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Topic: Messed-up factorial
Replies: 1   Last Post: Mar 28, 1997 10:31 AM

 Joe H Ward Posts: 743 Registered: 12/6/04
Re: Messed-up factorial
Posted: Mar 28, 1997 10:31 AM

Dick --

You must have created your message just for me. So here goes.

If you still have your copy of Introduction to Linear Models (by you know
whom), look on page 230. There is an illustration of a model involving
"missing cells". In the distant past, and occasionally in more recent
days, I have been at gatherings of statisticians that showed frustration
over missing cells -- and even cells with unequal or non-proportional cell
frequencies. Just two days ago, I was talking with college student who
was concerned about what values to plug into the "missing" cells.

For some categories, it may be impossible and meaningless to even think
about responses. Therefore, it may be unreasonable to even think about
"plugging in some value" for the "missing information". So, as I have said
many times before, if you show your friend how to CREATE A MODEL
APPROPRIATE TO THE SITUATION and impose restrictions implied by the
"questions of interest" then he/she will obtain the answers that make
sense.

As you know from reading about the "Case of the Missing Cell" in the
American Statistician, there is risk in using "canned" programs when there
are missing cells. Some computer programs can produce reasonable-looking
answers to uninteresting hypotheses.

Incidentally, the high school students with whom I work have no idea,
unless they are told, that there is a "problem with missing cells" since
they can create "cell-means" models and then impose their own meaningful
restrictions.

There is only minimum attempt to give researchers the power to create
models appropriate to the situation. This may be due to the desire to
"package" the pre-computer algorithms. The computer made it possible for
researchers to solve models that THEY created. Yet much of the time the
computer is used to run "standard" procedures. When the models are not
"standard" what is the unprepared researcher to do?

IT'S EASY TO TEACH STUDENTS HOW TO PLUG INTO FORMULAS, BUT IT IS NOT EASY
TO DEVELOP STATISTICS INSTRUCTION THAT ENHANCES STUDENTS MODEL-CREATING
COMPETENCE! I've been working on this problem since the 1950's.

Enough said! As my wife says "Don't tell 'em more than they really want
to hear".

-- Joe
***********************************************************************
* Joe Ward 167 East Arrowhead Dr. *
* Health Careers High School San Antonio, TX 78228-2402 *
* Phone: 210-433-6575 *
* joeward@tenet.edu *
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On Fri, 28 Mar 1997, Richard S. Lehman wrote:

> Date: Fri, 28 Mar 1997 09:00:15 -0500
> From: Richard S. Lehman <R_LEHMAN@ACAD.FANDM.EDU>
> To: Multiple recipients of list <edstat-l@jse.stat.ncsu.edu>
> Subject: Messed-up factorial
>
> OK. Here's one to chew on. I'd appreciate any wisdom you care to share.
>
>
> I'm working with a colleague in botany. He has what boils down into a
> factorial design--chemical (different chemicals thought to be
> growth-inducers) by increasing concentration (4x5 design, not that it
> matters much, I think). The dv is length of a particular segment in pea
> plants. (Ho hum. Isn't botany fun!!!) All perfectly straight forward.
> EXCEPT.... When running the experiment (and this is a multi-year project),
> they stopped collecting data on a particular chemical solution when they
> found the concentration that produced the effect. So there are holes in the
> data.
>
> Suppose that for chemical A, they observed the effect on stem length at
> concentration 5. That gives them complete data for chemical A. But maybe
> chemical B produced its effect at concentration 3, and so data were not
> collected for concentrations 4 and 5. Get the idea?
>
> What do we do? There are a few options that occur to me. (1) Run the
> missing cells. (A *LOT* of work, I'd guess.) (2) Assume that all missing
> cells are equal to the final value achieved before they stopped collecting
> data (that is, set them to the mean of the highest concentration for which
> they have data). (3) Use some sort of regression model to predict missing
> data. (4) Use row mean + column mean - grand mean as an estimate. (5)
> Other??????
>
> Thoughts? Is there a standard way to do this that not aware of? Is this
> unusual? What do we do next?
>
> Thanks.
>
> Dick Lehman
>
>
> --------------------------------------------------------------------------
>
> Richard S. Lehman R_Lehman@ACAD.FANDM.EDU
> Professor of Psychology (That's R-underscore-Lehman)
> Department of Psychology
> Franklin & Marshall College Voice (717)291-4202
> PO Box 3003 FAX (717)291-4387
> Lancaster, PA 17604-3003
> "I'd rather be blowing glass."
>
>
>