---- DENNIS ROBERTS WRITES -----
----- Original Message -----
From: dennis roberts <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, December 05, 1999 7:24 AM
Subject: ancova
| some time ago, i sent out a note about a handout i had re: ancova. now, in
| that handout, i illustrated a very simple case of how ancova might account
| for some of the within groups 'error'. in that handout, i showed, near the
| end ... some minitab output for the analysis. now, in that output ... the
| adjusted SS adds up to MORE than what the simple anova adds too. NOTE: the
| dependent measure in the Exp and Cont group example was performance on a
| test .. and the covariate was IQ.
|
| the one way shows:
|
| One-way Analysis of Variance
|
| Analysis of Variance
| Source DF SS MS F P
| Factor 1 252 252 1.54 0.231
| Error 18 2949 164
| Total 19 3201
|
| and the ancova shows:
|
| Analysis of Variance for TOTY, using Adjusted SS for Tests
|
| Source DF Seq SS Adj SS Adj MS F P
| TOTIQ 1 1539.9 2057.9 2057.9 39.26 0.000
| Group 1 770.0 770.0 770.0 14.69 0.001
| Error 17 891.0 891.0 52.4
| Total 19 3200.9
|
| in the handout, i showed that the adjusted SS(TOT) equals the sum of the
| 770 and 891 values for Group and Error in the Adj SS columns ... but where
| does the 2057 come from and, when you add to the 770 and 891 values .. you
| get a much larger value than the original 3201?
|
| what would be the simplest way to discuss this with students? in what way
| could you use the original data on the dependent measure ... and show how
| this new SS(TOT) value could be obtained?
|
| thanks
| ----------------------------------------------
| 208 Cedar Bldg., University Park, PA 16802
| AC 814-863-2401 Email mailto:[EMAIL PROTECTED]
| WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm
| FAX: AC 814-863-1002
---- JOE WARD COMMENTS -------
Hi, Dennis --
You probably can predict my comments!!
It is very difficult to try to explain the computer outputs
without knowing (or guessing) what hypotheses are being "tested".
A continuing situation that is observed on various Email lists
involves interpretations of computer outputs without
concern for understanding what questions are being "answered" by
the computer package. In some situations -- particularly the "case
of the missing cell" -- the answers might be for "uninteresting questiong".
The communications provided by the internet continue to reveal the short-comings of
statistics education.
Until we change our statistics education these problems will not go away.
Without going into details of exactly how to proceed your
students should:
1. State their hypotheses of interest in "natural language".
2. Create an ASSUMED MODEL that allows them to express their
"natural language" hypotheses in terms of parameters in their
ASSUMED MODEL.
3. Impose the restrictions on the ASSUMED MODEL to obtain a
RESTRICTED MODEL.
4. Compare the Error Sum of Squares from the ASSUMED MODEL with
the Error Sum of Squares from the RESTRICTED MODEL using an
F statistic.
In the 1960's, when we presented short courses on
Prediction/Regression/Linear Models at the American
Educational Research Association (AERA) it was indeed rare
to find anyone who knew the meaning of the MAIN EFFECTS HYPOTHESES
(ROW and COLUMN MAIN EFFECTS) in a TWO-FACTOR ANOVA. Of course,
everyone knows it these days --I hope.
After your students have become acquainted with the
PREDICTION/REGRESSION/LINEAR MODELS approach, then it is fun
to ask them to do some DETECTIVE WORK to indicate the hypotheses
that are being tested in the computer output that you show in your
example -- and for more complicated computer outputs.
The "homework" or "exam" assignment might be as follows":
Indicate the hypotheses that are being "tested" in the computer
outputs shown below.
1.Explain in as much detail as you can, including
a "natural language" statement and/or in terms of ASSUMED and
RESTRICTED MODELS.
2. How do you use the ANCOVA output to test for (NO)INTERACTION between
IQ and GROUP? Is it possible? If not, why not?
3. Create a model that will allow you to test for (NO) INTERACTION
between IQ and GROUP. Impose the restrictions needed to test for
(NO)INTERACTION. Compare your ASSUMED MODEL with your RESTRICTED MODEL.
Incidentally, talented high school students SHOULD be able to handle this
if they are given the opportunity!
| One-way Analysis of Variance
|
| Analysis of Variance
| Source DF SS MS F P
| Factor 1 252 252 1.54 0.231 (EXPLAIN THIS HYPOTHESIS)
| Error 18 2949 164
| Total 19 3201
|
| and the ancova shows:
|
| Analysis of Variance for TOTY, using Adjusted SS for Tests
|
| Source DF Seq SS Adj SS Adj MS F P
| TOTIQ 1 1539.9 2057.9 2057.9 39.26 0.000 (EXPLAIN THIS
|HYPOTHESIS)
| Group 1 770.0 770.0 770.0 14.69 0.001 (EXPLAIN THIS
|HYPOTHESIS)
| Error 17 891.0 891.0 52.4
| Total 19 3200.9
|
Your students might appreciate your 'GIVING THEM THE POWER THEY DESERVE"!
:-)
--Joe
*************************************************************
Joe Ward Health Careers High School
167 East Arrowhead Dr 4646 Hamilton Wolfe
San Antonio, TX 78228-2402 San Antonio, TX 78229
Phone: 210-433-6575 Phone: 210-617-5400
Fax: 210-433-2828 Fax: 210-617-5423
[EMAIL PROTECTED]
http://www.ijoa.org/joeward/wardindex.html
*************************************************************
----- Original Message -----
From: dennis roberts <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, December 05, 1999 7:24 AM
Subject: ancova
| some time ago, i sent out a note about a handout i had re: ancova. now, in
| that handout, i illustrated a very simple case of how ancova might account
| for some of the within groups 'error'. in that handout, i showed, near the
| end ... some minitab output for the analysis. now, in that output ... the
| adjusted SS adds up to MORE than what the simple anova adds too. NOTE: the
| dependent measure in the Exp and Cont group example was performance on a
| test .. and the covariate was IQ.
|
| the one way shows:
|
| One-way Analysis of Variance
|
| Analysis of Variance
| Source DF SS MS F P
| Factor 1 252 252 1.54 0.231
| Error 18 2949 164
| Total 19 3201
|
| and the ancova shows:
|
| Analysis of Variance for TOTY, using Adjusted SS for Tests
|
| Source DF Seq SS Adj SS Adj MS F P
| TOTIQ 1 1539.9 2057.9 2057.9 39.26 0.000
| Group 1 770.0 770.0 770.0 14.69 0.001
| Error 17 891.0 891.0 52.4
| Total 19 3200.9
|
| in the handout, i showed that the adjusted SS(TOT) equals the sum of the
| 770 and 891 values for Group and Error in the Adj SS columns ... but where
| does the 2057 come from and, when you add to the 770 and 891 values .. you
| get a much larger value than the original 3201?
|
| what would be the simplest way to discuss this with students? in what way
| could you use the original data on the dependent measure ... and show how
| this new SS(TOT) value could be obtained?
|
| thanks
|
|
|
|
| ----------------------------------------------
| 208 Cedar Bldg., University Park, PA 16802
| AC 814-863-2401 Email mailto:[EMAIL PROTECTED]
| WWW: http://roberts.ed.psu.edu/users/droberts/drober~1.htm
| FAX: AC 814-863-1002
|
