Background: The chi-square test of independence is a very useful statistical tool that helps in identifying if two variables are related to each other. In a functional sense it is very similar to a correlation co-efficient of determination R^2, however the key difference is that chi-square test was developed to work with nominal or categorical data, where as standard R^2 works only with numerical data.
When would you use the chi-square test of independence:
Any business situation where you are essentially checking if one variable, X is related to, or independent of, another variable, Y. The use of chi-square test is indicated in any of the following business scenarios.
1. Suppose you want to determine if certain types of products sell better in certain geographic locations than others. A trivial example: the type of shoes sold in winter depends strongly on whether a retail outlet is located in the upper mid-west versus in the south. A slightly more complicated example would be to check if the type of gasoline sold in a neighborhood is indicative of the median income in the region. So variable X would be the type of gasoline and variable Y would be income ranges (e.g. <0k, 41k-50k, etc).
2. Suppose you want to test if altering your product mix (% of upscale, mid-range and volume items, say) has impacted profits. Here you could compare sales revenues of each product type before and after the change in product mix. Thus the categories in variable X would include all the product types and the categories in variable Y would include period 1 and period 2.
3. A final, somewhat classic application of the chi-square test of independence is to verify the influence of gender on purchase decisions. Are men the primary decision makers when it comes to purchasing a big ticket items? Is gender a factor in color preference of a car? Here variable X would be gender and variable Y would be color.
No matter the business analytics problem, the chi-square test will find uses when you are trying to establish or invalidate that a relationship exists between two given business parameters that are categorical (or nominal) data types.