# Math 113 - Grocery Store Project

## Introduction

Everyone requires food to survive. For those who have had psychology, this was mentioned as being at the very base (biological/psychological needs) of Maslow's Hierarchy of Needs. For those of you who haven't had psychology, try going for any length of time without food and you will see how important it is.

Although people are eating out more, the average American still ate 917 meals at home in 19991.

Some people may eat out every meal but many of us aren't that wealthy and have to buy our own food at the grocery store. A naturally arising question is "Is one grocery store cheaper than another?" That's the question we're going to set out to answer this semester. Hopefully we'll have some fun and learn something about statistics along the way.

This is a semester long project involving many of the aspects of Statistics. It will involve planning an experiment, collecting data, describing the data, analyzing the data, and making inferences from the data. It can also serve as an example for the project that students will have to perform the second half of the semester.

## Group Composition

The class will be divided into groups of approximately 4 students each depending on the number of people in the class. Each group will be assigned one grocery store. The different grocery stores in town that we'll be choosing from are Aldi's, Cub Foods, Kroger's, Schnucks, Eagles, and WalMart.

The groups will be assigned by factors including store preference, available times, and computer skills. Although there will be some class time given to work on projects, there may be some instances where you need to work together outside of class. Most of the time, the work can be accomplished either right before or right after the class.

The assignment of groups will occur at the beginning of the semester, either the first or second day of class.

## Assignments

Periodically, information will be turned in for a grade. All assignments submitted for a grade should have the name of the grocery store and the name of all the students in the group at the top of the paper. All information submitted to the instructor is to be printed. SPSS output should be cleaned up and annotated.

Parts of the project will be due at different times. Due dates and point values are available at the end of this document.

## Phase 1 - Grocery List (10 pts)

Sample Grocery List
Grp Item
1 Chicken
1 Crackers
1 Hamb. Helper
1 Ketchup
1 Macaroni
1 Pepsi
1 Soup
1 Spaghetti
2 Dish Detergent
2 Toilet Paper
3 Batteries
3 Light Bulbs
3 Toothpaste
3 Tylenol
4 Hamburger
4 Pork Chops
6 Bananas
9 Milk
10 Pizza

Your first assignment is to come up with a typical grocery list for your family. The grocery list must contain at least 20 items and at least three items from each of the major categories, although you are encouraged to make it as realistic and lengthy as possible. If you don't do the grocery shopping in your family, then talk to the person who does for an idea of what to put on the list. These will be compiled into a master list that will be used to compare grocery prices.

Assign each item on your grocery list into one of the following categories:

GROCERY (39.72%)

1. Dry Grocery (Food)
2. Dry Grocery (Non Food)

GM/HBC (General Merchandise / Health & Beauty Care) (9.66%)

3. GM/HBC (includes prescriptions)

PERISHABLES (49.67%)

4. Meat/Fish/Poultry
5. Service Deli
6. Produce
7. Baked Goods
8. In-Store Bakery
9. Dairy
10. Frozen Foods

The percent values following the major categories represent the percent of 2000 sales that category accounted for2.

You may include name brands if you shop for name brands.

Once everyone returns their list, we will compile it into a master list of items to gather prices for.

## Phase 2 - Data Collection (20 pts)

Once the master list is compiled, the groups will go to their grocery stores and find the prices for the items on the list. Follow these guidelines for collecting data.

• If a specific name brand is not listed, choose the cheapest brand.
• If there are two sizes available, choose the larger size.
• If there are more than two sizes available, choose the medium (second smallest) size.
• Some stores have membership cards with special reduced prices. Use the reduced prices where available.
• Record the number of brands and total number of offerings for each item. We will use this to compare selection as well as price. For example, consider ketchup. Let's say a store has Hunt's (40 oz and 24 oz), Heinz (24 oz, 32 oz, and 48 oz), and a generic (24 oz and 32 oz). We would enumerate three brands and seven offerings.

All stores will be visited during the same week.

After the data has been collected, it will be entered into SPSS.

See the data definition section for more information on how the file is composed.

Each group will save their information into a file for just that group. Save the file on the acad1 server in the \stats\01\food\ directory. Use the name of your store as the filename. You can specify the complete filename as \\acad1\stats\01\food\cubs.sav or \\acad1\stats\01\food\krogers.sav (SPSS data files have the extension .sav, you don't need to enter this). Do NOT use spaces, apostrophes, capitals, or other special characters in your filename.

If you were unable to collect a price for a certain grocery item, be sure to let the instructor know. When we compare prices, it is important that we are comparing the same things at each store, so some items may have to be eliminated from the final list.

Once the data for each group has been entered into SPSS, we will combine it into one master file for the entire class to use. That file will be called food.sav and will be in the \\acad1\stats\01\food\ directory.

## Phase 3 - Descriptive Statistics (20 pts)

Use the data for your store only to answer the questions in this phase. The SPSS commands necessary to complete the task are in italics after each instruction.

1. Generate a side-by-side boxplot for the prices of each of the three main categories of groceries. Comment on any similarities or differences. Graphs / Box-Plot / Simple.
2. Generate a summary table of the price with the mean, sample size, standard deviation, minimum, median, maximum, and total (sum) for each of the major categories of food. Comment on any similarities or differences. Analyze / Compare Means / Means.
3. Generate a histogram with a normal curve displayed for all of the price data from your store. Does the data appear normally distributed? Graphs / Histogram.

You will probably want to save your output as you go along so that you don't accidentally lose anything if the computer crashes.

## Phase 4a - Inferential Statistics, part 1 (15 pts)

Use the combined file for this phase of the project. This portion of the project uses information from chapters 7 and 8. Each group's results will be different from the other groups.

1. Does the mean price of your store differ significantly from the mean of all the stores? Begin by finding the mean for all of the data and recording that value here ________. Now, apply a filter (Data / Select Cases / If condition is satisfied, store=#, where # is the number of your store) so that only your store is selected. Compare the mean price of groceries at your store to the overall mean price. Analyze / Compare Means / One-Sample T Test.
2. Does your store have a larger brand selection than the other stores? Go through and compare the brands at your store against each of the other stores. There will be one less comparison than the number of stores, so if there are four stores, you will make three comparisons. Analyze / Compare Means / Independent-Samples T Test.
3. Are the prices for each of the ten grocery categories normally distributed? Split the file (Data / Split File / Compare Groups by category ) and then do a Kolmogorov-Smirnov test for normality. Analyze / Nonparametric Tests / 1-Sample K-S

The output from SPSS should be cleaned up and annotated. Be sure to add the store name and the group members to the top of the output.

## Phase 4b - Inferential Statistics, part 2 (15 pts)

This portion of the project requires information from chapters 10 and 11 and so it will be due at the end of the semester. You will feel frustrated and pressured that there is little time to complete the task, but there is little that can be done since we won't have covered the necessary material until the end. The report given by each group will be the same for this portion.

1. Is there any relation between the store and the major food classification with respect to the number of item offerings? Generate a contingency table and test to see if there is a relationship. Analyze / Descriptive Statistics / Crosstabs. (Be sure to turn on the Chi-Square statistics.)
2. Is there a significant difference in the mean prices of the stores? Perform a One-way ANOVA to determine if there is a difference in the prices. Analyze / Compare Means / One-Way ANOVA. If there are significant differences in the mean prices, which stores are different? Which is the cheapest store? Which is the most expensive store?
3. Perform a two-way analysis of variance to answer the following questions.
1. Is there a difference in the prices between the stores?
2. Is there a difference in the prices between the major grocery categories?
3. Is there any interaction between the store and major grocery categories?
Analyze / General Linear Model / Univariate. Use the price as the dependent variable and the store and major food categories as fixed factors.

## Phase 5 - Project Evaluations (20 pts)

### Project Evaluation (10 points)

As a group, comment on the entire project. As a minimum, address questions like

1. Was there any data that was collected that wasn't needed?
2. Was there data that wasn't collected, but it would have been nice to know?
3. What changes would you make the next time this project is done?
4. Was the project relevant / interesting?
5. Are there topics that you would like to see investigated?

This should be typed and only one document submitted per group.

### Individual Evaluations (10 points)

As an individual, evaluate each member of your group including yourself. Comment on how much they contributed to the group. Did they show up for all the meetings, did they participate when they showed up, did they pull their weight or did they not do anything.

In addition to a paragraph describing each person, assign them a score between 0 and 10 points for their effort in the group. Remember you are evaluating yourself, also.

The score that you receive for this part of the project will be the mean scores given to you by each person in your group. All evaluations should be on a single sheet of paper that may be typed or handwritten. This is an individual assignment, not a group project.

## Data Definitions

### Collected Data

Some of the information will be collected and entered by the students into SPSS.

store
The grocery store. 1=Aldi's, 2=Cub Foods, 3=Eagles, 4=Kroger's, 5=Schnuck's, 6=WalMart
item
The grocery item. The coding for this will be determined after the grocery lists are obtained. A separate sheet will be handed out with the codings.
price
The price of the item. See notes under data collection for which price to record when there is more than one available.
brands
The number of brands of this item the store carries
choices
The number of choices (offerings) of this item including different sizes and brands the store carries.

### Calculated Data

Other data can be calculated based on the information collected.
cat
Grocery category (1-10). See phase 1 for a description. This can be calculated from the item number.
group
Major food category (1-3). 1=Grocery, 2=GM/HBC, 3=Perishables. This can be calculated from the item number or the category.

## Summer 2002 Due Dates

 Date Description Jun 10 Phase 1 - Grocery List Due Jun 17-21 Phase 2 - Collect Data from Stores Jun 26 Phase 2 - Data entered Jul 3 Phase 3 - Descriptive Statistics Due Jul 12 Phase 4a - Inferential Statistics, part 1, due Jul 23 Phase 5 - Evaluations due Jul 24 Phase 4b - Inferential Statistics, part 2, due