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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 > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Chi-square test for Categorical Data Analysis***From:*"Hugh Colaco" <hmjc66@gmail.com>

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