models and assumptions

Bob Hayden (hayden@oz.plymouth.edu)
Sat, 13 Aug 94 20:32:03 EDT


In case you are wondering what we've been fighting about re
transformations, etc., I recommend an example on pp.86-110 of
Cleveland's _Visualizing Data_. It's real data from a real published
study. The originators fit a straight line, but alas the data are not
ON a straight line. Cleveland demonstrates a quadratic fit, which
gives good fit, but the residuals do not satisfy the assumptions of
least squares. So he tries a logarithmic transformation and finds a
model that fits the data and has residuals that satisfy the
assumptions required for inference. However, he refrains from doing
any confidence intervals or hypothesis tests, as I think he should.

A personal opinion (not Cleveland's fault) is that a lot of the
apparent conflict between traditional inferential statistics and EDA
is due to sociological causes. I think you gather data and do EDA
until you know enough about the phenomonon to frame a sensible
hypothesis or model. Then you design an experiment or otherwise
gather NEW data to test your hypothesis or estimate the parameters of
your model. Of course, you use EDA techniques on the new data to make
sure your methods satisfy assumptions and your model is a reasonable
one. Each type of statistics has a role to play in this process --
they are not competitors nor mutually exclusive.

This sequential, interactive process takes years -- even generations.
In our society we have a peculiar institution called the thesis or
dissertation that forces people to try to cram all this into a year or
two. The result is lots of inference based on models or hypotheses
with no empirical justification. Indeed, sometimes there is no
justification of any kind, and sometimes the (are they perpetrators or
victims?) folks involved have no idea what the assumpions or the model
they are working with IS.

a quotation of a p-value is part of the ritual of
science [??], a sprinkling of the holy waters in an
effort to sanctify the data analysis and turn
consumers of the results into true believers.

Cleveland, ibid, p.177
_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College
| | Plymouth, New Hampshire 03264 USA
| * |
/ | (603) 968-9914
| ) (603) 535-2489
L_____/ hayden@oz.plymouth.edu