Jun 222012

My AP Stat learners had a project for their final exam, it was very straightforward. In our area, we have 4 grocery stores.

The North Valleys w/ grocery stores
If you click the image, you will see the larger image that shows on 2 exits of the freeway the four stores (Scolari’s is a local chain) and on the far right of the map, our school. Walmart opened up only 3 months ago, so it is the new kid on the block, and of course, their marketing screams at us every day that they have the cheapest prices on groceries.

Our question was, do they really have the cheapest prices? The rest after the break.

There were several parts to the project / final. A proposal, a preliminary data report, a more involved look at the data (analyzing the data) and a presentation along with a final report. I will break down each section and then show some results from the learners. The handout I gave them is below.

We began, though, with a class discussion on what the project would require, what the boundaries of the project were to be, and to settle some basic questions.

  1. Groups would be allowed, as long as no more than 3 per group (although I did have 1 group of 4 and 2 groups of 1 person).
  2. No purchase is necessary, they just need prices.
  3. A “C” project would be 20 items and if you wanted a shot at an “A” you had to have 35 items. Yes, the 35 max was arbitrary, but I did want to constrain the time they were spending since it was around finals.
  4. We came up with a list of 10 basic items, but I refused to specify brand or details. The only thing I would allow is “milk” “bread” etc.
  5. No sale price items would be allowed. Only “everyday” prices, because Wal-Mart’s marketing says they have “Everyday low prices.”
  6. Smiths Food and Drug really caused my class some heartburn. Smiths has a free card that gives everyday discounts to it’s customers. The card is free, but it gives everyday prices that are cheaper. Should we do the card price, or the non-card price? It honestly took about 20 minutes of great conversation as to the merits of both before the class decided we have FIVE stores in the North Valleys. Walmart, Scolari’s, Raley’s, Smiths w/o discount card AND Smith’s with discount card. Problem solved.
  7. We would ignore the fact that spending $100 in groceries at Smith’s with the card also gives you a 10 cent per gallon discount on fuel. We have no way to track this, and no other grocery store offers this feature.
  8. I required them to take pictures of the prices in the stores with their phones. This ended up saving one group, because they lost their data and had to reassemble it from their phones.
  9. They had to get exactly the same thing in all 5 stores. If they “purchased” 2% milk in one store, it had to be in all stores. (This requirement also caused some problems for some learners.)

First, the proposal: This was incredibly difficult for them. I asked them to have a document that would answer every question that would arise as they are collecting data. They had to come up with a list of items, and they had to be specific. What items? What sizes? Name brand? Store Brand? Price per pound for meat? Before I would sign off on their project, they had me read their proposal, and then I asked them questions. If they couldn’t look at their document and answer from their document, I wouldn’t give the okay. It took some groups 3 class periods before they finally understood that the planning of the study was more important than the data collection and had it done.

Second, the data collection. I asked to see their data with 2 class periods to go before the final exam day. the goal was just to make sure they were making progress and not slacking off. I had one team almost finished by this date, and 1 team with only 1/2 their data collected on this date. Very spread out.

Third, analyzing the data. They quickly figured out they needed to do a matched pair t-test on the data, and JMP made the entire process dead simple. They also realized that there was 10 different matched pairs to do in order to create a good ranking of the 5 stores.

Finally, they wrote it all up in a report and created a presentation to the class on their results. Some of the results are summarized below:

  • One group that used all name brand items “Kraft Macaroni & Cheese” for instance found that Wal-Mart was cheaper, by a large margin.
  • Another group that made the assumption, “For each item we will look for the cheapest brand.” For example, they specified 2% milk, and in each store shopped for the cheapest 2% milk. This group found that there was no difference between Wal-Mart and Smiths w/ Discount Card
  • In the end, the 9 different groups fell into 2 camps. Wal-Mart IS statistically cheaper than all the other stores. These groups used many name brand items in their lists. The other groups found that there was no difference between Smiths with Discount Card and Wal-Mart.
  • Wal-Mart was absolutely statistically significantly cheaper than all stores including Smiths w/o Discount Card.

So to answer the question, is Wal-Mart cheaper than the other grocery stores?  The answer the class came up with was, it depends. Very nice. It showed them how important it was to think carefully about the assumptions one makes prior to collecting data.

But, we now had 9 groups of data, all from the same stores, with different items on each list. They all came up with their list independently of one another. The stores all price their products independently of one another. Having each group make their list without consulting the others is effectively randomizing the list.

Let’s see what happens when I combine the entire class into 1 data set.

Wal-Mart: Not a lot of different prices.

Smiths with discount card (since that is the only one the groups found interesting) Lots of variation among the prices, compared to Wal-Mart.

and the Matched Pair t-Test

Clearly, there is not a statistical difference, although Wal-Mart is slightly cheaper. This doesn’t take into account the discount the card gives you on gas, however. Depending on the family, it would be easy to earn a one time fill-up discount of 30 to 40 cents off per gallon every month. That would clearly offset the 6 cents per item that Wal-Mart is averaging.

I know where I am buying my groceries! Wal-Mart does NOT have the cheapest, every day low prices.

Below is the handout I used for the project.

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