Sorry -- my earlier reply was interrupted by someone attempting to use
the telephone line.
On Thu, 27 Jul 2000, Terry Chan wrote:
> I have numbers (arranged in a 2x2 contingency table -
> smokers/nonsmokers, respiratory disease/no disease) for our study
> population (of about 1,000). I also have numbers (arranged the same
> way) for the general U.S. population (from the U.S. Office of Smoking
> and Health).
> Is there a statistical test that allows me to compare both populations
> (e.g. a test that compares the chi-square value from each population)?
As I started to write earlier, construct the 2x4 frequency table (your
study population / general U.S. population, vs. the 4 subgroups defined
by your 2x2 tables) to see whether the distribution of the study
population into the 4 categories differs from the distribution of the
U.S. population into those same categories. This will give you a
chi-square test with 3 d.f. Alternatively, you can construct expected
frequencies for your study population based on the proportions in the U.S.
population, although the U.S. population ought to be enough larger than
the study population that the results of either procedure would be very
nearly the same.
> Is there a statistical test that assesses if our study population is
> biased (compared to the U.S. population) and if it is biased,
> associates some type of value to this bias?
Depending in part on what you want to mean by "biased", the procedure
described may provide a test. Standardized residuals may or may not
satisfy your request for "some type of value" -- they would indicate, for
example, the degree (and the direction) to which the proportion of your
study population to be found in a cell is greater (or less) than the
proportion of the general U.S. population to be found in that cell, if
the overall chi-square is large enough to reject the null hypothesis
(that the proportions in the 4 cells do not depend on which population
one is considering).
I am rather freely interpreting your original question, partly because
of its vagueness and partly because the specific questions I addressed
above could, with a little imagination, have been (among) the questions
that led to your original inquiry.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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