DIFFERENCE OF PROPORTIONS
 

 

 

 

 

 

 

 

 

 

 

 

 

Chi-square and difference of proportions can be applied to the same problems. Although the results are not exactly the same, the results are similar enough for comfort. we determined the likelihood of champion and challenger results being the same using the difference of proportions method for a range of champion response ratesrepeats this using the chi-square calculation instead of the difference of proportions. The results from the chi-square test are very similar to the results from the differ­ ence of proportions—a remarkable result considering how different the two methods are. 154 The Lure of Statistics: Data Mining Using Familiar Tools : Chi-Square for Regions and Starts A large consumer-oriented company has been running acquisition campaigns in the New York City area. The purpose of this analysis is to look at their acqui­ sition channels to try to gain an understanding of different parts of the area. For the purposes of this analysis, three channels are of interest:

 

 

 

 

 

 

 

 

 

 

 

 

 

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Telemarketing. Customers who are acquired through outbound telemar­ keting calls (note that this data was collected before the national do-not- call list went into effect). Direct mail. Customers who respond to direct mail pieces. Other. Customers who come in through other means. The area of interest consists of eight counties in New York State. Five of these counties are the boroughs of New York City, two others (Nassau and Suf­ folk counties) are on Long Island, and one (Westchester) lies just north of the city. This data was shown earlier in. This purpose of this analysis is to determine whether the breakdown of starts by channel and county is due to chance or whether some other factors might be at work. This problem is particularly suitable for chi-square because the data can be laid out in rows and columns, with no customer being counted in more than one cell., and chi-square values for each combination in the table. Notice that the chi-square values are often quite large in this example. The overall chi-square score for the table is 7,200, which is very large; the probability that the overall score is due to chance is basically 0. That is, the variation among starts by channel and by region is not due to sample variation. There are other factors at work.