Re: st: RE: multi-dimensional chi-squared?

[Steven Samuels <sjhsamuels@earthlink.net>]

Download -mgof-, Goodness-of-fit tests for multinomial data,  from SSC

There are assumptions behind -mgof-.  One is that there is no  
dependence of the counts in different weeks (This is different from  
assuming that the decision to put an item on sale each week was  
independent of the decision for the other items that week.) . A second  
is that the probabilities were constant from week-to-week.  Without  
more information on how the data were generated, it's difficult to say  
more.

Steve

On Jul 20, 2010, at 10:54 AM, Chevalier, Judy wrote:


Hello.  I am fairly new to this listserve.  I have a question about  
how one my think about constructing a test statistic and then  how to  
program it in STATA.  I may be missing a good way to think about it.   
I will present this in the context of an economics/marketing dataset,  
though it may have a close analog in other domains.

Consider a dataset with multiple products (let's call them 4 different  
brands of peanut butter to be concrete) observed over multiple  
weeks.   I have coded whether each product for each week is at its  
regular price or on sale.    I am interested in the question of  
whether one and only one product being on sale in a given week occurs  
more frequently than would be predicted if the product sales were  
independent of one another.   So, I have (easily calculated) the  
frequency with which:

0 items are on sale
1 item is on sale
2 items are on sale
3 items are on sale
All 4 items are on sale.

Also, given the overall frequency that each item is on sale, I have  
also easily calculated the predicted probability (under the null  
hypothesis of independence) that 0 items would be on sale, 1 item  
would be on sale, 2 items would be on sale, 3 items would be on sale,  
etc.

I can see that 1 item is on sale more frequently in the data than  
would be predicted under the null hypothesis of independence, and, of  
course, the other categories are somewhat less frequent than would be  
predicted under the null.  However, I am stymied as to how to  
construct an appropriate test statistic.    I can test for the  
independence of the sales for each item, pairwise, easily, using  
Stata, but I can't quite manage the right test statistic nor how to  
compute it in Stata.   I will actually repeat this test for some other  
samples--- the products will be different, the number of products will  
be different, but the hypothesis will be the same-- that 1 and only 1  
product is on sale more often than would be predicted under the null  
of independence.

If you have gotten this far-thanks for reading!

Judy

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