Vendors work hard to put their products in front of consumers, whether choosing the right site for advertising on the Web or getting the best location in a crowded super-market. Is the effort worthwhile? How could you tell? To find an answer, vendors often collect their own data from experiments like the one considered in this exercise.9
These data describe an experiment conducted by the maker of a popular brand of snack food (tortilla chips). Stores charge a premium for placing products on the middle shelf, near eye level for most shoppers. The bottom shelf is cheaper, and the top shelf “rents” for the least cost. The chipmaker wants to learn if shelf placement matters: are customers who buy chips more likely to purchase the brand occupying the coveted middle shelf?
To obtain data, the chipmaker ran an experiment. Employees randomly changed the location of products on the shelves every few hours in a cooperating market. Each day, over a period of two weeks (14 days), agents randomly moved the packages from shelf to shelf. Check-out scanner receipts recorded results for customers who bought any of the 3 brands in the test (the chipmaker’s product, Competitor 1, Competitor 2). The data for each purchase identify the brand and the shelf location (top, middle, or bottom).
Motivation
(a) It would have been easier to record sales with the products in a fixed location for, say, one week, then move them, rather than run an experiment. What’s the advantage of performing an experiment?
(b) How can the chipmaker use the results of its experiment when negotiating shelf location with retail stores?
Method
(c) Verify that the data meets the conditions for the chi-squared test of independence.
(d) What problem might arise if the experiment lasted, say, 2 months?
Mechanics
(e) Compute the test statistic and its p-value.
Message
(f) Summarize the results of the test for the chip-maker.
(g) Identify any key limitations of the experiment and its results.