How are fixed factors interpreted in ANCOVA?

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nocturnal elephant

Posted: Tue Apr 08, 2008 2:21 pm

Guest

Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4
0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Ray Koopman

Posted: Tue Apr 08, 2008 8:18 pm

Guest

On Apr 8, 5:21 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:

Quote:

Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4 0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Why is Teacher treated as a fixed factor, and why does the analysis
omit Treatment, Teacher, and Gender interactions? In research like
this, Teacher is usually treated as a random factor, to enable
generalizing the results beyond the particular teachers in the study,
and the error terms for testing the fixed effects would be their
interactions with Teacher. (Yes, that means the error terms would have
only 4 df -- this is a terrible research design!)

Richard Ulrich

Posted: Tue Apr 08, 2008 9:17 pm

Guest

[cross-posted to sci.stat.consult, where the same
question was posted, in two parts. NOTE: Please
"cross-post" with two Newsgroups in the heading
instead of posting separately.]

On Tue, 8 Apr 2008 17:21:13 -0700 (PDT), nocturnal elephant
<berto.riddles@gmail.com> wrote:

Quote:

You can state, "after controlling for..." if that is what
the analysis did.

However, the listing above has a heading, "Seq SS"
which I have to read as indicating "sequential Sum of
squares" -- That is the option that says, each Effect is
evaluated while controlling *only* for the ones that
are listed before it. That can be a very sensible option
when you use it intentionally to define logical ordering.
That is not the case, above.

Using Sequential SS, "Pre_Raw" is logically the first entry,
and Treatment (assuming it is the main hypothesis)
should be the last one.

This may serve as an example of why it helps to have
an actual statistician involved with your data analyses,
when you want to do analyses properly.

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html

nocturnal elephant

Posted: Tue Apr 15, 2008 4:01 pm

Guest

On Apr 9, 4:18 pm, Ray Koopman <koop...@sfu.ca> wrote:

Quote:

On Apr 8, 5:21 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:

Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4 0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Why is Teacher treated as a fixed factor, and why does the analysis
omit Treatment, Teacher, and Gender interactions? In research like
this, Teacher is usually treated as a random factor, to enable
generalizing the results beyond the particular teachers in the study,
and the error terms for testing the fixed effects would be their
interactions with Teacher. (Yes, that means the error terms would have
only 4 df -- this is a terrible research design!)- Hide quoted text -

- Show quoted text -

Teacher is fixed because each of the teachers is assigned to teach
both the control and experimental classes.

Ray Koopman

Posted: Tue Apr 15, 2008 8:23 pm

Guest

On Apr 15, 7:01 pm, nocturnal elephant <berto.ridd...@gmail.com>
wrote:

Quote:

On Apr 9, 4:18 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 8, 5:21 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:
Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4 0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Why is Teacher treated as a fixed factor, and why does the analysis
omit Treatment, Teacher, and Gender interactions? In research like
this, Teacher is usually treated as a random factor, to enable
generalizing the results beyond the particular teachers in the study,
and the error terms for testing the fixed effects would be their
interactions with Teacher. (Yes, that means the error terms would have
only 4 df -- this is a terrible research design!)

Teacher is fixed because each of the teachers is assigned to teach
both the control and experimental classes.

That means only that Teacher and Treatment are crossed. It does not
imply that Teacher is fixed. Treating Teacher as a fixed factor means
that the conclusions apply to only the five teachers in the study.
To generalize to other teachers, Teacher must be treated as a random
factor.

nocturnal elephant

Posted: Tue Apr 15, 2008 11:31 pm

Guest

On Apr 16, 4:23 pm, Ray Koopman <koop...@sfu.ca> wrote:

Quote:

On Apr 15, 7:01 pm, nocturnal elephant <berto.ridd...@gmail.com
wrote:

On Apr 9, 4:18 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 8, 5:21 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:
Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4 0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Why is Teacher treated as a fixed factor, and why does the analysis
omit Treatment, Teacher, and Gender interactions? In research like
this, Teacher is usually treated as a random factor, to enable
generalizing the results beyond the particular teachers in the study,
and the error terms for testing the fixed effects would be their
interactions with Teacher. (Yes, that means the error terms would have
only 4 df -- this is a terrible research design!)

Teacher is fixed because each of the teachers is assigned to teach
both the control and experimental classes.

That means only that Teacher and Treatment are crossed. It does not
imply that Teacher is fixed. Treating Teacher as a fixed factor means
that the conclusions apply to only the five teachers in the study.
To generalize to other teachers, Teacher must be treated as a random
factor.- Hide quoted text -

- Show quoted text -

thanks for the input. gretly appreciate it.

nocturnal elephant

Posted: Tue Apr 15, 2008 11:36 pm

Guest

On Apr 16, 4:23 pm, Ray Koopman <koop...@sfu.ca> wrote:

Quote:

By the way, Ulrich mentioned about sequential ss. Does that mean
treatment--if it is my most important factor--should come after
gender? and for covariates, pretest should come after all other
covariates considered in this prepost test design? or does the
ordering really matter?

Ray Koopman

Posted: Wed Apr 16, 2008 8:23 am

Guest

On Apr 16, 2:36 am, nocturnal elephant <berto.ridd...@gmail.com>
wrote:

Quote:

On Apr 16, 4:23 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 15, 7:01 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:
On Apr 9, 4:18 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 8, 5:21 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:
Hello,

I am no expert in statistics, and am in dire need of help in
interpreting how fixed factors are interpreteed in ANCOVA. Below is
that statistical summary. I have covariates and fixed factors
included. Typically, from how I understand, when interpreting ANCOVA
one usually states the findings as "after controlling for the impact/
effect of covariates, the treatment effect showed significant
difference between blah, blah...". I wonder if the same phrasing is
used for fixed factors?

Aprreciating any expert opinion here.

Cheers,

Factor Type Levels Values
Treatment fixed 2 0, 1
Teacher fixed 5 1, 2, 3, 4, 5
Gender fixed 2 F, M

Analysis of Variance for Post_Raw, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Treatment 1 74.0 213.3 213.3 4.79 0.029
Teacher 4 1352.6 878.5 219.6 4.93 0.001
Gender 1 533.0 869.5 869.5 19.51 0.000
Pre_Raw 1 10815.8 3220.6 3220.6 72.26 0.000
IQ 1 649.2 1.4 1.4 0.03 0.858
MATH_SS 1 3545.2 2806.7 2806.7 62.97 0.000
ENGLISH_SS 1 191.0 191.0 191.0 4.28 0.039
Error 297 13237.0 13237.0 44.6
Total 307 30397.9

Why is Teacher treated as a fixed factor, and why does the analysis
omit Treatment, Teacher, and Gender interactions? In research like
this, Teacher is usually treated as a random factor, to enable
generalizing the results beyond the particular teachers in the study,
and the error terms for testing the fixed effects would be their
interactions with Teacher. (Yes, that means the error terms would have
only 4 df -- this is a terrible research design!)

Teacher is fixed because each of the teachers is assigned to teach
both the control and experimental classes.

That means only that Teacher and Treatment are crossed. It does not
imply that Teacher is fixed. Treating Teacher as a fixed factor means
that the conclusions apply to only the five teachers in the study.
To generalize to other teachers, Teacher must be treated as a random
factor.

By the way, Ulrich mentioned about sequential ss. Does that mean
treatment--if it is my most important factor--should come after
gender? and for covariates, pretest should come after all other
covariates considered in this prepost test design? or does the
ordering really matter?

As Rich said, the "Seq SS" values are not relevant to your problem,
because you want each source adjusted for all the others. That is,
you want each source to be last in the sequence, which is exactly
what the "Adj SS" values give you.

Richard Ulrich

Posted: Wed Apr 16, 2008 8:20 pm

Guest

On Wed, 16 Apr 2008 11:23:21 -0700 (PDT), Ray Koopman <koopman@sfu.ca>
wrote:

Quote:

On Apr 16, 2:36 am, nocturnal elephant <berto.ridd...@gmail.com
wrote:
On Apr 16, 4:23 pm, Ray Koopman <koop...@sfu.ca> wrote:
On Apr 15, 7:01 pm, nocturnal elephant <berto.ridd...@gmail.com> wrote:
On Apr 9, 4:18 pm, Ray Koopman <koop...@sfu.ca> wrote:
[snip, previous]

By the way, Ulrich mentioned about sequential ss. Does that mean
treatment--if it is my most important factor--should come after
gender? and for covariates, pretest should come after all other
covariates considered in this prepost test design? or does the
ordering really matter?

As Rich said, the "Seq SS" values are not relevant to your problem,
because you want each source adjusted for all the others. That is,
you want each source to be last in the sequence, which is exactly
what the "Adj SS" values give you.

My apologies for the red herring - I missed the detail
that "Adj SS" is what was used for the analysis.

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html

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