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Perhaps someone interested in the levels of measurement question might
be able to help me too.

I have been acting as informal statistical consultant for my wife, who
is a physician with only an elementary statistical background, in a
project where she wants measures of association between a fairly large
number of binary variables in a sample with n=500 and in a subsample
with n = 260.  (These numbers may increase in the future.)  

We have been calculating standard Pearson correlation coefficients,
which to my way of thinking are as good as anything else at describing
binary associations, since scaling is not an issue for binary data.  I
do not claim to have studied the issue in depth, however.

I am an econometrician and I know that different fields have different
statistical subcultures and norms, so I am not sure that this is what
other physicians, biostatisticians, epidemiologists, etc. expect.  My
impression is that medicine is the field where statistical practice is
most codified, meaning that there are conventions that must be
satisfied if you want to get published, even if they don't make a
whole lot of sense in the particular application.

So here is my question:

If you were in my shoes would you stick with the Pearson correlations
or do something different?  If the latter, would you provide a
reference please.

Related and more interesting question:

What is "the right way" to do this from the point of view of
statistical theory?
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209

In article <thompson.724607838@daphne.socsci.umn.edu> thompson@atlas.socsci.umn.edu writes:
>Perhaps someone interested in the levels of measurement question might
>be able to help me too.
>
>I have been acting as informal statistical consultant for my wife, who
>is a physician with only an elementary statistical background, in a
>project where she wants measures of association between a fairly large
>number of binary variables in a sample with n=500 and in a subsample
>with n = 260.  (These numbers may increase in the future.)  
>
>We have been calculating standard Pearson correlation coefficients,
>which to my way of thinking are as good as anything else at describing
>binary associations, since scaling is not an issue for binary data.  I
>
[....]
>
>If you were in my shoes would you stick with the Pearson correlations
>or do something different?  If the latter, would you provide a
>reference please.
>
>Related and more interesting question:
>
>What is "the right way" to do this from the point of view of
>statistical theory?
>--

I would compute polychoric coefficients - conceptually they are
correlations of latent normal variables for which below a threshold we
observe the case being in one category and above we observe it in
another category.

<U53076@uicvm.uic.edu> writes:

>   Let me first apologize for boring you with such a mundane question.   Anyway
>I am in a dispute about levels of measurement and the appropriate statistics to
>use when dealing with data at the ordinal level.  I'd like to compare performan
>ce on a communication task across two different contexts.  In both cases,
>competence is measured on an ordinal scale, for simplicity's sake, 1, 2, 3.  It
>has been my practice in the past to compute a Pearson product-moment correlatio
>n between the two tasks and to use the resulting r as an indication of the
>degree to which performance is consistent across tasks.  I recently was told
>that this was an inappropriate test cause I was only at the ordinal level.  But
>my references (see esp. Glass & Hopkins, 1984; Heermann & Braskamp, 1970) say
>that the whole levels of measurement question has ben blown out of proportion,
>and that the sort of usage I describe is just fine.  What do you think?

I agree that the levels of measurement question has been blown
out of proportion, but you can easily avoid the whole issue in
your case.  A Pearson product-moment correlation computed on
ranks is also known as a Spearman-rho rank-order correlation.  So
just call your statistic a Spearman rho and everyone should be
happy; you'll be happy because you don't have to recalculate
anything.

gary mcclelland
univ of colorado
mcclella@yertle.colorado.edu

thompson@atlas.socsci.umn.edu (T. Scott Thompson) writes:

>Perhaps someone interested in the levels of measurement question might
>be able to help me too.

>I have been acting as informal statistical consultant for my wife, who
>is a physician with only an elementary statistical background, in a
>project where she wants measures of association between a fairly large
>number of binary variables in a sample with n=500 and in a subsample
>with n = 260.  (These numbers may increase in the future.)  

>We have been calculating standard Pearson correlation coefficients,
>which to my way of thinking are as good as anything else at describing
>binary associations, since scaling is not an issue for binary data.  I
>do not claim to have studied the issue in depth, however.

[stuff deleted]

>What is "the right way" to do this from the point of view of
>statistical theory?

Many thanks to those who have responded so far.  I will summarize your
responses to the net sometime in the future.  (Probably in early
January.)

Since a few people have e-mailed me with requests for more detail
about the problem/data, here is a summary:

The sample consists of data taken from the charts of pediatric
patients who were seen in the pediatric outpatient clinic at one of
the large public hospitals in Minnesota on certain days chosen at
random.  The variables include age and sex of the child, various
variables summarizing the history of contact with the pediatrics
clinic (i.e.  whether or not it is their first visit, whether or not
this is their primary care clinic, etc.).  These variables are used to
define the smaller subsample, which can be thought of as the group
that regularly visits the clinic for medical treatment, and for whom
the medical history appears to be reasonably complete.

(Yes, we know that there is a selectivity problem.  No. We are not
doing anything about it yet.  Any suggestions on how to handle it are
welcome.)

The remaining variables consist of binary indicators coded from the
patient's chart for whether or not the patient has certain "morbidity
factors."  These come in three flavors, which I can loosely describe
as "clinical conditions" (e.g. ear infections), "developmental
conditions" (e.g. whether or not the child was born premature, whether
or not the child's physical growth is delayed, diagnosis of speech
problems), and "social conditions" (e.g. whether or not the mother is
a teenager, whether or not the child has been refered to a family
protection agency because of child abuse, whether or not the child has
been placed in a foster home).  There are about 150 morbidities
altogether, of which about 20 have an estimated incidence greater than
2 percent.  We are mostly looking at these 20.

The main goal, as nearly as I can tell, is to find patterns in the
diagnostic groups, i.e. patterns of association among the morbidities
and among the groups of morbidities.  Presumably these will be used to
help identify the kinds of services that the hospital should be
providing, and to aid in detection of problems that might otherwise go
unnoticed in the usual chaos of the clinic.

As you might surmise from the above, the clinic serves a largely poor,
inner city population, and most of the patients are seen on a "walk
in" basis.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209