M. Clark  (204) 786-9757
Department of Psychology(204) 774-4134 Fax
University of Winnipeg  4L05D
Winnipeg, Manitoba  R3B 2E9 [EMAIL PROTECTED]
CANADA  http://www.uwinnipeg.ca/~clark




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Re: one-way ANOVA question

[Mike Granaas]

On Fri, 8 Feb 2002, Thomas Souers wrote:
> 
> 2) Secondly, are contrasts used primarily as planned comparisons? If so, why? 
> 

I would second those who've already indicated that planned comparisons are
superior in answering theoretical questions and add a couple of comments:

1) an omnibus test followed by pairwise comparisons cannot clearly answer
theoretical questions involving more than two groups.  Trend analysis is
one example where planned comparisons can give a relatively unambigious
answer (is there a linear, quadratic, etc trend?) where pairwise tests
leave the research trying to interpret the substantive meaning of a
particular pattern of pairwise differences.  

2) planned comparisons require that the researcher think through the
theoretical implications of their research efforts prior to collecting
data.  It is too common for folks to gather some data appropriate for an
ANOVA, without thinking through the theoretical implications of
their possible results, analyze it with an omnibus test (Ho: all the means
the same) and rely on post-hoc pairwise comparisons to understand the
theoretical meaning of their findings.  In a multi-group design if you
cannot think of at least one meaningful contrast code prior to collecting
the data, you haven't really thought through your research.

3) your power is better.  It is well known that when you toss multiple
potential predictors into a multiple regression equation you run the risk
of "washing out" the effect of a single good predictor by combining it
with one or more bad predictors.  ANOVA is a special case of multiple
regression where each df in the between subjects line represents a
predictor (contrast code).  By combining two or more contrast codes into a
single omnibus test you reduce your ability to detect meaningful
differences amongst the collection of non-differences.

Hope this helps.

Michael

***
Michael M. Granaas
Associate Professor[EMAIL PROTECTED]
Department of Psychology
University of South Dakota Phone: (605) 677-5295
Vermillion, SD  57069  FAX:   (605) 677-6604
***
All views expressed are those of the author and do not necessarily
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Re: one-way ANOVA question

[Jerry Dallal]

Thomas Souers wrote:
> 
> Hello, I have two questions regarding multiple comparison tests for a one-way ANOVA 
>(fixed effects model).
> 
> 1) Consider the "Protected LSD test," where we first use the F statistic to test the 
>hypothesis of equality of factor level means. Here we have a type I error rate of 
>alpha. If the global F test is significant, we then perform a series of t-tests 
>(pairwise comparisons of factor level means), each at a type I error rate of alpha. 
>This may seem like a stupid question, but how does this test preserve a type I error 
>for the entire experiment? 

As you (nearly) say, "[Only i]f the global F test is significant, we
then perform a series of t-tests "

> 
> 2) Secondly, are contrasts used primarily as planned comparisons? If so, why?

It depends on the research question.


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Re: one-way ANOVA question

[Dennis Roberts]

At 09:21 AM 2/13/02 -0600, Mike Granaas wrote:
>On Fri, 8 Feb 2002, Thomas Souers wrote:
> >
> > 2) Secondly, are contrasts used primarily as planned comparisons? If 
> so, why?
> >
>
>I would second those who've already indicated that planned comparisons are
>superior in answering theoretical questions and add a couple of comments:

another way to think about this issue is: what IF we never had ... nor will 
in the future ... the overall omnibus F test?

would this help us or hurt us in the exploration of the 
experimental/research questions of primary interest?

i really don't see ANY case that it would hurt us ...

and, i can't really think of cases where doing the overall F test helps us ...

i think mike's point about planning comparisons making us THINK about what 
is important to explore in a given study ... is really important because, 
we have gotten lazy when it comes to this ... we take the easy way out of 
testing all possible paired comparisons when, it MIGHT be that NONE of 
these are really the crucial things to be examined




Dennis Roberts, 208 Cedar Bldg., University Park PA 16802

WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm
AC 8148632401



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Re: one-way ANOVA question

[Rich Ulrich]

On 13 Feb 2002 09:48:41 -0800, [EMAIL PROTECTED] (Dennis Roberts) wrote:

> At 09:21 AM 2/13/02 -0600, Mike Granaas wrote:
> >On Fri, 8 Feb 2002, Thomas Souers wrote:
> > >
> > > 2) Secondly, are contrasts used primarily as planned comparisons? If 
> > so, why?
> > >
> >
> >I would second those who've already indicated that planned comparisons are
> >superior in answering theoretical questions and add a couple of comments:
> 
> another way to think about this issue is: what IF we never had ... nor will 
> in the future ... the overall omnibus F test?
> 
> would this help us or hurt us in the exploration of the 
> experimental/research questions of primary interest?

 - not having it available, even abstractly, 
would HURT, because we would be 
without that reminder of  'too many hypotheses'.

In practice, I *do*  consider the number of tests.
Just about always.

Now, I am not arguing that the particular form 
of having an ANOVA omnibus-test  is essential.
Bonferroni correction can do a lot of the same. It just
won't always be as efficient.

> i really don't see ANY case that it would hurt us ...
> and, i can't really think of cases where doing the overall F test helps us ...
> 

But, Dennis, I thought you told us before, 
you don't appreciate  "hypothesis testing" ...
I thought you could not think of cases where doing
*any*  F-test helps us.

[ ... ]

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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Tukey test in two way ANOVA

[Stefan Uhlig]

Hi,

Suppose that you have a two-way ANOVA design where each of the two
factors has three or more levels.In the two way ANOVA there are no
interactions, so we want to test within each of the two factors which
level differs from the others. According to textbooks, this might be
done by a Tukey test first on level A and then on level B. However, is
the alpha-error still garuanteed if we perform two Tukey Tests on the
same data set ?

Thanks Stefan



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C code for Multiple Regression, ANOVA?

[Paul Thompson]

Hi everyone,

Does anyone know if there are any C code functions or libraries
available
(preferably free/on the Web) for doing multiple regression or
multivariate analysis of covariance (MANCOVA)?

I have often used Numerical Recipes in C, where there are some
very useful functions for doing t-tests, calculating Z-statistics
or F-statistics, and correlation coefficients (from data samples
represented
as floating point arrays). The functions return correlation values,
p-values,
etc. I have found these quite useful in building image analysis code,
and wondered if there are more general libraries available freely (in
C).
I am thinking specifically of functions that would do multiple
regression,
ANOVA, etc. and return the appropriate R-squared or F statistics, as
well
as associated p-values.

Of course all these tests could be performed in statistics packages or
more
general toolkits such as MATLAB, but basically I am just looking for
libraries
of C functions.

Any help is greatly appreciated - thanks in advance! - Paul
--
Paul Thompson, Ph.D.
Assistant Professor of Neurology, Dept. Neurology
UCLA Lab of Neuro-Imaging & Brain Mapping Division
Howard Hughes Medical Institute
73-360 Brain Research Institute
CHS-UCLA, Los Angeles, CA 90095-1769
[EMAIL PROTECTED]
http://www.loni.ucla.edu/~thompson/thompson.html
http://www.loni.ucla.edu/~thompson/thompson_pubs.html


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Re: ANOVA question on transformed variable

[Rich Ulrich]

On 24 Sep 2000 23:30:57 -0700, [EMAIL PROTECTED] (Beng Hai Chea)
wrote:

> I have a very basic ANOVA question regarding transformed variable.
> 
> Example: I have 6 different types of habitats and I have obtained 25 
> readings from each of the different type of habitats. After doing the ANOVA 
> procedure, I discovered that non-constant error variance is present.
> 
> Thus, I would need to transform the readings with natural log to be able to 
> use the ANOVA procedure.

 - Well, "need to transform"  is your conclusion, from some sort of
evidence.  Directly, the conclusion is that the test is not efficient
since the error is not i.i.d.  (identical and independently
distributed).  This also hints that the additive ANOVA model is not
adequate.

> 
> Question: After transformation, does any of the hypothesis regarding the 
> original variable still holds, using the latest ANOVA procedure?
> 
> If it still holds, may I know what is the rationale?
> 
If there is no difference between groups, there's no difference.

How different is it, to test the (a)  in   y=ax+b   or   log(y)= ax+b?

Well, how much does it distort the scaling of y, to take the log? -
that is how much the one test is a distortion of the other test.


> If it does not hold, why then bother on transforming the readings variable 
> in the first place?

 - Hey, that was your idea  presumably, to get a 'better test'.

This happens when a transformation "fixes the ANOVA" but 
is hard to justify in simple, logical terms:   we are faced with 
a good test of a somewhat-wrong hypothesis, or an inferior
test of the right hypothesis.

You have to listen to arguments for both sides.  But you won't settle
it until you learn (maybe) that one test works better in the long run,
for similar instances, and consistent with larger samples.
-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html


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Re: ANOVA question on transformed variable

[Beng Hai Chea]

> > I have a very basic ANOVA question regarding transformed variable.
> >
> > Example: I have 6 different types of habitats and I have obtained 25
> > readings from each of the different type of habitats. After doing the 
>ANOVA
> > procedure, I discovered that non-constant error variance is present.
> >
> > Thus, I would need to transform the readings with natural log to be able 
>to
> > use the ANOVA procedure.
>
>  - Well, "need to transform"  is your conclusion, from some sort of
>evidence.  Directly, the conclusion is that the test is not efficient
>since the error is not i.i.d.  (identical and independently
>distributed).  This also hints that the additive ANOVA model is not
>adequate.

Yes, you are right. The additive ANOVA model is not adequate since the 
residual vs. fitted plot is not showing normality and the error variance is 
non-constant. After the log transformation, the residual plots and error 
variance are OK. I guess I just followed the guideline on what steps to take 
if the data does not meet the ANOVA model adequacy checks. This is mentioned 
in almost all the books I read but, none mentioned about the hypothesis 
validity at all. That's why this question came about.

> >
> > Question: After transformation, does any of the hypothesis regarding the
> > original variable still holds, using the latest ANOVA procedure?
> >
> > If it still holds, may I know what is the rationale?
> >
>If there is no difference between groups, there's no difference.
>
>How different is it, to test the (a)  in   y=ax+b   or   log(y)= ax+b?
>
>Well, how much does it distort the scaling of y, to take the log? -
>that is how much the one test is a distortion of the other test.
>
>
> > If it does not hold, why then bother on transforming the readings 
>variable
> > in the first place?
>
>  - Hey, that was your idea  presumably, to get a 'better test'.
>
>This happens when a transformation "fixes the ANOVA" but
>is hard to justify in simple, logical terms:   we are faced with
>a good test of a somewhat-wrong hypothesis, or an inferior
>test of the right hypothesis.
>
>You have to listen to arguments for both sides.  But you won't settle
>it until you learn (maybe) that one test works better in the long run,
>for similar instances, and consistent with larger samples.

Yes, would like to hear from both sides of the argument based on practical 
experience. Any one out there had similar situation/problem?

Regards,
Beng Hai
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2 factor ANOVA with empty cells

[Jeff E. Houlahan]

Is it ever appropriate to do a 2-factor unreplicated ANOVA with 
empty cells if you aren't sure there is no interaction between the 
factors?  If so, when and if not, are there any reasonable 
alternatives?  Thanks.

Jeff Houlahan


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Re: ANOVA with dichotomous dependent variable

[Paul Thompson]

Gerhard Luecke wrote:

> Can anyone name some references where the problem of using a DICHOTOMOUS
> variable as a DEPENDENT variable in an ANOVA is discussed?
>
> Many thanks in advance,
> Gerhard Luecke

Such analyses may be done using either logistic regression methods or
generalized estimating equation methods.  In SAS, this is LOGISTIC and
GENMOD




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