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

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: Chi-square test for Categorical Data Analysis
Date   Tue, 18 Sep 2007 22:00:46 +0100 (BST)

--- Hugh Colaco <[email protected]> wrote:
> 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?

You loose information that way, and if you just want to test why not do
that on the whole distribution. More interesting would be to use
-intreg- as this command was specifically designed for this case.
> 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?

No, the Chi-square test just says that these distributions are
different. Again -intreg- will give you more meaningfull output.
> Finally, can somebody give me a good reference for the chi-square
> test for categorical data analysis?

Some people like Agresti (2002) "Categorical Data Analysis" Wiley. 

Hope this helps,

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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