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Re: st: Chi-square test for Categorical Data Analysis


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Chi-square test for Categorical Data Analysis
Date   Tue, 18 Sep 2007 17:02:39 -0400

Hugh Colaco <hmjc66@gmail.com>:
This is a subtler and more interesting problem than it first appears.
But I suspect you want an easy answer.  You can test whether the two
distributions differ with a simple chi2 test (Pearson 1900) but you
cannot conclude that group A is making more than group B--this
statement is not even well-defined. Compare to mean_A>mean_B, or inc_A
exhibits first-order stochastic dominance wrt inc_B, or
median_A>median_B.  See also articles by Roger Newson in Stata Journal
e.g. http://www.imperial.ac.uk/nhli/r.newson/papers/params.pdf

Pearson, Karl. On the Criterion that a Given System of Deviations from
the Probable in the Case of a Correlated System of Variables is such
that it Can Reasonably Be Supposed to have Arisen from Random
Sampling." Philosophical Magazine, Series 5, Volume 50, No. 302 (July,
1900), pp. 157-176.

On 9/18/07, Hugh Colaco <hmjc66@gmail.com> wrote:
> Dear Statalisters,
>
> I am working on some data from a survey and have a question about the
> chi-square test. I have 2 cohorts - lets call them A and B. Assume
> N=100 for A and N=50 for B.
>
> Participants were asked about their income level and had to choose one
> from below. Assume the income ranges are:-
>
> $0 - $25,000
> $25,001 - $50,000
> $50,001 - $100,000
> $100,001 - $150,000
> $150,001 - $200,000
> $200,001 - $500,000
> $500,001 or more
>
> Rather than report so many income ranges, I would now like to report
> just two, based on the median of all 150 participants. So, I will have
> 4 groups in all (i.e. Group A below median income, Group A equal to or
> above the median income, Group B below median income, Group B equal to
> or above the median income).
>
> I would like to then run a chi-square test to see if there is a
> difference in the distributions. Is this valid?
>
> Second question - does the chi-square test convey any additional
> information other than the fact that the distributions are different?
> That is, since only the number of observations in each group is being
> tested, can I, for example, conclude that Group A is making
> significantly more income than Group B?
>
> Finally, can somebody give me a good reference for the chi-square test
> for categorical data analysis?
>
> Thanks in advance,
>
>
> --
> Hugh
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